we have a a theory which is called Quantum electrodynamics which is our pride and joy it's so success F and it's such so wide in its application and what I would like to tell you about is that theory how it works or how it looks like it works what the world looks like from that point of view the uh physics has got a history at least this theoretical history of uh synthesis perpetually of course experiment is always finding new phenomena problem is to work them together and sometimes we see that they're aspects of the same phenomenon an example is of course the simplest and earliest one is that the laws of motion became in the theory explain the properties of heat because heat was motion and if you knew how motion worked you could understand the thermal thermal properties it also explained the properties of sound which is otherwise a mystery as the motion of the atoms and waves in the gas on side from that knowing the laws of motion you have to know Newton who gave us the laws worked out the laws of motion also gave us another theory about the forces between large masses and distances from one another called the theory of gravity well that's just a that thing the theory of gravity is not is well known and understood pretty well but is not what I'm going to talk about as the time went on phenomena associated with electricity you know rubbing combs in your hair and things like that and magnetism became uh interesting to the experimental physicists and they discovered relations between them experimentally until they saw ultimately that were not two different phenomena but different aspects of the of the same thing another phenomenon that Newton had studied was light so in that time it looked at first like there were many things motion and gravity electricity and magnetism later and light but when Maxwell put together the laws of electricity and magnetism he found out that the behavior that the equations that he had produced expectation that would be behavior of waves that would propagate at a speed which was figured out from electrical measurements but came out the same as the speed that light actually propagated and so there was a new theory of Light which is that it was an electromagnetic wave and Maxwell's great synthesis in 1873 was to connect electricity magnetism and light light is just one aspect of the electromagnetic wave which can have different kinds of wavelengths from that point of view and if you have different wavelengths if the wavelength is very short between about four 100 millions of a meter no of a centimeter 400 millions of a centimeter and 700 millions of a centimeter then you can see it directly with the eye but if it gets longer the wave is well it's a long end it's red and then the other end it's blue and if it gets more longer than the red we call it infrared the rays are there but the eye doesn't seem the pit viper has a eye that sees the infrared and if you go in the other direction into the AL Beyond The Violet then we can't see it again but the bee has an eye that sees the ultraviolet and uh if we go still further to the far ultraviolet no animal has it that can see it but we can make instruments that are detected or photographic plates and so on up into X-rays and so forth and down in the other direction far infrared uh get into radio waves and we can build instruments that detect them and we can use them to advertised soap in in addition so that that is an enormous range of one property the wavelength a range of phenomena that's a complete enormous Spectrum the Spectrum we see with the eye is a very narrow range and it's the entire Spectrum it's all put together with the one theory of electromagnetic waves I'm going to talk about that part of it if I'm going to call it light instead instead of saying electromagnetic radiation light is what we see is only one little part but from the physicist point of view the accident that the human eye happens to be sensitive to wavs from here to here is not essential the phenomena are the same over the whole range and we call I'm going to call them all light but it could be radio ways or x-rays or what have you next thing that was discovered was the structure of the atoms and that I'd like to remind you that you have I believe a Nobel Prize winner from New Zealand before Mr Rutherford who was I believe a New Zealander who worked out that the Adams had nuclear you know seem always here I've only been here a few days everybody's talking themselves down I thought this would be a happy country but something's happened to you you got plenty of room and not too many people and it looks like it ought to be good anyway you do don't forget you had Rutherford so it's okay anyhow he had a theory of the he developed the our understanding of the atoms as having a tiny core as very heavy with the particles going around that electrons now supposing that the electrons went around according to the laws of motion of Newton some properties of matter could be understood supposing the atoms were made that way but most of the time it failed and it became more and more of a crisis in physics to understand what matter was like uh because it looked so obviously right that it had to be electrons going around nuclei and yet nothing worked when you worked it out and the discovery was made then in the discovery of quantum mechanics first in the behavior of light and then in the behavior of matter and finally culminating in 1926 with the full equations of quantum mechanics which told us that the laws of motion of Newton were not right and had to be modified through other laws which are quantum laws of motion and when this Quantum Laws of Motion were applied to electrons to explain the properties of matter was a fantastic success the properties of the atoms can be all worked out mathematically in principle at least in the simple atoms in detail and therefore the theory behind chemistry which atoms combine with which at what rate and so forth is in principle theoretical chemistry deeply is physics it's not a joke it's a direct the chemist will admit that's exactly his point of view that the understanding of the atoms in the deepest level is physical physics except that the atoms have so many particles in them it's very hard to calculate what's going to happen so he has to use a lot of empirical rules to help him but in as far as we can tell there's nothing about chemistry that's not understood ultimately as the behavior of electrons following the laws of motion of quantum mechanics this defines the properties of all substances also and so that the whole theory of the properties it's ordinary substances and the chemical properties and so forth have all been reduced to the motion of electrons in the meantime the theory of light and its interaction with matter which was Maxwell's equations had to be modified to become a quantum theory also oh I forgot to mention that during this time one to somewhat to one side of the way I want to go in these lectures I would not going to discuss much about relativity but the theory of relativity was developed and that just makes it easier for us to guess laws it tells us if we know how something varies in space then we know how it varies in time or vice versa that there's a nice relationship between a behavior in space and behavior in time and that it's all sort of different aspects of the same geometrical thing called SpaceTime at any rate direct using the principles of Relativity and new Quantum and the new quantum mechanics found a wonderful Theory as simplest possible thing you could write down for the motion of electrons direct theory of electrons and that was the situation about 1927 or8 but uh the problem of the interaction of electrons with light which was a complete quantum theory of electrodynamics other words make Maxwell's equations of light electricity and mag and the theory of motion of electrons all into one grand theory was accomplished in 1929 in the theory was that was called Quantum electrodynamic trouble with it was nobody could figure anything out or better when they did figure it out they got nutty answers if you didn't do it too carefully got a reasonably good answer for a problem but if they carried it out very carefully you would get some silly answer like zero or infinity or absolutely absurd results this strikingly lasted for 20 years while people tried to figure out what the correct theory was during this time experimenters were measuring things more and more accurately the theory of uh the one of they measured a they found a few things with very subtle effects that the theory of interaction of light with electricity should explain and then they measured them and they found these effects but they couldn't explain that is a theory didn't explain it quantitatively because when the people made the calculation they got Infinity instead of the right result as an example an electron in a magnetic field precesses at a certain rate and the rate according to D was a certain amount but when you he didn't take into account the interaction of electricity and light and when he took it into account we knew that the answer should be wrong let's say that the re answer was right but when experiment was made it came out not to be one but to be a little bit more uh this number here the experimentals weren't good enough to tell us exactly it's somewhere between 5 and 21 here we write it as8 plus or minus three is the next digit that means this is not measured accurately so in 19 uh I'm Sorry by 1948 20 years we had at last measured something which showed that the original theory was without interaction is incomplete this is supposed to be the result of interaction when you went to calculate it you got Infinity so there was a very strong effort made then in 1948 because of the fact that experiments were showing such accuracy to try finally to get that theory straightened out and it turned out surprisingly it was worked out more or less independently by three guys who got Nobel prizes of one of which you see here and uh uh Professor swinger that's not me with the other one of the other ones first worked out a correct way we we found out that the original theory that was written in 1929 by Heisenberg and dur and poy was very nearly correct and the problem was that there was something wrong with the way they handled doing the calculations and we straightened it out and then we could do calculations and schwinger for example calculated this and found out that it was something like this theoretically and that was a tremendous achievement it's a great excitement because that meant we really understood more more subtle details and that the original theory of Heisenberg and dur and so on were fundamentally was fundamentally right just a little switch on how you calculated things now this is the theory then that we're going to talk about this theory has lasted now for 50 years uh 50 years 30 years I can't add from 1979 1949 oh it's 50 years yes from the time that direct and Heisenberg wrote it and it took 20 years to figure out how to calculate with it then the remaining 30 years the methods of calculations improved they calculated things much more accurately and the experimenters became more and more Adept at measuring things and this particular rate that they uh measured in 1948 to here now in 1979 has been measured to be in fact 10159 65 2 four and the four may not be four it could be somewhere between two and six after all the more you write it the some way you have to stop right and this I write to show you the tremendous achievement of experiment is during the last 30 years in order to test with the Precision the correctness of the theory in the meantime poor guys using calculators and sweating and writing marks on pieces of paper so I'm calculating the results of the theory under the same circumstances for the same phenomena produce the predicted value that it should be 6523 within plus or minus 3 why should the theories have a plus or Min they get exhausted in Computing the number of decimal places that they eat to to keep up with experiment there are this is not atypical there are two or three or four perhaps different places where it's been measured and checked to that degree of accuracy this degree of accuracy that number of decimal places corresponds to a Precision something like this if you were measuring the distance of Me to the Moon the question would come up do you mean from my chin or from the top of my head the difference between whether it's from the chin or the top of my head to the Moon is the plus and minus two on the end of that number in proportion all right that is uh to intimidate you that the theory is correct uh in high accuracy I have don't need to produce a large number of other experimental results they all have this feature it is remarkable that at this time is possible to say that there's no experimental discrepancy known between the predictions of the theory anywhere and uh results of experiment that doesn't mean we can compute everything the rules of the game by which we make the computation the laws underneath everything that makes nature work a simple it doesn't mean we can really figure everything out to give an example if you play the game of checkers I think you call a Checkers here maybe draws something the rules of the game are very simple the way the pieces move is simple and if you want to make it even simpler make the rule no Kings but when you come to the end of the board you start at the beginning does make any difference the rules are simple but imagine a checker board with 100 million piece squares on each side hundreds of millions of these Checkers in different positions moving through the board taking pieces and being taken from the other which way are they going to swirl which way is the game going to go that Tak a lot of thinking it isn't the difficulty of the rules that's involved but the multiplicity of its action and interconnections matter as you all know be May is May atoms and all this stuff is such a multitude of little particles that in ordinary circumstances so much is happening that in spite of the fact that the rules are relatively simple not quite as easy as the Checker rules but pretty easy it still is very difficult in almost all circumstances to figure out what could happen exactly when we can't figure it out exactly but can do a pretty good job of approximating the phenomenon is in the range that we expect when we have a situation that's sufficiently simple a corner of the board where there's only a few pieces then we can compute exactly what ought to happen and we do experiment in those circumstance it fits exactly and that's all we can say at the moment about this Theory this uh theory has been designed was originally designed in ideas of space and time and a geometrical framework the question is how small a scale can we go down to and during the time of this these period of time we not only me tried to measure accuracy but also tried to see how small a distance the theory would be correct at and I can only tell you the distance is 10 Theus 15 cm that means 0 15 zos before you get to 14 Z before you get to a first digit of distance in centimeters we that thing is that ACC we know that the laws are that accurate to put it another way it used to be thought that atoms were small that was a limit of measurement but uh at the time with the new instruments and divine during all this time we've been able to make instruments that can test this Theory down to distances that could be described this way if the atom is made 100 kilm on a side then we're measuring with 1 cm accuracy inside so the theory is right the distances correspond to a centimeter when an atom is 100 kilm so altogether I can only emphasize with delight and excitement the fact that so much of nature is so accurately describable by one Theory there an enormous range of phenomena all the things you ordinarily see the best way to describe what the phenomena are colors of things the softness of materials the weight of things the way they temperature when you change the temperature how much heat it takes and sounds and all these phenomena yet only best way to describe is to describe the phenomena that are not included in this Theory and and one of them is the accelerations produced by gravity the force of gravity is in another theory gravitational Theory or general relativity another range of phenomenon have to do with exciting the interior of nuclei a nuclear physics protons and neutrons radio activity and nuclear phenomena that excluded all the rest of the phenomena of nature are contained in this one Theory now you can see why it is that I feel a bit uncomfortable when come someone asked to give a talk please tell us the latest things because then I'm talking about our problems that we have in trying to understand the insides of a proton for example for a proton to tell you a contrast our understanding of the outside of the atoms the electrons and light that I'm going to talk about the theory it's our Jewel and great achievement to the things that people ordinarily have to talk about at these lectures it's as follow you take the corresponding number for a proton I don't remember it it starts at 27 I think 1 n I'm not sure or is it 2719 I don't remember and it goes on for a number of decimal places because the experiment they can measure it so well now we have a theory of the protons recently developed involving quarks and so on we can't make any calculations yet we haven't developed the technique good enough so the best I could say really and probably exaggerate is that the theory does say that this number should be around three and the eror and that's what I think I must be bigger I can't prove that it's as small as it might be three uh that gives an idea of how sloppy our understanding of protons is compared to that due Precision that we understand electrons all right so that gives us some idea of why it is I feel so uncomfortable talking all the time about what we don't know much about and nobody asked me about the stuff we do know everything about so therefore I'm forcing upon you a lecture on the things that we think we know something about okay so that's our job now the question is what am I going to do I'm going to tell you what the theory is I'm going to tell you what it looks like what we do to make the calculation just what the thing is because otherwise how are you're going to understand what world picture in other words this thing is and it is a world picture because it describes all the phenomena except for radioactivity and gravity the world that's a lot of phenomena it's possible even it might explain and should explain if everything is Thoroughly understood the laughter of the audience when you make a dumb remark now if I'm going to explain this Theory the question is are you going to understand it will you understand uh the theory when I tell you first that the first time we really thoroughly explain it to our own physics students is when they're in the third year graduate graduate physics then you think the answer is going to be no and that's correct you will not understand but this business about not understanding is a very serious one that we have between the scientists and an audience and I want to be at work with you because I was going to tell you something the students do not understand that either and that's because the professor doesn't understand which is not a joke but a very interesting I think and I would like to explain it my task really as a to explain all this is to convince you not to turn away because it appears incomprehensible that's what it takes four years of us to do to the student is to get him so he doesn't run away because it looks crazy the thing that's exciting about this is that nature is range as it can be in this sense that the rules that are going to be obeyed that I'm going to tell you about by which this stuff is analyzed by which we understand nature the rules of the checkers yeah are so screwy you can't believe them nevertheless if you follow out the consequences and see what they do sure enough all the ordinary phenomena that happen you can understand that's hard to do because you have to know how to count big numbers and do lots of arithmetic and so forth to see how it is that these rules really explain common experience that will be more difficult for you to understand what is not difficult is this well that's difficult enough yes because it's so strange but it's no more difficult for you than for the students and no less difficult I know sometimes I hear people coming to my lecture to say oh I'm going to come to leure although I know I'm not going to understand anything it makes me feel bad or when they come up afterwards they say oh I enjoyed your lecture it was lots of fun but I didn't understand anything you're saying I really am trying to make myself clear so I would like to discuss this with you you please keep coming in spite of the fact that you don't understand it because I don't understand it either and the fun of it is that we it's so mysterious okay that's the fun of it so this business about understanding requires just a few words and so I'm going to say something about the relationship and I would hope we get some of your cooperation sometimes you don't understand because say the language is the fellow customer America and he talks too fast that's my fault and I apologize I hope it's all right that's a kind of trivial difficulty relatively next kind of not understanding is because it perhaps use new words that's an accident that comes because I'm working technically and I use the words every day and I forget that everybody doesn't know what they mean and I have to be very careful again my job then there's a kind of saying that you don't understand it meaning I don't believe it it's too crazy it's the kind of thing I just I'm not going to accept it uh the other part well this kind I hope you'll come along with me I you'll have to accept it because it's the way nature works if you want to know the way nature works we looked at it carefully look at that's the way it looks you don't like it go somewhere else to another Universe where the rules are [Music] simpler philosophically more pleasing more psychologically easy I can't help it okay if I'm going to tell you honestly what the world looks like to to the to human beings who have struggled as hard as they can to understand it I can only tell you what it looks like and I cannot make it any said I'm not going to do this I'm not going to simplify it I'm not going to fake it I'm not going to make tell you it's something like a ball bearing on a spring It Isn't So I'm going to tell you what it really is like and if you don't like it that's too bad okay there's also the possibility that you don't understand because you're con you get a bit confused and you're sure that you must have misinterpreted what I said or uh something like that and you get turned off and that's what cause the difficulty let me assure you that most of the time you did interpret correctly what I said because if it do I'm going to it's going to be so shocking the way nature actually works that you're not going to believe that either I faked it I'm not telling you the full story that for the students I have another way of explaining it or something like that it is not true I'm going to be honest okay so I'm going to ask you to try not to get turned off and not to be afraid relax and enjoy it realize that nobody understands it what the hell were my students learning for four years if nobody I'm going to explain and I'm going to explain by a kind of an example uh I like I take the Mayan Indians they had a writing system and we know some of the things they wrote were astronomical things and they had a scheme for predicting many things in the sky eclipses and so on let's take the example of when Venus which was important to them because it represented evil of some sort was a Morning Star and when it was an evening star so they could predict ahead of time whether this bad influence was going to be in the morning or in the evening and so they discovered that if they waited that this cycle of morning evening morning evening morning evening five of those occupied just just exactly the same time as eight times a certain period that was important to them 365 days it's not exactly a year and they knew the difference but they still counted in 365 day intervals which they called the tune so they said that five of these Cycles has eight Tunes then they uh discovered of course Very quickly that if they did this five cycle bit for eight tunes 10 times they were off by about 6 days and so they had rule for shifting then making corrections as they went along and thus had a very good way to predict when Venus was coming on okay now let's uh look at this thing from a point of view suppose that the professors the priests in those days who wrote this stuff and taught their students these rules were giving a lecture to try to explain what they did in order to make these wonderful predictions about Venus then if the thought was any good at Exposition and really knew what he was doing he would say what we're doing is we're counting the days just like you're putting nuts in a par and we keep on Counting 58 uh 365 nuts and then another 365 and another 365 and another guys say what a lot of work and we get all finished we said that's five of these periods now they understood what he said that's easy they did not know a quick tricky way to add 365 time 8 I'm sorry I said five I meant eight times uh the students were learning in the meantime the laws of arithmetic something which is to us now because we have public and preed uh general education almost everybody has to struggle through and learn how to add numbers by a tricky scheme of writing them in place system and making carryings and so on so that if you buy wine for $415 and you is 287 or vice versa it cost 702 and the girl who does this the wait just ordinary person in 2 minutes does that how did she do it what is she doing when she's adding 415 to 287 she's doing this counting out 415 pennies then counting out 287 more pennies and telling you how many pennies you would have got if you counted them all from the beginning to the end but it's a highly educated and very trained to be able to do that with those log numbers quickly this training is is something in spite of the fact that everybody's got it it's something pretty good because in the 14th century mathematicians were they were called who could do that almost everybody in our civilization can do that but I would I took this example you can understand what's involved what the students are taught you see in our particular problems now about physics there are many bigger numbers the numbers are much bigger it's hard to numbers are so enormous you can't count them directly and so we've invented a fantastic array of tricks and gimmicks for putting together the numbers adding counting checking and so forth without actually doing it the way I could describe what we're trying to do if I say I draw this and I draw that and I draw this and I draw that and I see where the end point is we don't actually sit down and draw 7,000 arrows and find out where the end point we can have a way of figuring out we come just like we don't actually count 415 pennies and 287 pennies to find out that you owe me 72 pennies we do it by another trick this are the tricks of mathematics and that's all so that's the part I'm not going to worry about we're not going to worry about that so though relax you don't have to know mathematic all you have to know is what it is all it is is tricky ways of doing something which would be laborious otherwise so what that it's true that in the years we've developed enormous abilities in mathematics and it takes a long time to train the students and so therefore they're very highly educated in that but if you ask them why now we go back to the Mayans we ask them why why when you wait fill up a tub eight times with 365 day markers it comes out that the Venus is up five times they don't know no they don't understand it at all the more accurately they can do it the fact that they know that they have to change it by 6 days and so for adds nothing to their understanding of it the student who has learned all this mathematics and is able to make these calculations not only a Venus of the Mars the Sun the eclipses and everything else is a super priest doesn't know why any better and if he would explain if nothing but counting days he would be reded to the truth on the one hand and to an honest statement that he doesn't understand it the other hand and could tell somebody all about it who doesn't know how to count all these numbers so trickly and so cleverly as the priest students knew okay now probably I don't know about philosophy of Myers we have very little information due to the efficiency of the Spanish conquistadores and uh well mostly their priests who burned all the books they had hundreds of thousands of books and there's three left and one of them has this penus calculations in so that's how we know about that and uh just imagine our civilization reduced the three books the particular ones left by accident which one see so uh anyway I get off the subject if I make this up now that what I'm saying now is just a story suppose now that the students would discuss or people would discuss the possible meanings of this why then they would begin to think about well 8 * 365 is 2920 that's got two twos in it now two is a lucky number and it has two twos in it and then the nine represents the god of so and so which is related to Venus and so forth and that would be a good argument then but in another city some other guys getting together have a different kind of an argument about it they say look now the fact that there's a 20 at the end if I subtracted that away first I get 2900 which especially good number and so on and they would have different theories and then someone would come along and say you know it doesn't make any difference which one of these theories is right we still have this fact to go along with and that is our modern scientific point of view in the earliest days of science we got confused arguing philosophically what was a reasonable reason for nature of ho a vacuum or it seemed to be nice to gods were doing it different kinds of psychological reasons for thinking it probably is all right after you discovered what it was these things were never useful for predicting what should happen next and we soon learned not to make these arguments it's useless it doesn't add anything and so we're not going to make my imaginary May uh arguments about the various gods that make the numbers and so I'm left if I'm a modern scientist with a description of the situation all right now I prepared the audience used up all my time to prepare the audience doesn't make any difference I will continue anyway in spite of the fact I use up all the time to uh describe the theory and then describing and I will first describe some part of it the theory is the properties of light electrons and the interaction of light and electrons it's all one Theory I cut it into three parts that way and the first thing I'm going to start with is the uh properties of light okay I'm going tell you some of the properties of light and I hope if I can do it to get to the key point and then uh we'll continue in the following lectures to elaborate on it first uh I don't go through the history of the theory of light it had various things the first and most important thing I would say is that Newton found out that what we see is white light is a mixture of otherwise Pur stuff that's easier to understand if you understand how each of the parts works you just put the mixture back together again and they separate the light in the prism which is done automatically in ockland very often at Le as far as I can tell in rainbows and uh the various colored if you would separate light in the prison and take out the part that looked say yellow then you couldn't separate that any further in another prison it just stayed yellow and orang that's called monochromatic light light of one color so I'm going to discuss all my phenomena for a while with light of one color because it's simpler the first thing Newton believed that light was a corpuscular thing and had very turned out that very strange properties from that point of view and it was then explained that many of these strange properties was because in fact it was a wave which was wrong it turned out he was right it was a particle it is corpuscular uh the reason that he said it was corpuscular was based on an incorrect guess as to the behavior of waves and this argument was wrong logically but it turned out in the end that it was particles now how I talk about how I know it's particles is this if we make an instrument to detect light that's as sensitive as it can possibly be made we make it more more sensitive in fact this thing is called a photo multiplier and uh that's not the only instrument I just take one for an example and doesn't make any difference how we do it when we get to light that's sufficient weak an instrument to detect it hears clicks pulses uh as if it was rain falling on the something you get bang bang bang bang when a light is bright the rain goang bang lot of them when the light is very dim boom boom boom boom small the particular boom booms and the bang bang bangs and so forth are completely out of proportion the actual rate is enormous okay and a little bit less when that's less light it's very difficult to get it to a bo bo Boon you could so dark in here you wouldn't know what but uh this device to show you an example of how it works just so you understand what happens when we detect the weakest possible light is it works like this there's a metal plate here made cesium or something when light shines on it it knocks an electron out then you have another plate here with a voltage that attracts the electron so the electron so to speak Falls it's attracted and speeds up and hits the plate when it HS this plate got about 100 volts of energy it splatters other electrons get knocked out of the two or three five perhaps on the average now those are attracted to another plate and they all go sailing down here with another 100 volts five of them this time and each one of those knocks out on the average five or six other electrons now I got 25 and that subtracted to another plate and that hits those and so on and you have a maybe 10 or a dozen plates by the time you get out the other end you got such a chunk of charge and electrons so many of them you multiply five times five times 5 * 5 You' be a long time counting pins to discover how much that is you get such a tremendous pulse that you can number of electrons high up it can go directly through circuits and so forth and turn on and off switches and do all kind of things make voltages to pin make noises do these that's Amplified now what happens when we have a device like this and we put it in the dark is it goes click click click click click click every once in a while a light particle comes in a photon this is a particle in every sense the experiments of all the right properties as follows that if you have a very weak light and you have one or two just one of them every once in a while if you put two cells out and there's just a few of them coming then it goes on one or the other they don't go off together they go off together you got too many coming and you can't resolve it but if it's very weak the particle is either here or there and it comes in particle I don't know how I can much I can emphasize this especially to Young students who have learned its waves it is particles in every way whenever you can detect it it's unfortunate for us that we can see the light I mean it's unfortunate for us no not quite not quite that we if we were 10 times more sensitive to light than in the dark we would see that what we're seeing is little flashes little tiny dips dots of light the nerve would go off just like this photo multiplier in spots but the human eye is not quite that sensitive and takes five or six of these particles photons five or six photons to make one nerve fiber go off so it isn't so we cannot detect with the eye light quite low enough to notice the fact that it comes in the form of raindrops all right got that they're particles right you can detect them with an instrument you can count them so and so many per second bright light more per second dim light less per second okay now we start to describe the properties of light a little further next property I want to talk about is reflection uh from a glass surface or a water surface I believe everybody knows that you can see the Sun or the moon let's say in the sea as it settles of course Reflections are a happy thing in art pictures the moon light reflected from the water you have a a window uh when you look through a window you there must be millions of examples right back there there is one you look at a window you can see through it but also some reflection now already there's a problem because the light that's reflected is not as intense as the light that's shining some of the light goes through the window say or through the water down in only some of the light comes back if the light is headed for water for example straight down only about 2% reflects what does that mean only 2% reflect that means that if we had a photon counter here let's say uh draw the experiment so you know what I'm talking about it's hard to make a water surface that's vertical yes so we'll make the water surface horizontal and uh light's coming down and some of it's reflected and we put a counter here to see one of those photo multiplier things and we count the count and we know how much we should have got and we find what how can it be partly reflected when I forgot to say when I was talking about the particles when you have light of a definite color the energy that the first one knocks out is always the same each particle is the same strength there's not half particles it's a full Photon what you get is full Photon which you only if the light is dimmer what does that mean there are fewer of them right simple so of a 100 that come down here perhaps uh four now this way a 96 go through what determines which four how does it which one that's coming down of the 100 knows would to come back up all right so the situation is that the phenomena is probabilistic it takes odds it comes down here and has a 4% chance one out of 25 trials I think you know what odds are if you have for instance a die and you want to get a a one and roll it well it doesn't come out so often but it comes out sometimes one out of six and uh what that means if you roll die a 100 times let's make it 600 times a little easy you roll a die 600 times you might get5 on or maybe 92 ones or something like that right you get about 100 and in this if the numbers were bigger the accuracy in percentage is bigger not accurate so if you have billion six billion no not six I got 125 25 billion of these coming down about a billion will come off okay now let's see if the the next features how can it be probabilistic suppose that I had a light so weak that I had only one Photon coming every few minutes will this counter go off or will the one down here go off one out of 25 times this one goes off which time what determines that possible theories nothing pure chance the world is made of chance that would mean that the physicist can't predict the future it would mean that if you set up an experiment with exact conditions you cannot predict what happens in the future because you can't predict whether it's going to go up or going to go down you just got 4% odds your whole beautiful structure of science is reduced to Computing odds nature instead of being definite does everything by chance not so good other possibilities there little spots on here and all has to Photon has to hit a spot on the surface and Newton had several things you'll find out later when I give you more phenomena how these are various explanations which way it's going to go and why the spot one doesn't work but I'll give an argument that Newton made about that he said it can't be that because he said you can polish glass it's wonderful I love to read these old guys you know they they knew you could polish glass but they had the intelligence to deduce from the fact that you can polish glass that there's no spots on it like why what's polishing see he polished he C his own lenses he ground his own lenses so he knew what it was doing he takes a coarse grain sand like stuff for what do they call it the the the polishing powder I mean the grinding powder and that shapes it it cuts but it cuts fairly obvious grooves and you take a finer one with finer particles and you cut the grooves are finer and you make the f finer and finer and finer and after they're fine enough suddenly it's smooth and the light comes right through when it's coarse it's bounced around and so he concluded that light cannot see the gloves that when I polish it it's not that it's smooth it's it's still bumpy but on a small scale whereas when I have the big grains it's on a big scale it can't be any different when I polish with the small grains it's just a small scale regularity but somehow light doesn't see anything on a small scale correct all experiments have shown that this is absolutely not the right explanation if it was there'd be all kinds of ways of testing that I told you if we can measure down to 10us 15 cm and so forth and that what would happen would be you'd be able to find some area to focus very carefully the light so that the two that the reflection coefficient would be higher than 1 and 25 because you happen to be near a place where there was a spot you can't do it no matter what you do it's 1 and 25 other possibility the light that's coming down here the photons are doing uh well uh like footballs and they spin and depending upon whether they hit with the nose point or with the Flat Point depends on where they bounce back in other words something inside the photon is determining which way it goes again no because you can if that were the case the light that went through would be all of a certain kind of football and if you try to reflection again you'd expect a different number than 4% because of the fact that they're all lined up and you can't line light up you can't fiddle around up here by any kind of filtering that'll change that percentage all the lights photons are identical if they're the same color in one color they're all identical and they behave with 4% are we therefore reduced to this horror that physics has got reduced not to these wonderful predictions but to probabilities yes we have that's the situation today in spite of the fact that philosophers have said it is a necessary requirement for science that uh setting up an experiment exactly similar to will produce results exactly the same the second time not at all one out of 25 it goes up and sometimes it goes down unpredictable completely by chance all right I already see you turning off I sincere you say you don't understand me you can't understand that it could be chance I don't like it tough I don't like it either but that's the way it is okay I don't understand it either I don't understand understand it must be that nature knows whether it's going to go up or down no it do not be that nature knows we are not to tell nature what she's going to be that's what we found out every time we take a guess as how she's got to be and go and measure she's clever she's always got better imagination than we have and she finds a clever way to do it that we have thought of and in this particular case the clever way to do it is by probability by odds and so the first aspect I have to tell you about then is that light works by probability all right by the way just incidentally the wave theory had no difficulty with this at all because what happened would be like the waves of something are coming down here and they shake and they just keep going but some of them are bounce back something like a sand bar sometimes partially reflects the waves in the sea so some of the energy went back but the waves don't operate this thing by the way when you turn the light on this might go off at any moment you don't have to wait for a certain length of time of course there's odd that it goes off at any instant but it could accidentally go off the moment you open the slit so it's not a question of waiting for the energy of the wave to pile up or anything it's hopeless I have to start with light as particles waves explain many things but not right it's partic okay okay it's Photon the problem is they have reflected with probability now the next feature having to do with reflection again that I would like to describe is something that you're all so familiar with perhaps not so directly but perhaps you've seen the colors in soap bubbles it's made out of soap water which has no color no color I've seen the color mix it together get a lot of soap water together and look at it no color you take oil which is a sort of a yellow fluid and you it drip with blackish yellow junk it drips out of an automobile on a rainy day you must have experience here with that and you look at the puddle to your Delight there are colors colors these colors are produced by Reflections from two surfaces near each other very close together if the surfaces are far apart we'll discuss it later the same phenomenon really occurs but it's much harder to see under normal circumstan what happens there is that in a soap bubble for example there's a layer of water and so we have two surfaces at some distance from one another so and then the photon can either come down here and reflect right away or it can come down this way and reflect from back there okay now as it turns out that's about the same percent if it's just water between air and air it's about the same one and 25 both times what's the colors if I'm going to do it with monochromatic light that light of one color what can you see in colors what you see on an oil film on a mud pudle or in a soap bubble when you use light of exactly one color is not colors but bands bright and dark band places where the light is reflected very well and places where it's not reflected at all across the bubble now the different the position of those bands if you looked at a bubble with red light you see bands black and black and red black and red band all over you look at it with blue light you also see blue and white blue and black blue and black bands but the pattern is not the same they're displaced from the where the red ones were and so when you have both red and blue you get purple and red and black and purple so on now if you add to that yellow with its pattern and so forth you get all these colors mixing okay so we're going to simplify experimentally as as Newton did and look at these uh this reflection what Newton uh most of his experiments he did this clever way he had a beautiful curved piece of glass which was a lens and a flat piece and put them next to each other and then this was only a very slight curvature and so he had this gap between the two and when he shine shown light this way and looked at reflected light which depending on where you looked see this is a cross-section of the lens which is more completely like that there is some reflection in the a which is irrelevant at the moment there another glass plate down here when he looked in different different places the light came down all over and he looked in different places he was looking at cases that corresponded to reflection with one Gap or another gap between this side and when he looked at this with monochromatic light looked down on it since it was a circular a spherical lens he saw in what I call bands in the soap bubble but more organized he saw Rings called Newton's rings with a black area starting and then red if it was red light he was using and black red and so forth these looked like they were coming closer and closer together but he was a clever man and understood immediately what it meant if he measured the distance from here to here and plotted the answer for whether it's red or dark against this distance not against this instead of measuring away from the center he measured how far apart these plates were then he found like our friends the Mayans every time you had 365 P they got black in other words if this was black and this was red then double that distance was black again and yes and triple the distance was red and four times the distance was black and five times the distance was red and so on nice and even in other words instead of measuring by this Distance by measuring the thickness you find the following experimental result reflection coefficient against thickness between the two layers okay the spacing between in this case if it's an oil film bubble with that that's the distance in this case it's the space in between the lens and the plate and if you're could change it as hard as to change in a soap bubble under control but it changes automatically as it dries out you get the following get no reflection if the thickness is zero then you get a strong reflection for certain thickness and then if you make it thick you get no reflection you th reflection then you no reflection you no reflection and so and so on and and now it's getting thicker and thicker does this go on forever yep if you got good enough monochromatic light and get the experiment under control you can make it go almost indefinitely you can make this work for distances of a meter or more still catching keeping track whether it's even odd even OD bump bump bump okay there's nothing that's interesting very interesting but you know that's ding why because what theory were you figuring for the Reflection from that that made the reflection 4% the odds 4% whatever you put another layer down here at the right thickness expecting to get 8% and you get nothing how does the layer down here turn off the Reflection from the layer up here or if you figure that out and you make the layer just a little thicker it doesn't turn it off but in fact the reflection is more than twice on this scale here this line would have been what you would have expected if you expected it always to be 4% plus 4% or 8% from the two surfaces this is what you would have got if you disregarded all this nonsense that actually happen but common sense it reflects with a certain odds and it reflects from the other surface with a certain odds and so all together you got twice as many coming back this is the twice as many but for some if the thickness is zero you don't get anything if the thickness hey that's not such a bad idea is it if you don't have any water there at all you wouldn't get any reflection starts out right anyway that theory was kind of dumb now that I come to think of it and that helps to explain Newton's observation when the distance is too small the light doesn't know anything about it if the thickness is sufficiently small it doesn't reflect it does exactly the same as it there's nothing there but the horror of it is it's all right that increases as the thickness goes up but it overshoots you see and then it comes back to zero again when the thickness is just right it's very difficult to invent a probability thing if I had these spots on this surface it's very hard to see how you're going to have spots on this surface which turns the spots on that surface off when they're the right distance away and so Newton went a little bit nutty and he talked about fits of reflection and transmission and so forth and I would like to now just finish this by telling you what is the answer now here's the answer this is the way we figure this out it goes as far what we're going to calculate is a probability the probability of a particular question and then probability that this counter goes on the probability that if I had one Photon coming down it'll come back to this count the probability which is measured by this curve and here the way the rule is for finding the probability now listen hold your seats now hold on don't be afraid just just go along all right never mind it don't like it huh just hold on it works like this what you do is you take a piece of paper a piece of paper has nothing to do with the original thing the piece of paper is only make marks on it's got nothing to do with the light have you following rules that you make an arrow to represent well for each reflection you make an arrow this arrow for example is for the Reflection from the front surface and this Arrow might be the Reflection from the back surface and I'll tell you in a minute how to make those arrows and then what you do is you tie the arrows together this way you make one and then the other all right that means you make this arrow and you put the tail of the other one on the head of that one there's a first arrow is a reflecting Arrow from the first surface and this is the second arrow is the reflecting arrow for the second surface and you put these two arrows together by this Rule and they look at where how far off you've come to the end yes yes to count the pins in the hole to count the number of beans you put in the barrel I mean you make these pictures and then you ask how big is the circle and area that area represents the probability that you get the thing back if the circle area is Big then you get a high probability of the circle area is small you get a small probity and I just have to say one more thing of how to make the arrows answer well the size of the arrow depends upon the particular materials I won't come into that right now the absolute size 4% is another matter what you do is you make an arrow and depending upon the time it takes for the light to get from The Source where it started to the place where you want to count it you turn that out like a clock depending on how much time so if it takes a long time you see you start out at the source there's the arrow for the source but that's not where you that's not the hour you're going to draw this is just a thinking hour and then you say turn turn ding D ding D ding ding round round round round round round depending on how much time it takes at a certain rate every second it goes around 75,000 goes around a hell of a lot of times it goes around one followed by 15 zeros time in one second but it doesn't take light very long to get to the from the source that turn but still turns around a lot of time you turn it around okay it's like the roulette wheel and just at the moment it hits the counter it happens to be sitting at some angle all right that's for the reflecting from the first surface now what about that was the That was supposed to be this one I I've gotten too many arrows on here what happen is you take the first surface reflection turn it through it this angle depending upon the time and it ends up here say that's not very big angle you said it was a big angle it is a big angle you know you keep on turning it look can look like a small angle when you're done but you had to turn around and around and around and around around right you know what I mean it goes around like a clock hand after 25 years is still saying 2 can start at 2 and end up at 215 yes 25 years it went around so here it is having been turned around a lot of time okay this is the from the first surface I should say that's the one the arrow for the first surface now the arrow for the second surface rule same as the arrow for the first surface but in the other direction it's just an accident it happens to be the opposite direction it starts because well but because the rule will turn out later when you go from air to Glass it's one way from going glass to air you change it around anyway you start this way for the second surface and you turn this one no which way did I turn yes for the time and when you get finished with this roulette wheel and the second one it comes out so and then you add them together the way I said you tie one on the other end and make the circle and that's the law of elect light and that'll tell you whether it reflects or it doesn't and what difference does it make why do I get these ups and downs well sure if you move this kept that the same and move that why do that going to do to my exercise over here answer the first hour the time doesn't depend upon where the other surface is it so it does exactly as I did before I'm doing the same experiment over with the bottom surface a little further along okay Top's the same place now the second one however when I went to turn it it's a little bit further it takes a little longer to get there and therefore it's turned to a new position so this second time the picture would look if the th was thicker the picture might look like this instead of being here since it had a turn further perhaps it's turned to here the second time and then when I add these two things together and tie one on the end of the other and I just do that again here you see that this line is now a long line whereas before it was a relatively Short Line This remember was the answer line the answer line is a longer line F and the area here is much bigger of this circle and the probability is larger and this upping and down Jing Jing Jing Jing and the answer is comes out exactly predictable just by this little game all right that's a shock huh that's you say yeah he's going to explain why it's like that that's exactly what I'm not going to explain I don't understand it that's the way it works the what I'm going to do in the next lectures is to tell you sort of the generalization of this this a special example for reflection I'm going to tell you how the rules go about turning arrows is in fact somewhat simpler than this example it's not bad at all it's easy it's not hard but much more generally and I'm going to what I've done is this is a prototype of the general result there is no secret behind it that we do any better than give you that result all I'm going to do is generalize it it's going to sound something like this this part you need to understand right away it's what I'm going to elucidate in the next lecture the idea goes as follows in general but just a statement then I'll come back and do it again so don't worry to calculate the probability of an event which can happen in a number of different ways the probability of an event is always what we call the square of an amplitude more in this model means the size of a circle corresponding to an arrow an arrow is called an amplitude for every event you calculate an amplitude which is an arrow on a plane the probability is the area corresponding to that Arrow right that's the first P second how do we calculate the amplitude for an event if the event is simply a particle going a photon going from one point to another of a definite color then it's simply an arrow which turns depending on the time that's the amplitude notice by the way there's no Reflections and no trouble it just turns the area stays the same the probability of finding a photon is not altered okay even though the arrow Alters its areas same it's when we get in trouble when we have more than one way to occur then the rule goes as follows if the thing can happen in more than one way then you find the amplitude what that was the arrow for each way see if it could happen in two ways you got the arrow one way and the arrow the other way and if it can happen three ways if it was a double layer stuff and so on then you put another arrow for the Third Way maybe that one's a short one and if there's a fourth way I put another arrow and when you all finished you put them on tail to tail all the possibilities and find the total what we call the total or the net result of making all these little arrow steps and that final arrow is a total amplitude we say for the event to occur the probability is as always the area corresponding to that Arrow that's kind of stinky right well it's fun and that's strange that nature is like that and I hope you come back to here how it works in general a little bit better statement of this to review it and one other thing I am going to try to explain to you how this rule explains several of the ordinary phenomena that you used to in life such as angle of incident equals angle of reflection on reflection that light bends as it goes air to water and that travels in straight lines from point to point and so on it's all hidden in that one rule and how that one rule carries all this information is part of the next lecture as well as uh I would tell you right away one more thing that this rule that to figure out what happens in nature you have to calculate an amplitude is not just for light it doesn't make any difference what happened an electron does something of nucleus explode doesn't make any how do you find it you can only calculate the probability it's going to happen and how do you do that you can get you calculate an amplitude that's a lousy little arrow and the probability is the square of the amplitude we call it that's really the you should call in our case the circle of the amplitude the circle that represents the amplitude measures the probability and that's true not just of light but of the whole structure of nature as far as we can tell and although quantum electrodynamics is only about electrons in light we discovered that part of the rule at least is valid also for nuclei nuclear particles quarks and everything else the thing that is special about electrodynamics is our complete knowledge of exactly what the rules are for drawing the arrows but the fact that you have to draw arrows and end up calculating probabilities like that which is such a shocking and horrible form for nature is something that I will talk about next time in further detail thank you very much these rotating arrows are all very well but is there another model the question is is there another model naturally we struggle to find it I'll tell you the answer what's going to be in the fourth lecture nobody can find one it's worse there's a we're not so dumb as you know we're pretty Advanced compared to the May we've analyze it very carefully you almost prove it's impossible to find one over a wide class of ordinary possibilities if it's going to be any kind of a model it's going to be at least as weird as this thing the reason is that the answers from this are so simple that is looks a little complicated you're not used to it but mathematically those forms and those curves are mathematically so simple and the rules are so simple it's hard to make any mechanism at all that can reproduce such Simplicity the Mayan thing was really fairly complicated the numbers were peculiar there's no explanation on them this analogy our numbers are not peculiar those they have an explanation for it's a different situation one more thing about gravity I would just remind you we don't really have a good bottle because what comes to why is it that there's a force inversely is the square of the distance and what do you mean inversely is the square of the distance that's mathematical and Newton was the one who taught us that we can make progress if you stop arguing about that he said I make no hypothesis I don't EXP the gravity law I tell you what the law is that tells you how the things look and you can predict where the stars are going to be and that's the pattern but I don't at the moment know but he left open the question just like you asked maybe tomorrow somebody will figure it out on your particular question it's always possible of Tomorrow somebody will figure it out but it's going to be very difficult and very strange do you like the idea that our picture of the world has to be based on a calculation which involves probab not really if I get right down to it I don't say I like it I don't say I don't like it I have very highly trained over the years to be a scienti and it's a certain way I have to look at things when I give a talk I simplify a little bit I cheat a little bit to make it sound like I don't like it what I mean is it's peculiar but uh I never think this is what I like this is what I don't like I think this is what it is and this is what it isn't okay okay and whether I like it or I don't like it is really irrelevant and believe it or not I have extracted it out of my mind I do not even ask myself whether I like it or I don't like it because it's a complete irrelevance it's a kind of a dumb answer but it's true and when I'm lecturing I shouldn't have said I don't like it when I was trying to say is you probably don't like it there's nothing I think we can do about it it might have been something else I I don't know how else to express it it's not really personally a dislike have you left out anything in this lecture which you need to add later it it's a very difficult and I worked very hard on the lecture to try to use as my examples things that I didn't have to change later the interpretation slightly you know I couldn't get an elementary enough process that I didn't have later on I have to make a little change you see we talk and we see as though it's reflected at the surface actually what's really happening I want a deeper understanding which I should do later on in the lecture but I might forget is that it's reflected by cause it affects electrons in here which Reit light here or here or here or here or here or here and what really is the things that we have to add is not the arrow from here and the arrow from here but a whole lot of little ones from all the distances from there to there but believe it or not you get the same answer okay so what I really ought to do and I would do if I were doing a corrected would be to talk about the Reflection from every interior part and adding arrows but I would rather add just two arrows the first time that an Infinity of them so I cheat didn't cheat a little bit but I got myself in a slight hole which you picked up the actual reflection is from the material the electrons in the material in the case of Newton's thing it's because the electrons which is reflecting from the glass here and here are interrupted in their pattern and when you add the arrows it comes out to be believe it not the same as if you just take the one one from here and one from there perhaps just for those who can I don't want to make it too hard but just to give you a clue of The Marvelous way it works if you added tiny arrows to represent Reflections from everywhere instead of just talking about reflected from here to here which is a good equivalent way but if you took a whole lot of little baby arrows each one a very very tiny angle from the other all the same length which is the reflections from all these places you see you generate a circle and what I was using instead of the circle were the two arrows which were the beginning arrow and the end Arrow of the circle and what you told me is I shouldn't talk about the Reflection from the front surface and the reflection in the back surface I should talk about the reflection of all the stuff in between and it's but it's equivalent the net result of going around here is the same as going up here and back on that one it even accounts for the minus sign that is the distance from here to here is what you get by putting onto this Arrow This One backwards well I got to the whole the distance is the same see I get I got it upside down in my but uh this line is the same line as you would get by going in a circle so it's really reflected from the interior but in the first lecture I thought I'd just get two arrows instead of an infinite number does your picture apply to anything besides electrons and Light this aspect is universal over the whole of the world's phenomena as far as we can tell not just light and electricity this phenomenon of drawing arrows and making areas for probabilities probability amplitudes we call them the amplitude and the probabilities are the squares of these amplitudes or the circles of the that's Universal the mix problem is a rule for how to draw arrows under different circumstances what kind of arrows do you draw different certain what are the rules one of the rules I told you is it turns at a certain rate for light and so on those are the rules that we do not know well in the case of the nuclear phenomena but we know ex virtually exactly or at least as far as we can tell experimentally I lost my numbers uh for electrons and light the rule for how to make the arrows is completely apparently completely known that nothing is ever complete but within the accuracy and so on it's known what's not known is how rules for me the arrows when it's protons that are moving around and so on okay when you are looking at something do you see only light or do you see the object the the question of whether or not when you see something you see only the light or you see the thing you're looking at is one of those Dopey philosophical things that an ordinary person has no difficulty with even the most profound philosopher in sitting eating his dinner has any difficulty making out that what he looks at perhaps might be only the light from the steak but it still implies the existence of the steak which he's able to lift by the fork to his mouth the philosophers that were unable to make that analysis and that idea I've fallen by the wayside through hunger [Applause] can you tell us whether in the future your theory will be found to be wrong or is it complete no of course not how can we know what the final thing is I tell you only what we know today can I tell you more do you want me to tell you more would you like me to tell you what we know tomorrow I'm sorry I have the Nobel Prize from the past not from the future I do not know the future and I answer in a similar way to your likes and dislikes if you ask me what I think will happen in the future I'll tell you I do not think I do my best to understand what I supposed to understand what we know so far I do not know what you're going to discover next okay I can't I know only is you're talking about the edge of the discovery business and it's impossible to say what Beyond the Edge so I can't answer you all right except to say that the history of physics has been that the things that looked like they were nicely set aside were and it turned out to be erroneous upon further Discovery and since Society is continues to be vigorous enough in its Endeavors to investigate nature it's almost sure from a social point of view not from a Theory of physics that new things will be found out which will not fit in and we have no way to tell whether some young man perhaps from New Zealand or somewhere will find another way or more about this stuff so it'll have a different picture in the future obviously I can't say I tell you what it looks like today you call it my theory it's not my theory it's Theory everybody uses I must going to make it a little tougher this time than I did last time the phenomenon I'm talking about now is the theory of the electricity light and so forth and we're concentrating on first tonight light and next time next Tuesday it'll be about electricity and uh finally we're putting and the two of them together and uh at the next lecture after that we'll talk about what's wrong with the the where what's the rest what's in the world besides electricity and light what else there is in physics and what new questions are left but in the meantime I'd like to talk about light Newton started by many experiments and observations which began this subject he found uh there are phenomena that are so very very common but are absolutely sensational ununderstandable and almost impossible supposing that light is made out of cor pusles or particles Newton assumed that light was made out of cor pusles or particles because he made a mistake in reasoning he said that he thought that the shadow edges were very sharp and that that meant that must be particles because if it were waves that went past the shadow they would spread into the shadow this is a misunderstanding of exactly how waves do in fact behave they do spread a little tiny bit into the Shadow and the shadow spreads into the light of it uh but not very seriously and in fact the wave theory of light was uh is much EAS finds the phenomena that Newton discovered much easier to explain but I want to start by taking the view that light is corpuscular that Newton had and remind you of what this phenomena are and then go back over Newton's attempt to explain them and see how pitiful it is so uh we start with that reflection of light from a surface of glass I last time I used water and I said it was 2% reflecting and somewhere along the line I changed it to one quarter and that was a mistake it's glass that's a quarter and light water that's a 50th 2% is not a qu I mean 125th it's 2% is 150th and for glass it's 4% or 125th so we'll talk about glass the first feature is that's interesting is that from glass the light is reflected only partially and if it's particles it means some of them will come back one out of 25 and some go forward uh 24 out of 25 yeah uh there nothing hard too hard about that if you would suppose something something is different from one particle to the other even in their Arrangement or something like that but further experiments have all shown that all light photons are exactly the same and in the same condition and there's nothing we can do to preset the photon to make it more likely to come back from the surface a single surface of water than to go forward there's no way and we have well I keep on going from a simpler point of view and we'll discuss other models in a minute but the really interesting feature is that the reflection of light from a glass surface is affected if there's another glass surface below it for example if you have a soap bubble which is two water surface between air and water and water and air then the two layers make colors in the bubble which aren't in the water but is produced by the effect of the Reflection from the two surfaces and if I choose light of a particular color say if I looked at the bubble with purely yellow light then I would see Rings or areas that are black and areas that are bright yellow relatively in other words areas that reflect well and areas that do not reflect at all in other words they Reflection from a surface which you would expect from a single surface be reduced to Zero by putting another surface here which Common Sense would imply would increase the reflection but it could in fact make the total reflection zero and the actual to a reflection probability chance that the photon or four pule gets reflected varies with the thickness of the layer this way if the thickness of the layer is zero it doesn't get reflected at all that's nice no glass no reflection if the glass gets thicker the reflection increases to a certain Peak and but if the glass is still thicker the reflection falls again to zero as I said and Rises Falls in southwalk in a repetitious fashion and Newton believe it or not you only working with very thin layers first discovered this with three or four at 10 repetitions and then was Able by clever experiment to demonstrate that it happened with after 34,44 Reflections a repetitions in other words with a quarter of an inch of thickness this bumpy thing kept was still going nowadays we can do this experiment in which these two things these two Reflections are separated by so far a me or more and if the conditions are just right get monochromatic light of exactly one color from a laser you can still see as you move this thing reflection strong weak strong weak strong weak from the two surfaces so it goes on forever now how can we explain such a thing from the point of view of pusles I do this to show you what a fix Newton was in to explain it because he thought it must be P prud the reflection must depend on both surfaces because it depends on the distance between them the wet one or the other surface that changed the reflection so they're both involved yet it can't be that the particles reflected from the first surface because if it were reflect from the first surface it would never know where the second surface is and that reflection depends upon the position of the second first surface for example if it was reflected from the first surface how could it be not reflected at all if there's a second surface at just the right distance and therefore it must be re entirely reflective on the second surface but the Reflection from the second surface is affected by the position of the first one and therefore it must be as follows the first one an influence which which follows the generat some kind of a wave in a medium or something of a kind that follows the particle along and changes its disposition to be reflected or not reflected that is it gets the particle of light as it comes through can be in different conditions either a condition of easy reflection or easy transmission the opposite no reflection and whether it's easy reflection or easy trans transmission is determined by some kind of an influence which propagates along from the front surface and overtakes the light particle and adjusts it so to speak to make sure which way it's going now this uh had a lot of difficulties with it it was called a theory of fits of reflection and transmission it's not good for the following reason you can't get along very well with the idea that it's not reflected at all from the front surface because suppose you had very deep water just a little dirt in it then you still see the reflection just as well and if it's not reflected the first surface it's impossible to explain because that stuff which is coming looking for the bottom surface never gets there and yet some light is reflected second if it's all the decision about reflection is made at the second surface then it should not expected that it would be possible to alter that decision by putting in a third surface now Newton did not have available experiment which do more than two sub but had he done that he would have found that the amount of reflection is altered Again by the presence of third and fourth surfaces and even though with two surfaces one might get a 100 a very strong Reflection by putting more surfaces underneath you can reduce that again to zero so that the decision is not being made on the second surface the decision is made on the last surface then how does it know is it's going along whether there's going to be a last surface or not now uh Newton uh is a way I would say is a genius about something actually he's a teacher of something he's the man who taught us how to do or how to think about science in a modern way so that we can make some progress he's the one who distinguished very carefully between the facts that he would develop and experimentally determine this really happened that is to say what really happens is that the amount of light for brightness does go up and down depending on the sickness and that is to be distinguished from a theory to explain why it's so he hasn't got a satisfactory theory he did his best I'm sure I can tell from reading it that in the back of his mind he knows there's something to matter with him he know the explanation is going to get him into trouble for somewhere he can feel it because he puts that part in the form of queries or questions of how does it work can it not be that there's a part influence which propagates along and overtakes the light and so forth he doesn't say there is which is going to get into difficulty now you're all happily laughing at poor Newton but you have to laugh at yourself because you live in the world and this happens and you have these very good ideas about how things happen and you can't figure out how such a thing can happen from Common Sense ideas save one possibility it's not particles all right and so it turned out that uh people propose that instead light is waves which come down and like there waves in the sea and parts of them bounce back here and they bounce back here and the crests come together under some circumstances of timing and the crest or troughs come together under other circumstances you get strong or weak waves going out and that's what what you see in brightness is the strength of waves so that for many years it was all these wonderful phenomena were happily explained by the wave theory of light the difficulty there the idea there was that if you had a very dim light the W that would represent very waves hardly moving at all just a little motion carrying very little energy so when they went to investigate dim light with the most sensitive instruments to see what it looked like you found that the dim light wouldn't make an instrument like a photo multiplier any other device that was very sensitive go off said there's a certain amount of energy here no there's nothing nothing nothing that's a bump of energy the energy came in lumps it wasn't a tiny little bit dribbling in all the time and so the experiments with photo multipliers which I unfortunately don't have a direct experience with but they characteristics of them are that light is made like a COR pusle so that although Newton's logic as to why they have to be cor pusles was wrong it turned out he was right about there having to be corle and his paroxysms of reasoning that were produced by this thing the torture of the mind that's produced by this phenomena plus the fact that light is cor pusle is uh had was returned to the physicist as a real problem and it has never been solved in a completely well solved in a way in a description method by which we can predict what happens here what happens here is that this is not the intensity of a wave that is the amount of wiggling of the wave of some kind but it's instead the chance that a particle comes as being counted by a photo multiplier when I have the thickness so big so and so many particles come if I sent a light so weak there was only one particle I send only one core pusle one particle of energy one Photon to the system and sometimes it bounces back and sometimes it goes forward and this gives you the odds that it bounces back and goes forward for a single layer the odds would be 4% this maximum height here is 8% and uh 4% around here and it can go down to zero now it's we have not been able to find any system of logic that's consonant with ordinary ideas of causality and some you know ordinary ideas about what think things go how can it not know when it's at the front surface it's in the back surface all that stuff that'll explain this or describe this and so in order to keep going in order to describe nature we've had to generate a set of ideas which are empty of uh a set of rules rather which describe how to figure out these probabilities which are empty of model that is to say empty of a model of the type You're Expecting particle is like a billiard ball that bounces against a wall and so forth it doesn't work or that it's like waves and what I would described last time to you was this picture I would say that it was in about the beginnings of the 1900s that it was discovered that light as a matter of fact behav like particles which is the terrible shock after great success of the wave perod and then the problem of trying to see how particles could make these wav likee phenomena that are so easily explained by way became known as the wave particle duality things would be said like light behaves on part as particles on Thursdays and on ways on Tuesdays and that's course is not a satisfactory Theory the quantum mechanical it turned out as a quantum mechanical be that light is not unique in this connection but things that were supposed to be honest proper particles like electrons behave sometimes produced effects like this exactly the analogous so things that start out as waves be behave like particles and things that start out as part behave like waves until both was clear behave the same way they behaved in their own in Quant mechanical way worked out in 1926 at first the equations were discovered and then it was in fact a man you don't hear of very much when they talk about Quant mechanic a man named Bourne who proposed somebody's blowing their nose Max born who proposed the interpretation of the equation in terms of this idea that we're calculating probability of event that it's a statistical matter and that it's not possible to uh predict exactly what'll happen in a given experiment now I want to repeat the the rule that we have here which looks completely artificial and I prepared you last time if you all knew [Applause] [Applause] he had a similar difficulty last [Applause] time heavy I'll take it out okay right all right okay now I predict that the probability that I'll have a microphone of that kind next time is very low all right now what are how do we describe this in modern physics first that we cannot predict what will happen we can't tell you for a given particle whether it's going to be reflected or not horrors of Horrors but it's true we give up and second in order to find the only thing we do calculate is the probability let's say in this example that it'll be reflected more accurately I should say better this way that if you have a source of light here and a photo multiplier here to look the probability the photo multiplier goes off that's what I'm calculating I should have I said the probability the four time went down and bounced back that's bad otherwise I get back in the old problem again which surface did it bounce from no no just the probability the photo multiplier goes off all right right now how do you find the probability that the photo multiplier goes on as follows general not only about light the whole of the world is built this way according to these modern physicist it's just an example photo multiplying go electron counter goes off things like that probability you calculate probability of events this way the probability of an event this comes out in the end is proportional to the size of a circle made by an arrow on a plane a calculating plane over here it's got nothing to do with the geometry of that this arrow on the plane is called the amplitude sometimes called the probability amplitude for the event so everything that you want to high like the chance that the counter goes off has a probability no it has a probability amplitude there's an amplitude that it goes off the square of that that is the area or proportional to the area somebody bothered me about a factor Pi last time correctly correctly uh is the measure of the chance that the counter goes off right now the theory that's the framework of Nature and the rest of the theory of nature is to compute these probabilities amplitudes that is to tell the rule for finding the length of the arrow and where it's located and that's what we talked about last time again and I'm reminding you in this particular case it works as follows for light that's monochromatic of a single color let's say red it's the following as the rule that uh you draw you draw an arrow for the reflection let's say for instance that this is say a single surface reflects let me suppose 4% that is in fact 125th of the light so if a unit of light if the light one unit of of probability is represented by that and its size circle when light is reflected the length of the amplitude arrow is 1 because its square is 125th so here's the amplitude arrow for Reflection from the front surface should be 1/5 the other one incidentally the same manner the Reflection from the back surface produces an amplitude arrow for this is the amplitude rule 1/5 that's the rule for reflection and this from the one top surface this is the corresponding rule from the bottom surface is to make the5th in the opposite direction and finally one more rule that you have to figure the time to go from The Source all the way back to the photo multiplier if it was going at the speed FL and the proportional to that time you move this around like a clock so the effect of the Reflection from the first surface is in in fact an amplitude which is 1/5 long but is tilted at an angle which is what would result from a very rapidly moving rotating clock hand going along as if you wish for the length of time that you would calculate ordinarily for the light to come to the first surface and bounce back goes around like a son of a g one followed by 15 z a second going around and then what it finally reaches the photo M by it some position likewise the second one this is the first one let's say this is the first surface the second surface but more correct when you put the timing in that's the contribution of the first surface now for the other way that the thing can happen we have the second Arrow turned also around a great deal but not by the same angle let's just for a moment suppose that the two surfaces were exactly on top of each other then the times would be exactly the same and the angles would be the same and in that case the other one would come out this way but if it's further down it in general will come out at some other angle because the time is not the same so let's draw it at another Angle now the rule is this that if you can the general rules thought something like this probability is equal to the square of an amplitude amplitude for an event that can happen in more than one way is the sum of the amplitudes for each way now I mean by some how do you add two funny arrows rule for adding arrows you put one on the tail of the other so hit this was number one and this is number two you draw them like that and see what you get left well in this particular case we have only two ways they have only two arrows and I've added them together by making one chase the tail of the other this is the arrow representing the contribution in the first surface and that's from the second surface and you're all bored because I told you all that last time but hoping that that there's a few more some people I cannot believe that everybody who was here before came again and there and there's the same number of people as there was before so I deduce that there are some people who weren't here before now this uh this then produces these effects in the following manner that if the thickness is zero the first Arrow points this way for the case of zero thickness say and for zero thickness the second Arrow points that way and if you put the this tail on the head of the other one you go up and back and the net result is nothing whose circle is zero and there's no probability on the other hand if you have a thickness a little bitsy thickness you got just a little bit more turn and you get something that's somewhere up climbing up here the best you can do is if you get the thickness just right so that the this one is turned around so it's exactly lined up this way so with a certain thickness that's just right the first one is turned a certain angle and the second one which would be out here is turned more by another half turn and therefore the second one is this way also and when you put the Tails together you get it twice as long right and then you would have had by one alone and therefore what is the probability four times that what it would have been for one alone because the probability is the size of the area of the circle and for one alone if there were only one surface the circle is only so big and it's twice the radius is four times the area of the circle so therefore the height of this is four times should the probability here should be four times as much as it is from one surface and since from one surface it's 4% and 4 * 4 is 16 this has to have been 16 and it is [Applause] now in this manner of course if we take greater thickness the thing turns around further and further and uh it goes down again gets back into the same condition in a repetitious fashion when the timings are so and so we understand why this keeps on going up and down up and down up and I me I'm sorry we don't understand a damn thing but we have described how it behaves you'll notice that the average here if you didn't you had some circumstance in which you could you average this and didn't look too closely at the thicknesses you had in irregular plate or something like that for any other reason want to average it the average is about halfway up in fact it turns out because of the symmetry of the curve to be exactly halfway up and the average is 8% which is the amount of light that you would get expected to have gotten if 4% came from the front and 4% came in the back and her life was easy if it weren't for these bumps there'd be nothing to that we could understand 8% childishly 4% from coming from the first surface and 4% coming from the second surface but it doesn't do it that way it sometimes gives us instead of 8% nothing and other times it gives us 16% which is more than we want it ends up on the average giving us 8% it gives a clue of how the old theories the simple-minded views of what was happening what happens in the world why you can bounce balls and count things and things do things as you expect them to do works it happens that these irregularities involve this distance of thickness is something like thickness of glass of the general nature of 10 millions of an inch and uh therefore for ordinary pieces of stuff with reasonable dimensions in which you're not so accurate as 10 1 millions of an inch you're doing a lot of averaging and then Common Sense dumb stuff like look it reflects 4% on the front surface and 4% on the back surface it's got to reflect eight come out right but that's CU you're averaging all this fancy business with these arrows now uh what I would like to do in this lecture U is to show you if very to start you off in a certain direction and to show how it is that although this model of the world is so thoroughly and utterly different than anything you've ever seen before or expect and hope never to see again it will explain the simple properties of light that you know and uh properties such as angle of incidence equals angle of reflection that's in there that light goes in straight lines that's in there that light when it goes go from air to water it deflects the light goes in a certain line you know that and when it goes light goes from air to water it changes Direction yes all that's in there that if you build if you have a lens you can focus light to a point and things like that all of that's contained in this thing plus many other phenomena and the great difficulty I had with this lecture was this it's so easy to derive all these phenomena that you take so long to learn about in school that I did one after the other until I found I was doing too many and then I realized I'm doing it to people who know that for example what is the exact Behavior how much does light go into a shadow I wanted to explain it's easy but I'm not but since not many people know how much it really you know how it looks they haven't seen defraction anywhere I wouldn't bother with that phenomenon so what I had to do is to control myself and not produce a large number of examples but only a few to show you how it starts but I can guarantee you of course because otherwise I would be would be illegitimate what I've been saying that all this agrees exactly with every phenomenon that everybody has ever observed with light every detailed phenomenon so I'm just going to start with the simplest possible ones that are common all right we start with a mirror we start with the problem of determining how light is reflected from a mirror and we have a here a source of light and here the photoelectric cell which is I mean the pH uh multiplier that's going to measure very low intensity light we have one Photon at a time go here through here and we would like to know what the chance is that this thing gives a count it's also possible if the light goes straight across to avoid that we put a black box in here so we have to think and we would expect that what we'd have is that the light would reflect from the mirror like so and there that's what we usually say and that all you need is this piece in the mirror here this got nothing to do with the price of cheese under these C cumstances right and then in fact the place where it reflects is where the angles are equal that might be obvious to you because it's so Dar symmetrical but if I put this thing further down you can still prove the angles are equal and I'll show why it is by this rule yes sir as follows rule probability that thing occurs is a square of an amplitude amplitude is the sum of the amplitude for every way that the thing can happen in that experiment there were two ways it could happen in this experiment there's virtually an infinite number of ways it can happen to make it easier to understand suppose that this mirror surface was temporarily divided into little squares it's best if the Mind forgets for a while that there's another dimension to this mirror this way this is a cross-section of the mirror and just for the hell of it I can forget that but we can do it the other way too now what happens is that there's several ways in which the photon could have gone to the photo multiplier could have come down to this part of the mirror and bounced off and went to here you're crazy the angle ain't equal I'm not crazy that's what happened another possibility is it could come here and go or it could come here and go or it could come where you'd like it to come and go and it can go over here and go and so on and so on and these are all possibilities and the idea is that there's a certain amplitude that it does it this way an amplitude that it does it that way and so on and now we have to figure out the total probability that it does it at all naturally instinctively you're going to you know I'm going to tell you the rule that the amplitude is biggest for the one where the angles are equal no no the amplitudes are there're slight variations which we not going to worry about them it's almost the same for this one as for that one let us take it easy we make approximations here to make it easy to do and I'm not want to absolutely exactly mathematic I just want to explain the idea I'm going to suppose it's exact the same amplitude for every one of these things but the timing is different that is let's suppose that the rule of that the chance that you get reflect the amplitude to be reflected in a in a little square here there's some little arrow very small I thought but because it I have to count the total time to go from here to here to here this Arrow the contribution of this one gets rotated Z depends upon this time and the one that go from here to here is also rotated but not by the same amount because I think you can almost see that the distance from here to here is certainly not the same as the total distance from there there there's a time it would take you don't it's not obvious all right then let's take a place way over here the time it would take to go over here and then go rushing off to here is certainly longer than it would take to go the easy way in fact if you were in a hurry and you had to run over to this wall and run back you'd know more or less that the best way to do is is somewhere in the middle there and it isn't a good idea to run to the wall here and then have to so what we're going to do here is to figure this out by a series of drawings to help us calculate the second drawing underneath here is a kind of a graph right let's see if I can do this with Colors by some I don't know how to do it with colors I didn't figure it out ahead of time this is a graph in which I measure this way yeah let's do it this way the time that it would take to go from here to the mirror and over here and I'm plotting it this way directly under the place where I wanted to go in the mirror you see now the time it takes to go here we just found out was pretty large and getting going down more or less as we got near the center and of course it's a kind of a symmetric curve and it goes up here what do I mean by this is this this at this let's make it very different if you're going to reflect from this point here this particular roote then this is the amount of time this height is a graph of the amount of time there a lot of time if on the other hand colors color if on the other hand you were to go somewhere near the middle and come down this way and go so then the time it would take is less and it's plotted on this scale as this height from here to here you don't have to worry about the plot if you understand the idea the time is Big comes down and goes back up again that's all depending on where you are and now what does that mean for our arrows it means this that the contribution from this one corresponds to an arrow like this a little baby Arrow baby because I make these things very tiny in the end uh I told you in the last lecture that we have learned that students take four years of undergraduate work plus four years of graduate work to learn how to add these arrows cleverly and quickly and we'll just do some simple examples so I tell you what we we'll have to just work it out ourselves for one or two examples but that's all they learns how to add the arrow now this what you do here is you take this arrow and you turn it around a lot a lot that's I call a lot from here to here and you come out with the arrow in some direction because it's spun around and spun around at so much time now in the next Point here which I didn't draw in a color but just let's talk about is less time it doesn't turn around as much it's more like that okay the next one is less time it doesn't turn around as much I should be coming toward the green one in case and this time it's not well let's say let's say this one's around here and this one you see what I want to point out that well I didn't do it too well but the change is less each time as I go along that this one is I don't mean it that it's an accident that it comes out nearly horizontal I don't care where it came out but unfortunately it's nearly horizontal let's say that the next one is hardly any change from it and corresponds perhaps to that direction there's no meaning to the absolute fact that it happened to come out that way but it's important to point out that as I go on to the other side the timing is increasing again and so the contribution the arrow I would have to draw to correspond to the contribution from this would be again slightly inclined as I went further over the inclination would increase again further and further if I do it very carefully like we should have at corresponding places out this side the same kind of arrows as on this side in other words the contribution that's made according to this Dopey rule that to get the total amplitude that the thing arrives over there square is the probability we have the head an amplitude for each route and each amplitude is the same except that turn to different degrees depending on the time and now I have to add all these things together of course it goes on and on on both sides of the mirror way out and it's hard to get started because they're way over here but let me just start over here or further back what happens is I'm going to put the arrows on each other's tail this one represents the first one here and now this one comes you see I put the arrows on each other's tail and then the next one it isn't working out too it's hard to make the drawing clear but maybe you'll believe me when I tell you what happens if you do it very carefully and then it comes an arrow this way and then the green one which is hardly any difference in Direction and then the next pink one that is just tilted up there a little bit again and then tilt it up some more and then tilt it up some more and then tilt it way back and now let's for the fun of it keep on going but what'll happen if the things get turned more and more and turned more and more so the next one's this way and the next one's this way and the next one's this way and next one's this way and next one's this way okay Bo and in the same way the stuff that I hadn't drawn yet over there correspond to an arrow tilted still further cockey and still further cockeyed and so on all knotted up and low thank now that from one edge of the mirror which is the last the 74th Arrow over there that I to the the other edge of the mirror which is a seven minion actually Arrow because this a usually with a reasonably sized mirror since these angles in Vol turns involve millions of an inch there are millions of turns so that this got down to really down in the middle here and it goes to the middle here and so that the total amplitude which is the sum of all these arrows added together of which last time I added two I now add three no I add five no I add millions of them I get a line for the net result of the whole the total amplitude to arrive which is this tremendous line from here to here at the result of all those little arrows okay now let's investigate what determines how long that line is that the size of that square determines the probability now we notice a number of things first that the edges of the mirror are not important that were I to have chopped a piece of the mirror off over here a piece that you intuition know I was wasting my time ping around with it wouldn't make any difference because that part in there the arrows are going I throw it all away I know understand it doesn't make any difference because so I start a little bit off here shade it doesn't hardly make any difference therefore I can really chop this mirror down a bit where is the part of the mirror that makes the real difference that makes this get a real length that makes it likely to be big it's the place where the arrows are all pointing nearly in the same direction for a while think a while it means it's the place where the curve stops changing for a while and after much mental effort you'll discover that's always the place where the time is least or possibly of the way sometimes most most often in practice it's least but it can happen most anytime the time curve stops changing it's a place where the time is least and so it turns out that the raid that's most important the thing that determines the probability is the part of the physical world which is close to the place where the time is least and that's why you don't have to worry about the other part of the mirror and that's why crudely speaking you say a hell with the rest of the mirror I can just use a little piece you're wrong if the piece gets too short if it gets too short you don't get much of these you get a few of them and not enough you get different answers but that's a few maybe thousands of an inch and you're not used to experiments with thousands of an inch mirrors although in the laboratory we have many such experiments and I would am strongly tempted to tell you what happens with such things and so on but that's not everybody's experience and so I have to stop myself somewhere and so I stop here I say what I've done is I pointed out that only part that really counts and give you the answer there is what happens in the center of the mirror that the other parts canel themselves out in their effects they're just as strong there's just as big an arrow from here as there was from here but just move a little shade over and there's another big one trying to undo it because it's twisted and uh in the Middle where the time is least the arrows for a while point in the same direction that's why in the proximation we say you can get away with a crude picture of the World by saying the light just comes to the middle part where the time is least and it's mathematically easy to prove that in any circumstance when the time is least it turns out it means those angles are equal and I again have attempted to prove that but I won't bother you in straining your geometric imagination now it perhaps bothers you a little bit to have to say that the reflection that all this is happening that there's Reflections from all this part of the mirror when all it does is cancel out and so uh let's discuss this a little bit Let's do an experiment to find out how much light is reflected under similar circumstances and I guess uh since I have one more color and I don't want to erase everything I've got there let us just imagine for definiteness that uh only this well here let's say this piece of the mirror I just used a piece of mirror it's so big no bigger I just use a little piece it's a big piece it's in the wrong place and I expect to see the light reflected from here to there not very likely H but this Dopey physics says that yes you have to calculate all the arrows from all this stuff from here to here and they're all changing it corresponds to the arrows up to there from the beginning so it's just a bunch of arrows go this for a while and I stop okay you know that line means these arrows are not in the picture anymore because that part of the mirror isn't there and so you see that the distance from where I started to where I finished is very small not zero but very small and it's true uh experimentally with a finite piece of mirror you get a tiny amount of light reflected in an odd manner it's called the fraction from the edges but I don't want to go into that it's very tiny so let's say it's zero this idea that the whole thing can be there and doing nothing seems like a kind of a waste of time and a mathematicians thing only it's not real physics to have something that's not doing anything but watch this they going to prove that it's right by the following dirty trick I perhaps should uh expand this side a little I'm getting pushed off the side of the the board there by uh the way I've drawn it this is the way the time was going and the arrows were pointing in a sequence of directions which were very different from one another and now I'm going to to do a more fine calculation which I cut it even finer and you would find if it's fine enough that I haven't got much difference in time but I find a bunch of arrows essentially going around in a circle very close to a circle getting nowhere going around and around in a circle because some of them are pointing forward and some of them are pointing backward virtually continuous but for some contribution this way and some contribute that way now let's have some fun let's see if it's really true what we're going to do is we're going to make the mirror less effective by painting it black in the right place we are going to paint the mirror black in just those places in which the arrows are pointing the wrong way for arrows if it turns out that the timing is such that the arrow points this way don't use that part paint that part of the miror a black don't use it make it not reflect I don't painted the wrong curve I should have painted my drawing is unfortunately way over here the idea is if if the arrow is this way I take it but any time the arrow comes out that way if that's the time between here and here then I paint that part of the mirror black so that those arrows don't operate in other words in order to test this idea that everything's canceling out I take the parts of the mirror which the for which the timing is just right to make arrows that point this way or more or less that way or at least have a bias in that direction and the parts of the mirror that were contributing arrows whose bias was in this direction I paint out or if you don't like this idea of painting out and they have enough patients you simply cut the silver away there there's nothing the light goes through worse it can't reflect it didn't reflect before you got less mirror it's going to reflect less no it reflects perfectly well because according to this picture if I add a sequence of arrows which are turning rapidly and then as soon as they're supposed to come oh here's the circle here it is down here excuse me excuse me and it's also in yellow I add the arrows this way they're going along all right and as soon as they start to turn back I don't let it go I don't a it anymore I I've cut the silver away and now it gets around and starts to go in the forward direction again so I let them come I don't paint that silver away until it starts to back up and then I paint the silver away I get it out and what I end up of course a lot of little strips of silver separated by clear glass and each time the thing does thiso yeah over this whole distance and wow what a net Arrow I've got for the final result lots of light and so it's possible to take an ordinary mirror flat and cut away strips correctly in the right places Just Right strip after strip very fine it turns out thousandth of an inch so that when you shine light down on it this way it bounces it off that way this thing would only work with one color if I've designed this very this called a grading it's a line of lines and it works like a charm it's beautiful if I use red light and I've got that thing exactly right it'll go right if I use blue light it won't work what I have forgotten to tell you in the beginning and I don't know whether I said it last time cuz this is what happens with red light with blue light you get the same result except the thicknesses are shorter all the timing is quicker and what the rule is for blue light is the same as it is for red light except the speed at which you turn that for time is faster you turn it more now you'll notice that the place that we put those cuts was especially designed just for this rate of turning if it turned a little more because it's blue and I had the cuts in the same place as I made for my theoretical red one it turns out it all gets kinked up and it doesn't work very well but as a matter of accident it happens to be solved that if I make two changes first I use blue light and then I put the photo multiply at a somewhat different angle in fact less angle it works again with the same line that I use for red it's an accident I cut it carefully for red put that pH photo multiplier over there it also happens luckily that if I'm change the color it doesn't work but if I move the photo multiply and change the color it's cut again about the same place it comes out just geometry and therefore what happens is actually that if you shine light down here blue light will come over here and red light will come over there and it's a beautiful thing to see if you take this thing and turn it when the light is fixed you'll see colors red and blue I don't know whether it's come down in New Zealand or must have we have them in the United States now on automobiles people have these wonderful colored signs that you wonder where the colors come from they're so bright and as the car moves it changes from red to green to blue and all they are is mirrors with lots of lines on them instead of so they're not reflecting in a normal manner all right so that is shows really that we cannot get rid of the area which gives zero that it really is canceling out and we do torturous and clever things to it we can demonstrate the reality of the reflections from this part of the mirror and produce some striking Optical phenomena depend on how much of your experience is whether this appealed to you or not if you knew about gradings or you didn't that's the problem with this lecture I can go on like this explaining Holograms and lasers and everything else easy except you don't know anything about them there's no use but never mind I try something else this time I'm going to talk about light going from air to water we would like to put the photo multiplier under water we suppos the experiment they're going to arrange that this is water maybe it's easier to put the source under water and here's the source of light that we would like to know photons have a small number of photons want to know if they're going to get there and we have again the same situation that the light can go this way to the water surface and then that way to the photo multiplier we go this way to the water surface and that way the multiplier and it can go all possible different possible angles and every one of them contributes an amplitude and it makes a bunch of arrows at all different kinds of angles and what's going to be the result same picture as we made up there the only part that really gives a result is when the time is changing slowly in other words it's a minimum or a maximum minimum now in this particular case in water I didn't tell you about this but in water when you're find ing the amplitude the rate at which the thing goes around in water is slower than in air or better maybe it's a better way excuse me better I made an error what I said was wrong light travels slower in water than it does in air so that the time in when you calculate for a length in water is not the same as in air because the light go slower so that these lengths are more important so to speak than in here what you need to do to find out what's the most important important of these pads remember as was before in the case of the mirror many of them all canel out and didn't make any difference but there were some that were important when the arrows were always the same when the time was minimum so what we have to do is we have to figure out to go in here and to come down here where the time is minimum the idea is suppose that you could you had you were really in water and you went in a boat you could only go slowly and then you can run quickly on land but the beautiful girl is drowning here and you're the life God and you can swim slower in water than you can run on land where do you uh hit the water you rush this way to the water and swim like hell actually there is a place that's a minimum which it would be foolish of a life guard to analiz and calculate under the circumstances but the fact is there is a computable position at which the time is minimum and it's some kind of a thing that looks like that the idea is it is not the straight line because the line has too much water in it so to speak water path and by moving for less water path and more land path one makes a compromise and comes out so and that is the reason why light is bent into water and as a matter of fact if you follow this thing all the way through you can prove that the ratio of the signs of the angles of the this and that is the ratio of the speeds in the air and the water but the reason it's a minimum time is the same reason as it was for a mirror okay in the same way we can understand why life goes in a straight line line it's us if we had a source here and a photo multiplier here there are many ways the light could go we could say the photon can go from here to here certain amount of time fa that's the way I've been doing it before anyway but I'm going to be more accurate this time and tell you that the story that I said it went in straight line before in calculating things was only an approximation if I didn't do that I get the same answer as I if I do the following I say not only does it go in a straight line it could also go this way to here it could go this way it really really they can really do yes it can go only way it wants but almost always the contributions from these different ways cancel out with each other completely because there's a nearby way they got the arrow the other way but if you can find a way where if you change the pads a little bit nearby pads don't make any difference to the time then you've got the place where most of the contributions comeing from and uh the story is as follows that if you have a path like this a nearby path can be made that's shorter that is has a different time distinctly shorter a lot shorter by moving it in and so you can get a very different time but that the minimum time comes for the path that's a straight line and so the most important contribution is from the straight line remember that in the case of the mirror I I say the most important part of the contribution is near the place that is the minimum it isn't exactly that one arrow that does it no it's the contribution of a quite a range and so it turns out that a light does not really go in a straight line but it smells the neighboring lines and it uses the area around it just like a section of mirror is necessary to get the full reflection a section of space is necessary if you were to put blocks in here so as to not allow the pair to wander too far away and made these very tight so that was try to go in a straight line you would discover that the light from this soil if you put the photo multiplier here for instance and didn't have these blocks now if you put these blocks in like this and had the photo multiplier here let's say the blocks are pretty far apart and put the multiply in such a way that that line is not allowed that corresponds to using the piece of the mirror that's in wrong place but if this thing squeezes Tighter and Tighter after a while light begins to come here reason it comes is that you've only got a few of the arrows it's just as if you used to I didn't show you in this case the same idea if you did have the mirror in the wrong place but used the very short mirror then there's not enough range for the arrows to cancel each other just a few that go one way and it stops and so what happens is that there's a little if you cut this very far L the light spreads that is it doesn't go in a straight line and if you try therefore to squeeze light into a small hole to make sure it's going in a straight line you discover that no longer goes in the straight line This is a few examples of how uh the theory of uh thing has worked out uh let me just do one or two one more which is interesting instead of dealing with all the the net result of adding all these the in space of adding all these different possible pads is in fact turns out to be the same as if you just took this one PAAD very closely is for approx well essentially that uh if uh I mean by that that's just another factor with the angles are the same if uh we think about this in a special case let's draw an artificial line here that that means nothing it's just the G like the equator of the earth it's just the line and then consider paths which are straight in 2 second and ask what about light going this way this way and this way this so we don't have too many different paths to add we restrict them to be double straight line section then by exactly the answer is exactly the same as for the case of the mirror the time to go this way is a big time and this changes and changes and it changes rapidly and if I plot it this way the time for these different things this is a long one that's a short one that's a long one this time you can figure the time immediately in your head cuz the time is just the length of that line and you can see that that's long and that that's short now let's have some a different kind of a game let's do something to make this one longer so it's the same as that one let's fool the light so that all the pairs all the pads are the same length of time how can we I told you it went slower in glass than in air so let's put a piece of glass in here to slow it up so it's to take a little longer let's say we're not going to do anything to the path out here that's going to be the key time that we're going to make everything equal to now the one that would go through here straight would have got there too fast we slow it up for a while and by slowing it up we bring it so that the time it takes is the same now there was a path that went like this and then had a time so it's all also too short not as much as the other one we have to make it take a little longer so we have to put a piece of glass in here this glass is not as thick as this one because we don't have so much to offset the nearer we get to the top the less we have to use glass to slow it up and the very last one needs no glass at all you put all these funny pieces of glass in there the net result of course is that you're putting in a piece of glass shaped like so the result of that is at the time now with the glass in by careful design and the exactly right shape and right thickness you just found out how to calculate the thickness exactly just put the right thickness in to compensate the time you will find that the times now are all the same no matter which path it is of these straight line typ what happens then now each one of them contributes its amplitude yes amplitude same time same whatever the angle of one of them is the next one's the same next one's the same I straightened out the arrows I what a dirty trick stra down here and there's a lot of arrows there's millions of arrows and so the result of this is that I get for the final result from the front to the tail it's sensationally large unexpectedly enormous Arrow a high probability of going of course you know what I'm describing a focusing lens if you have a source of light here and it just sends light to here it's kind of weak because it spreads but if you put a lens here it'll concentrate it right away again back to here and that means concentrated light means high intensity and really high intensity mean lots of photons or if the light was weak the chance of a photon AR rting is very strong at this particular point and very small everywhere else and so by the trick of arranging things so the times are equal we focus life and so by this I use these examples to show you how what looks at first like an absurd rule with no causality and nothing like anything real produces effects that you're more used to it also produces other effects which you may not have been used to such as the grading and the number of other things and so this this is uh the success of this point of view and it continues to be successful I would summarize it by saying what we know so far is that the probability is equal to the square of an amplitude then they need a calculus of the amplitude and amplitude for an event that can happen in several different ways in different ways I should have written this in the beginning is the sun of an amplitude for each way now I have uh the rest of the that should be really all that is is really necessary to understand but in in order to get a full flavor of the theory I would like to tell you a little bit more about how people calculate these amplitudes and uh a little bit more about the law for the amplitude for example I kept bringing in funny things like uh from when you have a reflection you have a little arrow when it's from the other surface you make the arrow backward uh when you go through glass you have to use a faster timing and so forth all right all these things should have to be explained and they will be not this however the particular feature that I can describe a little better a few things of how we analyze the amplitude a particular problem to show you the type of thing is this suppose you had a surface here and that we have a reflection suppose this was a 4% surface so that the amplitude the intensity that came out here was 125 or that for that surface the amplitude of reflection is a fifth now that and I put the photo cell here well you could put a double CC why I have it already drawn I'll draw it again I have a double surface and the source and the reflections and all this stuff and I computed the amplitude for the light to arrive here now I'm going to try another thing instead of putting the photo multiplier there I make a little hole I'll let the light keep going and I let it bounce through a couple of other surfaces three surfaces whatever it is all right and come out over here and put the photo multiplier there how do I figure out what happens what the amplitude is now this amplitude in this particular thing can be thought of in as so to speak two problems one if light starts here what's the amplitude to get here the second another problem that's interesting is if I put the source here directly what would have the amplitude to have been got there been it turns out from you know those two things you can figure out this combined problem Problem by an operation you could call the rule for successive amplitudes rule goes like this let us suppose that this section here if you don't understand this too well doesn't make you get some I'm trying to give you some flavor the flavor tastes B just relax now here some people like ginger snaps and somebody don't let's say if this problem we've already worked out the amplitude for all the possibilities added together to arrive here let's call this point a this point B and this point C so we have if or the amplitude to be to get to B from a that is a source a of unit strength one Photon has an amplitude to get the beat that's been worked out let's suppose we start out this is the source strength one unit we begin and what do we get out is the result being the amplitude comes out some crazy Arrow so let's say that that thing is this Arrow that's the amplitude that get to from B to a with this Source what is this thing it's 1/5 is long let's say it was one surfaces 1/5th is long and a certain timing let's suppose this surface over here ends up as a 4% uh 116th reflector or 9 9 11% and one nth reflect makes it easy for me the length of this thing is a fifth you see so that the thing will be 25 125th and you have to turn it through an angle now this next one if it would worked all by itself if the amplitude to get to C from b along is this if at B there was a unit amplitude if at B it really was one then there's a certain time delay and the reflection there's some time delay corresponding to some angle and there's a length of 1/3 this have to do with the time delay the time delay I mean from B to C now what would the result be why do I say a third because the area of the square would be 1 nth which is how I said the reflection should be now what will be the amplitude to go to go get to C from B from a all the way it is hard to guess first of all the total time means that the angle whatever it is you go around and around and around the sum of the amount you went around for the first part plus the second part because the total time is the sum of the two times so that you're going to draw something whose angle is the sum of this one and this one it would have turned around while it was going to bead it goes around around around around it goes to B and it goes around around around around some more and that's how much more so the net result is an nrow sum like this at an angle which is the sum of that angle and this one you turn this and then you turn it that much more and you come to here here's where we start with the one and here's what we're coming out with and how long should it be well the chance that it gets of all the light that comes down here 125th is reflected here and of all the light photons that come here only one nth is reflected there so it turns out that that means that the to of a of the light let's say I had a th000 uh I have bad numbers I should have taken better numbers what what you have when you finish is 125th * 1 nth of the light one over 225 Parts out of 225 photons about on the average 125th or nine photons get through here and of those one those here so one out of 225 come out which is by the way 115 * 115 15 so therefore this size of this is 115 now the 115th can be that this this composition this the rule of composition add the Angles and multiply the lengths so you have two events in succession you combine them by this rule of composition that you addir the Angles and multiply the length putting an arrow on the tail of another arrow to find a final Arrow we call adding the amplitudes composing them this way multiplying their lengths and adding the angles we call multiplying the amplitudes the reason we call it multiply it's interesting therefore that arrows can be added can be combined by two operations putting them on each other's tail and multiply them together like this which we have called adding and multiplying and the reason we call it adding and multiplying is it obeys all the right rules of arithmetic for addition and multiplication all of the rules such as well I don't remember the rules a * B is the same as B * a for instance A and B are these arrows combining it this way and meaning by times this composition rule then it continues to be right now the rules of algebra are things that are studied by mathematicians and mathematicians have tried to find all the combin all the objects that you can possibly find which obey those rules the rules were originally made for Counting Apples it was improved by using negative numbers it was improved still further by inventing fractions it's still true you can add and multiply fractions you can use unending decimals to represent numbers and add them and multiply we have today become very sophisticated in the early days when mathematics was first developing and it was said that a number is something like when you count the number of apples or people or something like that then the whole idea of a half a person was a a problem but today there's no difficulty at all and nobody has any moral or discomforting G wor y feelings when they hear that there are 3.2 people per square mile in certain regions it doesn't bother them they don't try to imagine the0 2 people but what they do is they know what they mean that if they multiply that by five it gets to be 16 and so forth and so some things that can satisfy the rules of arithmetic can be interesting to mathematicians even though they're not represented by numbers of apples absolutely and without having a picture exactly what it is and these arrows on a plane which can be combined by two operations tying them on each other's tail and combining them by this multiplying and adding angle business those two rules adding and multiplying obey the same rules as uh algebra and these amplitudes are in fact called some kind of numbers by mathematicians and to distinguish them from ordinary numbers they call them complex numbers makes it hard in other words so so if for those who have studied four years of University or enough algebra to have come to comp complex numbers I could have said all this by simply saying amplitude the probability is a square of a comple absolute square of a complex number the amplitude is a complex number I mean and the probability is a square and that when the thing can happen in more than one way you add the complex numbers and when it happens in succession you multiply the complex numbers and have I said any more than I did before no it's just a different language it may be sound better and the only reason I use that different language is because some few of you have may have heard of that language and it would be nice to make sure I just wanted to make sure to you that it was U really the same thing for those who have never heard of it before the idea that that is multiplication may be disturbing and I think I waste a little time on the side and nothing to do with well I think I waste time I'm late so I shouldn't waste time I wanted to explain why it's reasonable I can't [Music] resist I want to explain why that is a a reasonable way to Define multiplication this is a stupid has nothing to do with a lecture I call it a multiplication that's enough but I have to play anyway what is a multiplication and the Greeks use num wanted to use numbers that were not necessarily integers and they did it by talking about line if this is a unit then the line This length represented the number one whereas a number like two would be represented by a line which would be twice as long that way you can represent fractions and so forth the third is long 2 and 1/2 times long so forth so here's one two is a relationship of this line to that now three you might get is the relationship of this line to that right I have to write the unit in order to understand what this number is I have to tell you how big one is and what's six the product of two and three it's a line also it's a the line it sticks way out and it's like so we' got six notches out six notches and the way of looking at it is to say that the problem is this I want to convert three to six I want to multiply by two the idea is that the three line that I had before Bears the same relationship to the answer that I'm trying to get the six line as the two bears to the one six is twice three in the sense that this relative to that is the same as the two to one right the idea is then that the answer should bear of multiplication should bear the same relationship to one of the things you're try to multiply as the other thing does to the unit voila let's see I want to multiply this by that and what I have to do then is to create a line which Bears the same relationship to this line as this one does to that yes I have to just like I did over there I have to find a new this answer has to have the same relationship to this line as this has to that now let us draw the answer that I draw over here over here so you can see its relationship to that line what's the relation of this and this the relation of this and this is a certain proportion in size and a certain angle can you imagine that thing turned so it's in this and you see that it's the same angle and the same proportion as the original one this to one in other words relation of this line to that is the same geometrically and so that's why it's multipli because it has the same geometrical property a property though that fits on lines which are tilted not just lines which are horizontal it's interesting the mathema mathematicians developed all this mathematics for these crazy numbers without having anything to apply it to directly in physics and that it should turn out to be so fundamental to the bottom laws of physics to be using such funny numbers or complex numbers so that's the other feature and I'll just uh uh say one more thing to finish this that means that we can understand what happens in a given situation by a sequence of as if it's a sequence of events instead of see when I was talking before I would say the thing comes from the source and goes to the to the photo multiplier and I gave you the answer for one operation you turned it and you made a little line but I can talk about it in several operations I can say it goes from here to here to start with an arrow when it goes from one point to the other just turn it around according to the time reflection reflection is a little 1/ hour multiply by that that means shrink it down next go from here to here that means take the result and do again the same next thing which is rotate now finally I would like to say what I'm going about to say is to show you that we have still simpler laws than the ones that I talked about we have been talking only about one color light and talked about the amp depending on the time in that fashion what is the difference between one color light and another color light the speed at which they goes around but in space light is light is light is light and doesn't know where it came from and what another pictures different pictures did that light if you want like they know the amplitude that it arrives at a at a certain time I'm going to put time into this argument now it arrives at a certain time in a photo multiplier we suppos well I I think since I haven't figured out I'm sorry this is very uh immature isn't me I haven't figured out what I'm going to talk about completely next lecture and I haven't got quite enough stuff to fill it up and therefore I'm going to leave leave this little thing the next lecture so I can fill it [Applause] up I will tell you what the idea is that the time has to do with the uh well I'll discuss that next time there's other the other thing is I have tried and I in the case of monochromatic light I have completely described the rules for the amplitude if I add one more thing which I haven't that is I have to talk about what happens in a vacuum first and when a particle go light goes a certain distance it's true that the angle turns but there's another rule which I have not discussed because it's not very interesting relatively and that is that the amplitude to go a certain distance beside turning shrinks if you go far it gets smaller everybody knows that the chance of finding a particle far away from the source goes down as a square of the distance and that means that the amplitude goes down as the distance in other words if you when I was drawing these arrows as I made them go further I should have shortened them a little bit those are kind of approximations have nothing to do with the excitement of how it works and I didn't want to bother you with such accurate detail but if I once tell you that the thing turns at a certain rate and goes down in length proportional to the distance that it went I have completely defined exactly the properties of the propagation of light of one color except for one other technical thing light as it turns out it turns even if you specify the color I have to say this in order to tell you exactly you know how much you know and how much I haven't mentioned if you even if you specify the color of the light there's one other feature that light can have there are two kinds of photons of the same color we say they're polarized uh if you use Polaroid for example you let through a light that has only one kind of axis and another piece of Polaroid lets through the same kind of photon but if you set that other piece of Polaroid for its axis the other way so that it'll pass light with the other kind then no light will get through with the first one only passes one kind in the second na all these effects of Polaroid and polarization have been entirely left out of this discussion why because my purpose is to give you a complete feeling of the difficulty of the subject of the confus the interesting philosophical problems about probability the succession of amplitudes how little we really understand and so on and the fact that there's two different kinds of photons is not qualitatively different it just means a little bit more calculation but at the same style it doesn't change the style of the analysis and therefore in spite of the fact that I've left out a number of things such as how the amplitude changes with distance and the fact that there's polarization makes my lecture incomplete in the sense that I therefore have not given you the exact law for the propagation of light not quite but damn close so close that it contains all the Mysteries all the peculiarities and so forth in a perfectly satisfactory way and I hope then that you're satisfied and you're confident that I haven't left any essential difficulty out the things I've left out are not difficult they take just another lecture of technical points rather than any new difficulty one thing though I must say and that is this we've been talking about light going through a vacuum and then I had a rule about it's reflected by a certain amount when it goes it has a certain shrinkage when it comes off a surface when it goes through a medium it gets slowed up and so on these it turns out are not really the properties of light it have to do with the properties of matter you can't get reflection without having a piece of glass it doesn't go slower unless it's in the glass it really as it turns out is not going slower It's Curious and we're going to find out exactly what it does in order to explain it we have to know what the electrons in the glass are doing and how they interact with the light and I'll summarize the most wonderful fact is that light never does anything really when you get down to it except to go in a vacuum from one place to the other it's emitted by one atom or particle and absorbed by another and it never goes and gets slowed down or gets reflected what reflection really is is a light goes down it's absorbed by something which shakes it and that emits a new light which comes back reflected light is really not the same Photon coming back as went in the photon from The Source went into the glass and from the glass comes out a new Photon this is a interesting thing that makes light in the end simpler and simpler and simpler and what I was trying to get to in the last steps was to show how ultimately simple it is when it's only in a vacuum and the complications of funny laws for reflection and funny laws for going through glass are really the result of the interaction of light and electrons and that's why this subject of discussing physics can't go on any further until I want to discuss matter and the next lecture will be about matter all right thank you I put together a theory about photons and electrons and I took it to my physics teacher who said it's not right now since he didn't describe the theory with great detail I cannot answer but I will say something that I forgot to say in the lecture one has the advantage of uh of uh using questions to finish the lecture I really had I didn't this is a I must emphasize something that is a very great danger of talking about what happens in an experiment with one Photon because after a while you get the idea that these arrows are somehow associated with a single Photon it's a mistake and I should have not permitted that mistake to be generated by mentioning as early as possible that it's not right and that what of is these amplitudes are not the amplitude of find a photon riding around somewhere but the amplitude that an event occurs and I give an example why your professor probably said no by giving you a problem so to speak of the kind that we answer with these amplitudes which is of a different style than the ones I've been mentioning and requires more thought and I would just at least and then as I say I don't know exactly what your theory is and maybe it's okay to satisfy this example but nevertheless let me know next time the idea is suppose that we have a problem with two photons suppose that we would like to know just to take a definite example that we have two sources of light each one been arrang to two sources A and B and it's been arrange that both A and B emit one Photon under some circumstance and you have two counters down here two photo multipliers and you would like to know what is the probability they both go off all right so the event whose probability you're Computing is the probability they both go off at the same time both admit that there's a coincidence that they both go off at the same time now this has an amplitude the amplitude for the two photons so to speak in one there's only one amplitude the amplitude that both go on and I have should have emphasized that no matter what the event no matter how many you're involved with and so on we talk about the complete event and calculate the probability of it not the probability for each Photon now in this case to compute the amplitude for a photon both pH counters to go off supposing that one Photon came from each of the sources it has to be done as follows one way it could happen would be that this a source made gave a photon that that went off and the B1 gave a photon and made the other count to go let's say this count is called X and this one's called y x went off because it received a photon from a and why went off at the same time because it simultaneously received a photon from B the net result of the is that both A and B have lost some energy and the two counters went off at the same time how do I compute that amplitude answer you compute the amplitude that a would reach X from Arrow that's the amplitude a would reach X you compute the amplitude that b would reach y another arrow actually very similar in this particular example because of the symmetry of the picture but just not relevant what is the problem of amplitude corresponding the thing that both should happen you can get a hint well what the answer is is the product of these two amplitude in the same sense that I talked about before multiply uh you're going to get an idea of why it's multiplied in this sense because of this it helps a little bit the time if there's a certain chance that this reaches here like 1/5th of them will reach here and 17th 1 nth of them will reach here then the probability that they both reach is the product and you got to get that back into the amplitudes and a clue at any rate you should multiply the amplitudes not only of things that happen in succession but things that happen independently at the same time this particular problem is especially interesting let's suppose when I multiply these two by the rules I'm talking about over there I get mult increase add the Angles and multiply the lengths I get this answer that's not the right answer for this problem incidentally and in curies because there's another way it can happen you're all sitting there saying how the hell did I know know that it wasn't a that went to Y and B that went to X well if I say that this was remember this one was a to X that was B to Y now if I say a to Y that's a different Arrow why because it's a longer and therefore different time and therefore this particular Arrow has turned more and likewise bet to Y has turned more I'm not drawing them correctly because there the Symmetry there similar at any rate the net result for that case is some other arrow for the other case now what do you do when has two possibilities if a thing can happen more than one where you add the amplitudes for the two ways and the net result for this problem is to tie one of these arrows onto the other and that's the answer the length of that and now what we have is something which is all the elementary textbooks say is impossible interference between two photons or more correctly you get pluses and minuses depending on the Angles strengthenings and weakenings depending depending on the positions of these two counters relative to each other this is used as a matter of fact and was invented I think locally perhaps not in New Zealand but at least in Australia uh to detect the diameter of uh Stellar objects quazar and things like that by looking for radio WS received them two receivers and looking for correlations of strength which just means a coincidence of photon it's called the brown twist effect but it's a perfectly definite effect that's understandable and computable this way most people's theories who have a theory about waves associated with Photon will not have a theory which is capable of dealing with situations where there's more than one Photon I do not know that your theory is incapable I only suggest that as an interesting problem how old is this theory of quantum electrodynamics present complete form is from 1947 uh 8 or 789 78 therefore it's uh 30 years old that's what the subject of these lectures is as you see the reason it's so difficult to filter down is that the resistance of your mind to such models people who hear that all I'm going to do is make a couple of arrows on a board to calculate the chance of something happens says this guy doesn't know physics but this is the guy who knows that that's what you have to do and admits therefore that he doesn't know why he's doing what he does and you can have the confidence that when I say I don't know what I'm doing that probably nobody else does [Music] either in what way is your theory different from wave mechanics question is whether this how is this related to wave mechanics now there's the reason I hesitate is there was a thing called wave mechanics which is the Quantum Theory uh of wave wave theory and there's also another sense in which we might be using the word the mechanics of Waves by that meaning water waves or sound waves or something like that there's a special Theory called wave mechanics which is discovered and developed in 1926 which was is just another name for quantum mechanics and that question there was two things first there was an equation for these waves these matter waves made by Shing and then there was an interpretation of these equations by Max Bourne within the year which was that the function that we're talking about is a complex number whose square is a probability I am saying no more than that at all that's exactly it the only thing I can add that for the 20 years after is merely a refinement or an improvement in discovering exactly how to calculate the wave amplitudes or these numbers these these Arrow amplitudes uh for Photon phenomena and electrical phenomena high energy and so on the complete formulas for Quantum electrodynamics took 20 years to get straightened out exactly and that was why I said 1949 but 99% well 97% of the uh thing was worked out in 1929 and the interpretational scheme about probability amplitudes and that you squar them to get probabilities which is so strange is the resolution shall we say or a description a precise description of what was for a while a confused wave particle duality you might say but you still have a sort of a wave in the sense of something turning or oscillating and the particle somehow in the sense of the particle going so it's still a duality but the words wave particle duality is a description of a c of a condition of the mind of physicist before 1926 in which it was best described as saying it looks exactly like a wave but that's on Thursday and it looks exactly like a particle but that's on Tuesdays but the answer is it doesn't not look exactly like an ordinary particle bullet with normal probabilities and it does not look exactly like ordinary waves because it ends up that you measure it in particles and how to put that got together answer is the way it looks then in your own mind do you think you have resolved this peculiar Duality not at all I have removed I haven't done anything but the the the wave particle duali represented a state of confusion it was a word for a that there was a wave particle duality was a phrase used to describe a state of confusion as to exactly what law to use to figure out what happened in each circumstance also a confusion of model whether it's w or particle this thing that finally weigh out in 19 worked out by born 1926 was to it still got dual aspects of wave and particle but it's precise in telling what to do and to predict the circumstances in any experiment and there's an agreement with Nature's with EXP experiment and so it it's a resolution of the confusion but it's not a resolution in the sense of producing a model which is uh clear physical in the oldfashioned sense of wagees or particles other clicks from a photo multiplier caused by the photo multiplier and in no way related to light the question is when a photo multiplier makes clicks is it the toal multiplier itself that's making the clicks or is it light and the answer is it's light in the sense and ins so far as it's actually quite true that photo multipliers make clicks all by themselves in circumstances in which we've done everything we can to make it as dark as possible in other words it's dark and there is no light various things in this this speak because is so extremely sensitive and one can do things to the photo multiplier to improve it such as cooling the seasum surfaces so they don't emit spontaneous electrons and so on until we get an instrument the idealize photo multiply which is better and better in the sense that it has less and less counting in the dark but whether it has counting in the dark or not when you change the circumstances that in normal Parlin in ordinary language we'd say light is coming in in the sense that the Sun was shining but we put a whole lot of black paper around it and we got a lowest count make a hole in the paper and all of a sudden the counts go up in all those circumstances in which we would expect in ordinary language to say light is going in and in all those circumstances the counts on the photo multiplier are increased and the increase is by an amount that depends upon how much light is Led in the increase if you improve the photo multiplier so the dark current is much less you get the same number of excess counts due to making holes in the black paper because the circum cumstances in which the photo multiplier increases its count are those which are commonly associated with circumstance in which the common English use of the word light is used we use the same word and say when you have a situation that you would say light's going in I'll guarantee you the photo multiplier will go off is light then wav like oh it's discreet that always works discreetly ah yes discreet because no other instrument has ever been designed or can be designed if people have tried and they've argued about it and discussed it whether I build a photo multiplier or any other instrument for the detection of light of low intensity it always ultimately behaves in this pulse-like manner I only use one example but every instrument that detects light at sufficiently low intensity always ends up discovering that light comes in these lumps also the behavior of light in many other circumstances like in Black uh in hot regions and then so on Clank discovered that he could not understand the many of the properties of the distribution of light from furnaces and so forth and other technical situations unless the energy of the light could not come in arbitrary amounts small amounts like the wave theory expected but had to come in definite lumps of certain amount of energy depending on the color and so it's all this uh not just a photo multiplier but all the other experimental situations and so forth which it's impossible in a in a popular lecture without four years of study to produce and to demonstrate again and again all these experiments to produce the kind of conviction which one would get from a long experience it's unfair of me to say you've got to believe me because there are all these experiments but the best I can do then is to refer you to other books and stuff where experiments are reported of all kinds which show you that that's the way it looks that's the best I can do can your theory explain the red shift or blue shift of light from Stars yes yes and that was a point that I was uh coming to uh but I'll try to because of the time I guarantee you if you promise to come next time which is next Tuesday I will contain it I had intended to put it in this lecture but I saw that was one of the things I was coming to the idea is rather relatively simple and I'll try to explain it the color of light has to do with the speed at which that amplitude turns around I never talked about how the detector would look or the photo multiplier would see if it was moving toward the source but what happens is that the time that we're talking about to get the amplitude is always shorter as it approaches the source and because of this changing timing from the motion on top of the root rting it appears as if the arrow effectively at this multiply is turning at a different rate and that is equivalent to what would have happened to the multiplier if it's standing still but the light source had a different color and therefore the behavior of an instrument which is moving toward a source is to react as though the source were standing still or the object was standing still but the color were Bluer all right it's not very clear but I perhaps make it better next time we must make a break there I'm sure Professor fan needs all the time he can to get his next [Applause] that I guess I'm not used to the kind of politeness you have in New Zealand because in America the audience is decreased these times so and not just talking to four or five people but uh I'll try to make it not so painful we've been talking about the or what we're aiming to talk about is the theory that works the best that we know the physicists like the best that deals with a part of Nature and that's Quantum electrodynamics and deals with photons and electron most of the time we've been talking about photons what we've uh discussed is it mainly the main idea of the talk is to give you some idea of the kind of framework of ideas which theoretical physics means in order to describe results of experiments and I I think by this time you'll agree after two lectures that they're very weird indeed and quite peculiar and difficult to believe but uh I'll just remind you review for one more time a little bit about what happens with photons and as we said many times two times we have a SCE here and the photo multiplier which makes counts of photons even if we have only one Photon at a time and if we have more than one way that a thing can happen and the example I've been making several times is that the light could in the photon we could imagine could be reflected from two different surfaces if there's more than one possible way that something can happen the whole structure works as this way in any situation where you have experiment looking at something microscopic which of course you have in the end to look at something microscopy that is large and the photo multiplier amplifies up when you have a system like that you can't predict exactly what will happen but only the chance that the system operate that you find something happen here and this probability is always given as a square or the of a of a thing called an amplitude uh and this amp it's a kind of absolute Square it's a special kind of it's a square of the length and the amplitude is nothing but an arrow drawn on a plane now when something can happen in more than one way the amplitude that happens is considered it's calculated by adding the amplitude for it happening one way plus the amplitude that it happens the other way and when you square that you get the probability in a problem like this we have found that the circumstances or the probability for this event might depend upon how far part you put the plate and you get Reflection from a pair of plates which varies with the thickness in that manner and so this uh in our particular example I finally found out that that was 16% and that was 8% from each surface there was 4% now if this were a more ordinary thing like uh you would expect an ordinary type of reasoning instead of this esoteric subject microscopic physics you would expect that the chance to arrive here could be analyzed by saying of all the ones that come down some Bounce from here with a certain probability and some Bounce from here with a certain probability let's say 1 fth bounce here or one what we say 125th and 125th here would be 225th of this what we would do would be to add the probabilities we find out that instead of adding probabilities in such logical circumstances we add amplitude in other words we can sit around and talk about it this way say there's a certain it can go either this way or it can go that way and we just add the amplitude before we spare but that means that the logic that we can say that it really goes either this way or that way is false you can't really say that in a Common Language way or you're meant to add the probability because if you were to say a to go this way some of them come this way and some of them come that way you're at a total loss to understand why when the sickness is just right there none of them come at all because if some of them come one way and some of them come the other way the fact that they can go both ways surely isn't going to make it that they don't come at all but that's exactly what does happen and so the idea to be able to say that it comes either one way or another it requires that you know what you're talking about you're not talking about ordinary either one or the other but either one or the other in the sense of adding amplitude so it's a crazy game we still I still find myself saying well it comes either one way or the other but it is not really true that for a given particle which arrives here you can say that it either came this way or that way you w get the sensible physical idea of that as a matter of fact it's entertaining the following thing is very interesting it is possible to put some kind of atoms on the surface here such that when light bounces but they leave some trait like the atom isn't left in some other state than it was before so that if it bounced the light from the surface an atom on that surface would be left in a different state likewise we can put atoms of this kind it's rather technically difficult with light but you can do it within many many analogous experiments in similar situations you imagine it can do that with this and then we could say let us bounce the light and then afterward look at the atoms and see which one are excited what you discover is if you have enough here that you don't miss them but you forget the cases where you miss that it's either excited here or it's excited there yes in other words it does look like the photon either goes this way or that way and when you have the atoms here and you count just those cases in which you can find you see I'm worried about the cases where you miss them forget the cases that you missing and take only the case where either one or the other is Adam is excited on one or the other sheet and ask for the probability of arriving here and you know what you get as a result of the the function of sickness a completely different result if you have atoms there that can leave a trail as to whether light was there or not you get 8% reflection no matter what thickness in other words it tricks you you're going going to be clever you know that you if if you have no way to tell from which one it comes if the light after it bounces off leads everything the way it was before then you get this funny interference effect if I you put something here to see if the light bounced here or here you can tell it bounced one or the other it tells you it leaves the atoms excited but low there's no more interference effect why how do we describe that it's not hard it's that we change the problem the first problem was given a source here and material here what is the probability that the for the following events that the photo multiplier goes off and that the system is left exactly as it was before that nothing changed in the glass that's that the first one but in the second experiment we're asking for a different final problem we're asking a different problem the problem is what is the chance if we have a source here and these layers here that the photo multiplier goes off and one of these atoms on this layer here say is exciting that's a different problem has a different amplitud and there has nothing to do with what happens down here and that amplitude is 4% or2 rather squar is 4% has some Dar angle I don't understand angle square is 4% and the probably that it's reflected from the front surface as detected by a adom there is 4% likewise if you ask for the following situation that the photo multiplier should go off and the bottom one should have an atom exited you get it also 4% so you see if we make try to test whether or not it's going one way or the other then the results of the experiment to change or another way we have to ask about a different experiment the case of interference is is this that it is such a situation that the rest of the system the glass is exactly the same before and after and there's no way to tell where the light BS otherwise if you had some way to tell you'd ask for a different physical result have a different amplitude and different result which means this these things I point out because as you've gone along you've probably struggle to find some kind of a simple-minded explanation of these things but when you see how annoyingly complicated it gets I mean not complicated but curious it gets it gets harder and harder to make a simple model so we've given up on that uh I also uh emphasize last time that you can get some very that that one of the things I wanted to emphasize is that things that are very common and observed all the time and which are perfectly obvious are quite different in this world it turns out that what we thought was obvious is quite wrong and it's much more complicated or not more complicated but just different in fact it's sometimes simpler and More Beautiful a particular example we had was that light was reflected by a mirror at equal angles or that light went into the straight Lin and we demonstrated that that mysteriously enough was the consequence of light going every which way not necessarily in a straight line in particular I pointed out that if we had a mirror which was made of little pieces of the right spacing and that light coming down this way it's reflected back that way sometimes but it has a good probability to be reflected at a special angle that's crazy that depends on the spacing here I have been using light and we've been using red and blue light when we change the color of the light the distance changes but I have explained in the first lecture the range of conditions is enormous and that we can have distances corresponding to hundreds of meters for radio wavs and distan of Correspondence of spacing between atoms or even much smaller for other RS in fact if these little spots were instead of miror Pieces Just atoms which are much closer together very Clos together then uh it's possible to find photons of such short wavelength much smaller than light this distance is about 10,000 atoms the thickness there but here one atom and when you have light of the wavelength of one atom that's called X-rays and when you shine x-rays on a crystal which is where all the atoms organize this nice pattern say a crystal of nickel or some other metal you'll find x-rays coming off at special angles that was discovered in 1914 and was the proof they said that X-rays were waves but at the time all the other evidence indicated X-rays were particles and we now know you all know about this puzzle at the same time this was very exciting because it not only determined the wavelength so to speak for x-rays it showed they were the same as light but much smaller wavelength but also much that is much quicker variation in time of the amplitude the amplitude changes slowly with red faster with blue super fast with right super super fast with gamma rays and so on and not only did that but by the way incidentally by measuring these angles you could determine the spacing an arrangement of the atoms and crystals and that's how we've gotten to understand how the atoms are attacked in various kinds of substances and so on which is exciting and interesting all by itself but I'm wasting time because the lectures on electrons and I've been talking about photons but what I wanted to emphasize was the structure the structure is amplitude we get talk about them all the time only later at the end we Square them to find probabilties amplitudes add when you have different possibilities we also T that amplitudes will multiply when the things happen in succession in fact amplitudes multiply just like probabilities multiply under the same circumstances if you had uh if we would like we could analyze this another way we can say there's a certain if this were really a chance thing we say there's a chance it gets from here to here and a chance it gets bounces off and a chance it gets from here to here it turns out that that's right you're can to analyze the amplitude the same way there's an amplitude to go from here to here an amplitude to be reflected and an amplitude to go from there to there and you multiply them all together just like you multiply probability multiplying I explained last time multiplying two arrows is done in the following magical way you have two arrows and you make a new Arrow whose length is the product of the lengths of these two and whose angle from horizontal is the sum of these two angles so in this case the product I don't know what the unit let's say the unit is this big the product is a small arrow and an angle something like this this is the sum of the two anyway we find we can add and multiply arrows the mathematicians call them amplitudes I mean and mathematicians call them complex numbers and that's the structure of the world electrons were discovered in about 19 1895 or so as particles and they were studied and believed to be particles they behave very much like particles you could count them you could put one of them on an oil drop and measure the electrical charge uh electrons responded to the presence of other electrons if you had a metal plate here and a metal plate here and had an excess of electrons here and a defect so that what's left over is protons here then an electron sailing through between the plates would be repelled from the other electrons and attracted to the proton and move and occur something like this millions of electrons moving through a wire represent an electric current and so on and so on and the entire picture of electrons has particles going around in in matter was or in explain many phenomena and everything was going along all right there were some puzzles about how they behaved in an atom if you heard about the atom as being a little solar system with a nucleus in the center like the sun and the planets going around like electrons then you're back in 1900 and something 1910 or so because it's quantum mechanical as it turned out by 1923 de BR suggested that this business about mixture this wave and particles properties like light was probably also true of electrons and know historically the wave part aside from Newton's era the wave aspect of light was most obvious and the particle aspect was discovered afterwards in the case of electrons the particle aspect was most obvious and the wave aspect was discovered afterwards by in 1924 only a short time after the ber suggestion Davidson and GMA was doing some experiments bouncing electrons off of nickel expecting them to bounce back this way which they did but they also discovered that some of the electrons went off on a crazy angle and when they read de bral's paper I can't pronounce it sometimes they call it the brogly sometimes the brly and sometimes the BR it's a French name so it's hopeless and uh they found that these electrons came off at a an angle and that they calculated the angle what the wavelength had to be because you know the spacing of that from the experiments with x-ray they found out that that was exactly right according to the bro's Theory and that electrons in fact did the same thing as light in the same kind of du Hocus Pocus in translating the word dual hocus fcus into better English or better physics it's this that even an experiment involving electrons going from one source they a punct and filament to a counter of some kind is exactly analogous of the situation with light in fact all of physics as it turns out as far as we can tell is all the same framework there's a probability for an event and the probability is a square of an amplitude and there's an amplitude that an electron goes from place to place the amplitudes can be compounded by addition when there's more than one way to happen and by multiplication when you can think of things happening in succession that means that all the possible events in the world might be analyzable into separate simple events of which everything is a compound for instance uh is it possible to describe like everything that happens as a series of events freaks it jumps it goes from here to here it bounces off it goes from here to here and song uh I'll give a specific instance in a minute what does turn out to be true and this is what I the content of the present lecture is I want to start all over again and tell you now that I introduced and I convinced you about the framework of probability amplitudes I must give you the laws for the probability amplitudes and that way give you the complete theory of quantum electrodynamics uh it turns out there are only three L okay but they have to do with the idea an amplitude that Photon goes from place to place an amplitude an electron goes from place to place and an amplitude that an electron IDs a photon I'll describe them in detail now now I would like to give a more complete description of the way the laws of physics look at least in this partial realm involving only electrons and photons in order to give this description I have to include something which I didn't include before for Simplicity I include now the time in the experiment which oh here it is in the experiment which I thought I had just erased but didn't we can ask another question we can ask if the source is made to emit a photon in a given moment what is the probability that the counter receives a count or goes off at a given moment this adds the idea of time to the things that we've been doing before we can ask a question that's in other words more complete not only where the thing is at at what time it arrives and so we have a the following World we have an amplitude ins of space time space and time things move around in space and they take time to do so they don't really move they have amplitudes for doing their thing okay but their thing is done in space and time you can ask for the amplitude that a photon arrives here at a certain time and an electron is somewhere else at another time and so forth now in order to describe both the space and The Time pictures I'm going to make a kind of graph which we call which is very hand handy if I call it by its name you'll be frightened so I'm not going to call it by its name I plot the position in space s sideways here and the time this way and I'm going to explain what such a diagram is by taking the old-fashioned world first not the quantum world and see what happens we take a baseball it's standing still here what does it look like on this picture the space is supposed to be represented this way of course we know space has more Dimensions but I don't have to draw them I draw one out this way for the other dimension space and a third one at right angles to both of these and this for the third direction of now if I rep to represent the baseball by a little spot here at a given moment there's the baseball later on the baseball is in the same place so later on means go along this way then later on the baseball off here that's the width of the baseball okay and later on the baseball here and so forth why did I bother to make it a wide baseball I don't know and so here I could have made it a point baseball and made it easier to draw the baseball as a function of time on this diagram be represented by that band all right now if a baseball is moving okay it's drifting across the room what does it look like this time I'm going to make a very much smaller baseball okay or you're so far away you can't see the size of let's say it's here now later on it's in another place here and later on it's another place here another place here so in this world it'll go SL if it's coasting at a uniform speed it'll be a straight line if the baseball goes for a while hits something and comes back then it'll go some like this there was something standing here right and it bounces back let's say this was a brick which were standing still and that would be a picture of a ball hitting a wall it all is goes Bo Bo and I stretch that out this way another way to uh well that's I think a pretty clear picture and this we represent situations in space time so if I would do in space and time which I inadvertently called SpaceTime which is what everybody calls it now uh we could say for instance that at this particular place we had a source which emitted a photon at a certain time this is the time and this is the place then later we can ask if at this place a detector at that time would discover a photon now if photons were baseballs we could say well maybe the photon went straight along here or what have you but we don't uh have to say we don't know anything about how it goes but you know what the answer is going to be there's going to be an amplitude H that a photon let out of here arrives here and that amplitude will depend upon the time of this one and the position and the time of this one and the position and I call this point for just a moment number one point and this a number two point and then we have a thing which is called the amplitude for a photon to go from well 2 two from one and that's one of the great fundamental laws of nature what that formula is for that it's a little mathematical formula and it's very simple I do not want to bother you with exact mathematical expression because it won't mean anything it's easy to describe for those who are more sophisticated of course you realize immediately that this formula for this is going to depend only on the difference of the time and on how far you had to move the difference of the distances so it's not so complicated if the difference of the time is T and the difference of the distan is is X then the answer for the for this thing is this fun function but I don't want to bother you with the mathematical thing only know that I can write it down in one second and people who know this magic this mysterious language know what that means so that this formula is extremely simple it's as Elementary as it can be oh it really is as Elementary as it can be as it turns out in uh if we added a couple of principles then you can deduce what it has to be knowing nothing except those principles the principles are as follows there's a knowledge of the relation of space and time the way things depend on time and the way things depend on Space are interconnected by a law uh which is a principle of Relativity and that tells us a great deal limits the functions a great deal the second proposition is that the probabilities that you get from this must have the pro property that if you add up the probability of every possible event you get 100% And if you make a wrong formula here it doesn't check you know the probability of everything all added together has to be every possibility which is 100% something's got to happen in other words and if you if you get the wrong formula it doesn't come out right you find out that the probability of something happens is one and a half or minus two or something so adding relativity and that principle determines this almost completely not quite completely I'll tell you a little more about in a minute this function that depends on these two things just for the sake of this discussion I'll call a d say why d p for Photon P is for Photon between two and one it's a amplitude of a certain size that depends on the distance between the two you might at first be surprised because when we were dealing with photons over there we said that the amplitude was rotating and dependent on the time by going around the proportional to the time depending on the color of the photon nothing has been said about the color of the photon over there something's wrong no it turns out as follows I will explain it better later the color of a photon is a result of the source The Source emitting has an amplitude to emit the photon which is a function of time which is going around uh when an amplitude for an event changes with Time by simply rotating not changing its length but by changing its angle it corresponds in the real world I mean the world you used to the Ordinary World to be a situation in which the energy of the system is definite and what we've been talking about before was situations in which the color of the photon the energy of the photon was definite and in those situations the amplitude of is turning around in time this is a fact a result of the source when we go back to discuss things as a function of time and all photons are exactly the same there's only one kind if the amplitude varies slowly it appears to his eyes a red Photon if the amplitude varies very rapidly it's an x-ray it's all the same it's just one thing there's only one kind of a photon when you cut the time so you see when you deal discuss it in time also so you see that things are getting simpler to represent that a photon is gone from 1 to two we represent that by a wiggly line for no good reason to represent a photon going from one to two now the next thing you have to do that's the first law of physics the second law of physics that's all about Optics that's the entire theory of life it is it is it really is the part that's not in it is how the light interacts with matter and I'm coming to that next FLW that has to do with electrons oh I did cheat a little bit yes wait I told you about polarization of photons which I've left out here it also turns out the electron has two states of polarization too which is sometimes called spin States and again I'm going to leave them out because they only they don't add anything to the idea they just add a little complication to the formulas which you're not going to work with right now anyway so if you want them I'll tell you the exact floors but this is very close with electron we have a similar situation I draw just draw the same diagram because I used up my paper and I rolled it away but if this was time and this was space we can ask the following thing if the electron is known to be started here at a position in time which I call one it has a certain amplitude to arrive at another position in time two it then will go from 1 to two which I'll draw with a straight line to distinguish it from the photon case and we need a formula for the amplitude for an electron to go to two from one that's a different function of the two that is the number it depends on it too and I'm going to write it down here no it turns out a little harder to write that one it turns out that that one involves not only the time and the X but also another number in the formula it's more complicated than this and that other number is a characteristic of the electron it's called its mass and I'll tell you in a moment a little more about it uh in other words what it this thing really depends on the position two the position one and the number m e the mass of an electron at rest mass of an electron if you put the right number in for that then that's this thing for electrons if you put zero in for that that's a photon that's this one that's D and as we'll see for every known particle that we hope in the end for every Point like particle at the H like a point it's got to be this way with some M you can deduce that alone this formula for this thing from relativity and this business about the probabilties adding to one the only possible function is one a particular one here which I haven't written down but I write it symbolically it's an arrow which amplitude of complex number which depends upon the two position and on some number in the case of an electron that's a particular numerical value now it would be nice for me to finish the job and write down the formula for that thing but I can't make it understandable to you because unless you have some more uh enough mathematical background to appreciate vessel function so but I will tell you a little bit about the function a special example a special example in fact of the use of such a thing so suppose that we have a situation where we know at the present moment time is this way as usual and space is that way we know at the given instant that the electron is is equal amplitude exactly the same amplitude to be everywhere in space then the question is with what amplitude will I find it at this particular place later answer it might have been here and then it would go to there or it might have been here and then it would go to there or it might have been here and then so on and so on so what you do is you take for each one of these places for these two points the value of this e and then for these two points the value of e and you add them all together because those are all Alternatives it might be here it might be here on I could write it this way the amplitude to arrive at point two from places one which are all different values of X at a particular time T1 we'll call this T1 this is mathematically complicated in fting but all I'm saying here is exactly perhaps I better not say it this way what you do is you take the amplitude to go from every one of these points to here and calculate it add it together in other words you add this thing for a given time but all different places and then the answer is very simple the answer is simply an amplitude of a certain of a unit length whose phase whose angle angle here goes around depending on how much time it's been from me to here sounds familiar but it's not a photon and that's rated which it goes around is very high it's something like one point some odd * 10 20th that's 130 million million oscillations a second right but that time that the speed at which this is going around if you change this time is uh characteristic of the electron and measures its mass furthermore it's pretty obvious that the amplitude to arrive at any other point is exactly the same because it had all the same amplitudes back here and if I started with another Point here and Drew all those arrows and everything would be the same picture so the amplitude to arrive everywhere is again the same but has a different angle so if the amplitude to be everywhere in space is exactly constant the amplitude to be everywhere in space stays constant but changes its angle only at a rate depends on the man the particle whose amplitude is uh the same to be everywhere in space it corresponds to a particle at rest stationary in the normal p also I told you when an amplitude is such that all it does it doesn't change anything except in time by turning by changing the angle it's a state of constant and fixed energy an electron at rest has a definite energy which is called its MC square I think it's Mass terms of speed of light I've taken the speed of light to be one in the units I'm using so that uh this just goes around depending on the M if I had had a heavier particle the situation would be the same I put a different number in here but it just be that this amplitude rotate faster in that case anyway there's a simple example of the one of the properties of this function which is very very simple as a matter of fact if you're clever enough you can deduce from this plus the principle of Relativity what that function was but you're not that clever so we go but I just wanting to try to emphasize that the particular functional law I haven't written it down exactly is as simple almost as can be finally there's one more Rule and that is that if an electron comes to a point at the same with a phot that come together at a point an electron and a photon that an electron can go off from there there possible to have a junction and there's an amplitude that there's a junction the amplitude that a photon is absorbed by the electron let's say or whatever kind of a junction is that we can talk about what the Junctions mean but every time you see a junction you get an amplitude that amplitude is given by a formula C is equal to 08542 and so on a number just a number one uh physicists like to remember this number in the form 1 over c^ s and they write C squ is 137 0359 9 plus or minus 3 and that's the result of an experiment that's a magical number a mysterious number good theoretical physicists put that at the top of their bed at night and dream and dream if they can figure out why that's the right the fact that we have we have no idea where that number comes from and it's one of the Mysteries and incompleteness is of the theory because it would be nice to get that number out of something and it's done by experiment I'll discuss that problem in much more detail in the next lecture when I talk about the limitations or the incompleteness of the theory and also other particles in nature and all the other problems of physics more complete not just electrodics well now they see we have just these parts and I would like to discuss calculating the amplitude for a number of different events so that you can see what's involved so the first example will be this suppose that I have two electrons again time this way space this way and so on I have an electron I know at State at position one and time the position time one mark one here and another one at two and I would like to know whether at a later time I will find one electron here well let's not put it in the same place and another electron say there all right so one electron should be at three and the other has four now to find out how to do it the first thing I do is I suppose that the electron number one went to three and the electron number two went to four so I draw a picture like that and I read the picture mathematically as follows that that amplitude for this event is the product as we talked because these are two independent things there's one factor which is the amplitude that this gets from here to here which is just that e thing which is some Arrow and there's an amplitude to get from here if you if I were writing it mathematically I'd write E31 times e42 but what I would mean is I get from the formula the size of the arrow here and then I multiply it by the siid for this arrow and that would be the answer but that's not the complete and exact answer because there's another possibility so I must consider other possibilities that can occur another possibility is that it was this electron that went to there I'm just drawing the same picture over again but making a a recombination this is one this is two this is uh three and four and the amplitude for this one would be e 3 from 2 e 4 from 1 and from what you've learned last time about photons if it can happen in two different ways you add the amplitude but for electrons there's a different rule when it can happen in two different ways for electron you subtract the ampe this subtraction has a very profound and remarkable influence on the behavior of electrons and is the reason why electrons behave more like particles experimentally than like waves when they were first found I talk about come back to that in a few a little while let's forget this for a while and let's talk about just situations like this that somehow you know it's the same electron going here this subtraction is extremely interesting but I'm going to come back to that because I want to concentrate on something else well there's another way that the first thing can happen beside that exchange and that's this it could be here's the particle at one and here's the particle at two and that particle that goes to three and the other one's going to go to four now I had them going directly that was the first thing but you must add an UD for every possibility so we have to keep on going and adding something it could be this number one could go to a some place in time and space which I'll call position time five the electron can go to here yeah and then go from 5 to three and make a junction here by emitting a photon and the other one go to the other point where the other end of the photon is six and go to four now if you're brave enough I'm going to write the amplitude for this thing in a high class mathematical fashion and you'll be able to follow it the answer to this amplitude for this contribution here is the following e35 e51 times uh E46 time E4 62 time anybody got another guess what else is in it d56 that's a up p p p4on 5 to 6 and U forgot something C * C how's it work if I haven't made a mistake here there the amplitude of the electron goes from 1 to 5 and then an amplitude electron goes from 5 to three times an amplitude that's say Junction that's a likewise here in addition there must be some amplitude the photon that's been liberated at this Junction has gone from 5 to six you put that in too you multiply all these together by those rules I know it's getting compated we're piling a lot of stuff together but it's like playing checkers there's a few rules and you just have to use them a lot you got triple jumps but they're nothing but single jumps repeated so it's like each of the thing is simple it's just repeated and repeated so we calculate this thing and add it that amp through with all its arrows and multiply to that one up there let's forget the other case for Mo add it to that and be improved accuracy it's not quite finished yet why because of course you could have something like this and so on I mean there's all kinds of wonderful things we'll come to all kinds of wonderful things in a minute you got two of them going across and so on well this is a hopeless task and you got to keep adding and adding and adding you never get finished but we going to get a good luck good luck you see this amplitude has a number of factors in it but also has C * C and C * C is a relatively small number of the order of 1% and as a turns out the contributions from a picture like this under ordinary circumstances is about 1% of the contribution of this the reason I say that under the ordinary circumstance it can happen that they've got a situation where this one is can adding a lot of cases in it a particular picture cancels out by interference and then something that's 1% smaller is the whole thing and so on forgetting all about that each time you add an extra Photon you add a c squ makes it 1% so therefore if I break a picture like that it's 1% of this one which is 1% of that one so by the time I got down to this one I got things correct to one in 10,000 and I would get to the lazy I got to putting three of these Dar things across but then I got to one part in a million and that's why we can calculate so accurately cuz we can do one two three never can get the four it's too complicated and uh there's another thing I forgot to say and that is that the where is five and where's Six you're sitting there ask anywhere yes anywhere those are all possibilities and those are alternative five might be here and six here and you have to take that then you have to put them somewhere else and add them and add it and add it for all different places that five and six can be all right so what I mean to do is to add this together for all places that five can be in all places at six can be I mean by it places positions in space and in time if six is later than five you're inclined to say the photon went from five to six if five is later than six that is if I got this around that way you would say the photon went from six to five in other words in one case this emitted a photon which the other one absorbed or vice versa this can emit a photon that that absorbs but it's a funny thing in relativity it's very difficult to say when two things are nearly at the the same time which is ahead and this whole business of trying to decide when they're nearly at the same time which one is emitting the photon and which one is absorbing the photon is in irrelevancy this function for photons is only is large when the distance is Big only when these two are at such an angle that you usually can get there at the speed of light you usually think light goes at the speed of light you used to think light went in a straight line light goes on many different lines and the result is it looks like a straight line to a gross scent light goes at different possible speeds at different kinds of angles here and the superposition when the distances are big is that it gives only a result when the speed is at the speed C so I have now finished telling you like one thing I cheated a little bit in the fact that I left out the polarization and this Junction thing has a whole lot of different numbers depending upon different polarization cases it could be one kind Another Kind Another Kind different combinations of of polarization cases here and those numbers are re those are little one aside from this Factor there either a one or a minus one or sometimes a pure vertical thing like that or sometimes a pure thing like that very very very simple so if I'm going to leave our polarization Al together I'm not giving you a wrong impression that the junction is just see this number times one it's not exactly one sometimes it's minus one it's a little different but that's for different polarization CH but I don't want to deal with that any further from that all the phenomena of nature occur result for instance you know that the light light can be scattered it comes from the Sun and it's scattered by atoms in the sky so you see Blue Sky how does it work if we have an electro well excuse me let me excuse me let me go in a slightly different order I'm going to come back to that that case I stepped on my own cord that time and it choked me I have now recovered an not to continue in order to understand the behavior of electrons in atoms I we have to add one other feature and that is the nucleus the nucleus is not completely understood and I will not give you the correct laws for the behavior of nuclei if I could I wouldn't waste any more time lecturing here but I would publish it immediately as it is unknown these functions that we know so well are the right must be the right functions when things behave like points and have no internal structure and it has turned out experimentally that the electron and the photon have no internal structure to a small as we've been able to look so far experimentally and that is to distances which I is 10us 15 cm approximately 100 no 10 million 11 millionth to the size of an atom small enough so it looks like a point but the nucleus doesn't look like a point point but for many many experiment phenomena in atoms you can approximate by supposing the nucleus as a point and so far as you can approximate the nucleus at the point you can do the same trick with a nucleus but put the mass of the nucleus there that is only approximate for the electron this is right for the nucleus it's proxim so if I want to describe a hydrogen atom I have to represent the nucleus so I'm going to represent nuclei by lines you know thicker line double line like this this is an electron that's a phon and this is a nucleus and nucleus let's say to take a hydrogen atom nucleus is just a plain proton that it looks fat because we don't understand it inside there but the electron is nice and thin and it goes along and it can nucleus might emit a photon which interacts with the electron it could be that over a million years or two millions of a second in practice that you can emit several times photons back and forth and the electron in general does some sort of a dance like so around the proton uh calculate the total amplitude an electron and the proton down here still looks like an electron and a proton after a long time you have to add the possibility that the electron and proton just went directly with ease or that the electron went for a while and there was an exchange and another one and another one of photons both of these things happen and the interference between them has an effect on the motion of the electrons in the presence of a proton an electron does not move the same way as it does when it's an empty space or free of a proton when it's free of a proton the amplitude to find an electron in a certain point is given by this function as a matter of fact you can show in a manner similar to the case of light that if there's nothing but an electron in the space it appears to go at a uniform speed in a straight line that is through the interference of course the same way with life but when there's a proton in the neighborhood or any other source of photons but let's take the case of a proton as the electron is moving its amplitude keeps changing because the amplitude of the situation it's changes because of the exchange of the photons and the result result of that is that the amplitude to find an electron anywhere is altered by the possibility of exchange of photons with the proton and that is all computable and quite complic that's the theory of atoms but uh if uh we have a very large scale event in which things are far apart and I drew it somewhere but it's long lost if I have some metal plates with an excess of protons here and some extra electrons sitting here then an electron going along here and mind you this is on a very large scale compared to my other drawings where atoms were big there now they're tiny it could be a photon go across here another Photon another Photon these billions of photons going across are all very long wavelength 2 cm half a cenm contain very low energy and hardly disturb the system the thing that's emitting them can emit them without any change it's such a small energy any rate at the main point is that the electron and going along in this space here is not going along the same way as it would if there were no place and when you calculate the chance of finding an electron to go from here to here you'll discover also just like we did with light that in this approximation of large scale the only only path which is important is a special curved path not straight because the photons are altering the amplitude actually yes that's right the interference I got the curvature in the right direction uh that's what was worrying if you in the case of light you remember that there was an angle at which the amplitudes came in and if we added all these amplitudes together at slightly different angles the only path that was important was one in which the angles are not changing in the case of light the angle depended only on the time and so it was a time should be not changing or least in this particular case the quantity which is not changing is more complicated than time it's a more complicated thing it happens to be have a different name it's called the action and the pairs of particles can calculated by Computing a certain quantity on a path called the action and the path takes the path the curve which looks like the PA curve of least action these this way of putting the laws of mechanics was discovered many many years ago as a what we call classical mechanics the relationship of quantum mechanics see quantum mechanics is is exactly right and the classical mechanics is an approximation the behavior of light Jumping All Around before is right but the idea that it goes in a straight line is an approximation the idea that electron goes in a curve is an approximation it's really amplitude jumping about this example however shows something interesting in many circumstances it's true that we have long wavelength photons which can be emitted because they contain so much little energy without disturbing the source and whether or not they're absorbed by an electron as a matter it doesn't make much difference to the energy of the electron and so we find an electron moving in a region in which there are available many photons enormous numbers the wavelengths are so long the energy is so low the numbers are very large but they're all about the same then we can describe this electron by saying it goes in a straight line except it's Disturbed it's disturbed by the possible presence of photon we say in a oldfashioned language that there's a field in the neighborhood an electric and magnetic field which Alters the motion of the electrons but what this electric and magnetic field is is amplitudes Def find phons in very large numbers under circumstances where their energy is so low that it's easy to emit them and that's the earliest ideas then about the motion of electrons was that they were particles being bent by forces generated by field this is now all P instead of that it's just the exchange of electrons exchange of photons between the electrons or between a nucleus and the electron the amplitudes for which are all given by this little constant and the amplitude for the photon to move is given by a known function and the electron like one and that's all there is to it and from it all the rest of the laws of physics come out another example is the scattering of light light according to that view would always go in a vacuum in a straight line or however it goes in a vacuum and if this diam the distan is are big it would look like a straight line but we know that we've talked many times about light being bounced and reflected from the surface or light going slower in materials and so on I have to explain that what's involved there is that in matter there are electrons and if this is a typical electron moving along again time is this way unlike this diagram this is an ordinary diagram moving through a piece of material we're moving through some place but here's time again in space we can have a photon coming in from the outside hitting an electron in an atom say or anywhere and after that a photon is emitted by the system so a photon comes in and the photon goes out and it's even possible that the electron's condition that was before is restored again although temporarily it's been changed of course another if you like this game you can imagine another diagram let's see another possibility crazy idea isn't it that it's emitted before it's absorb yes you add that too close together and it comes out right don't worry about anything you just add everything it's only the sum of these two which is the right answer for the scattering of life so you see that when we have electrons present a photon can come in and come out in some other direction that is the basis of our the rules that we made before and I should uh for complete this repeat these rules and explain them all over again because in this system I had a different rule I talked about four times having an angle dependent on time and everything was kind of funny and it doesn't look like it here so I have to explain that just a little bit it works more detailed now this is a more detailed description of what happens in here first we were supposing that we had monochromatic light that is light of one color that means that the source was emitting light of only one color how does it do that the way it does that what that corresponds to a source meting light of one color is this a source this is time again and this is space let's say the source is standing here it's like this it might have emitted the photon then it might have emitted it later might have emitted it later might have emitted it later the amplitude to emit it at each time is different so the amplitude to emit the photon at different times from the source is changing going around backwards yes backwards like so now to make a quick idea of it let us suppose for Simplicity that this function for the photon just simp only right at long distances only collects connects two points which you're going at the speed of light it's a simple model it's a simple approximation so if I were to come over here and get the pH if I would get the photon to get to Here by one root and compare it to another root when the time is longer it must have been emitted earlier if I asked for it to arrive here at a certain time if it came this way it was emitted at one time if it came this way it was emitted at another time the amplitude do be emitted earlier ear it's going around backwards with time yes so the amplitude admed earlier as a bigger angle that's why the one that takes longer has the bigger angle it's not really a property of the photon in the space like I cheated you in making believe it was it's really the amplitude of emitting if you get the photon at a certain time here it means that it left here earlier if it went this long route it left even further earlier and if this Source was emitting with an amplitude which is changing in time then the amplitude to arrive here by this route and by the long rote are different because the source was different so it's really due to the source that there's a difference in the phase or the angle rather of arrival of the light in addition there's one other thing wrong I talk about light being reflected from a surface and that's just nonsense it's not reflected from the surface at all what it really is is it's scattered by the electrons in the material so the correct picture of this thing is this I'll draw a better picture what really happens is the light comes down and hits the first piece of matter and then is scattered back by that kind of a picture on the last board over there down here in microscopic view or it comes down here and it's scattered there or down here and Scattered there that's all it done all it's really scattered in the inside not on the surface and so we have to add together a whole lot of amplitudes each of which takes a little longer and have come from the source at a different time and so it ends up adding a whole lot of little arrows each one is a little turned relative to the other by about the same amount and if you add arrows each one of which is the same length and they're turned relative to one another you go around on a polygon or if the arrows are very small a circle and so you see that the net result for example of a certain thickness is to have an arrow a net Arrow from this end to here by the way if this is the center of the circle that could be represented as the resultant from these two this and this together but I that's the way I cheated last time I just threw these two but what really was happening was the circle let me explain it again it goes each little contribution in the interior goes around in a circle and if I have the thickness just right exactly right the circle is complete and the net result is zero that's the first minimum if I go a little thicker I goes around again then comes back to zero if I use the half thickness it would go around halfway and stop and in that case I get the biggest possible amplitude and so on so those fluctuations were really not from the surfaces but from the interior at least we have the glare where the matter is doing the scattering of the light and not some imaginary sub stuff like the surface I uh cannot resist one of my problems is uh the problem is with this is that I I can make it more interesting by showing you how how more and more of the phenomena that you ordinarily see work out this way and at the same time I have a desire to tell you about all of the phenomena which are quite unlike what you see which are quite unexpected and exciting and I don't know which to do either to convince you that it's interesting because it's something you didn't understand before or it's exciting and the thing to do would have been to give eight lectures but I didn't I only contracted for four lectures so what I've decided to do this time is to tell you about something unbelievable but still true which is very interesting so it doesn't explain a phenomenon you know about but explain something you don't know about that's this let's take the simple uh situation where there's many possibilities I say it very neatly in in the we would talked about a photon going from a place to place and that we could also have it this way or turn it around we could have the points five and six six being definitely later than five six being nearly the same time as five or six being earlier than five and when six was earlier than 5 it was just a photon going the other way if you'd like now as it turns out the same thing mathematical form of these functions are very closely related I think I already told you if I didn't I meant to that the of 2 and one if I put zero in for the mass that F of 2 and one if I put zero in the mass is the same as this D so all the functions are exactly the same or just one number in zero for the case of the phon and their properties are very similar so at first you thought everything was understandable when I do a picture like that for example the electron's coming along the photon comes electron goes to another place and the photon comes out I did shock You by having the photons come in the wrong order but it's still all right but this is a a real good one isn't it suppose this point here gets earlier than this point and I start to draw something like that never mind about all the photon they're in there too but the point I'm trying to emphasize is the motion of the electron this is time and this is space question if this point is called five and this point is called six and six is earlier than five I hope to goodness this F is zero huh because I don't want things to go backwards but it isn't zero what it says is that this is perfectly possible and what can it be that's gone backwards here oh you say that's easy it's just an electron going from here to here almost almost it's this way though the electron carries a charge and it's good to put an arrow on to remember which way it goes in this particular case the arrow is going the wrong way and it turns out that this section going backwards has many properties exactly the same as an electron but it's not exactly the same as an electron it is possible by getting enough energy so on to get an isolate long piece of this backward moving section see it goes on for a long way maybe maybe it's connected to an electron this way an electron that way but it's got a lot of things happening photons coming in and photons going out and so on except it's going backwards you're can take a piece of that line and put it between those metal plates that we were talking about and it curves the wrong way if you figure out which way the amplitudes are coming and the changing it'll turn out that it'll bend the other way it moves toward electrons in fact it's just like an electron except it's positively charged it's called a positron and it really exists it's to make if you get enough energy with some photons and the fields and stuff you can produce this kind of a situation for instance you can take this and have the following physical possibility let me uh I need more Blackboard all the time let's see what happens yeah I want that one for later so I have to have this one good for example if I drew some terrifying thing like this with two photons this represents the possibility that an electron and a positron initially in space come together disappear no more electrons time is this way time is this way yeah I know I looked like I drew the diagram side like I didn't they got two photons out electron and a positron can annihilate and emit two photons directly observed easily in the laboratory or photons can come I can draw it the other way photons can come together and produce that produce an electron and a positron pair so that it turns out because of this mathematical business that every particle can go backwards as well as forwards in time if you want and and so for every particle in nature there's another particle that goes with it matched which is called its anti- particle and which has many of the properties of the original particle with some of them with the sign reversed in the case of the positron for example its mass is exactly equal to that of an electron comes from the same function and its electric charge is opposite in sign that you can find out by checking some numbers in here it's all the consequence of these rules uh in the same way there are antiprotons and an so forth and a proton and antiproton can come together and annihilate each other producing a lot of other particles for instance they could produce two gamma rays but it's rare but it can happen the other particles I don't want to mention because they come next time and so we have the possibility of having any kind of combination of these things in space and time sometimes going forwards and sometimes going backwards the backwards ones are positron when a positron is actually made the way I described there in the laboratory on the earth it doesn't go very far before it disappears because it finds an electron and the two combine like the first picture and two photons come out but you can make them see them go deflect them with plates the wrong way and they annihilate again they were disc discover predicted by da from the theory he had which was really a calculation of this function for the first time and uh discovered very soon afterwards by Anderson in the laboratory this also permits well let me now finish well I don't know if I finish I yes not finish I one thing I can't resist this minus sign is so interesting it means that when you cross up which is which you change the you have to subtract the amplitude that has an interesting consequence suppose the two points one and two are very close together that you want to emit two electrons in the same condition at virtually the same position at the same time so if one and two are the same put one here and one here and one here and one here because one and two are the same place and same time now you see that this expression differs in the way from this then therefore the difference between them is zero that means you can't make two electrons or you can't expect to find two electrons anytime where they're made at the same point in the same place same time at the same place or if you try to put three and four at the same point you see if 3 and 04 are the same these cancel that means that would mean that two electrons can never be found at the same place at the same time it turns out what it means is that they try to stay away from each other not just because of the exchange of photons which is one influence which does make them stay away from each other but by a completely different thing which is this interference of the amplitude actually because of the fact that there are polarization cases it turns out what I said is right but if you take into account the polarizations also then you can make two electrons at the same point but they must be in different conditions one must be polarized one way and One Polarized the other so you can still keep track of which was which so as a matter of fact you can get two electrons into the same condition of not just you can put two electrons into the same condition of Motion One polarize one way and One Polarized the other way but that's all you can't put any more it is on this uh fact with its consequences which is one of the other things I unable to show you because of lack of time the very beautiful fact that all of the chemical properties of substances can be worked out if we start with a a nucleus which has some protons in which are attracting electron we start with one proton and it puts one electron or around it if you start with a nucleus which has two protons in It's called The Helium nucleus then you can put one electron around and put another electron nice and close in the same place they try to get as close as they can the other one can be in the same place because there's two possible directions of polarization now you take a another next nucleus number three and you want to put three electrons around it one goes in nice and close the other one goes in nearly the same place but polarize the other way and the third one because there's only two ways of polarizing an electron can't be in the same condition as the other two and has to be wander around out here waiting to get in it's not repelled by any electrical force it's just beel by canceling amplitude by interference it has to stay out there it's easy since it's far away the photons which is exchanges with the nucleus have small effects it's small it's easy to remove it the last electron in other words is easy to get off and that represent an atom which is chemically much more active than helium because it's easy to remove an electron it gives electron up easily such a thing is called a metal in fact when you compress a whole lot of these atoms together the electrons are so easily outside one it's so easily removed that they just swim around in a kind of sea around the they don't even stick on one they they wander off another one and wander off them they wander all around inside but two of them on each nucleus is still there bo bo bo bo but one extra dark the ones are wandering around such a material with very little electric forces you can make all the electrons shift one way or the other does electrical conductor and that metal I'm describing is lithium it's this first metal the element before is helium and it's hard to get its electrons from the inside helium is chemically almost inactive and lithium is chemically quite active and makes a metal and so on and so on I am very sorry to have such a brief time to explain phenomena that you know about in terms of these ideas as the ideas are by themselves are rather difficult to get at and I want it to be complete in telling you about the most mysterious aspects rather than uh cheat by leaving out something important I guarantee you aside from the polarization which is not important I have now left out nothing and the whole theory of electricity electrodynamic our understanding of the world comes from just these pictures each picture is interpreted this way when you draw a picture you write an amplitude for this this this this and this and multiply it together right wa and two c they cut it down finally I would like to describe the beh motion of an electron in a uh going along here's an electron all by itself going from point to point all right nothing to that but it has to be corrected it's also possible that as the electron was instead of just going directly from point to point goes along from for a while decides to emit a photon and then Horrors it absorbs its own Photon something perhaps immoral about it but it does it it does it all right it might not be the nicest thing to it does this and just uh you understand what this symbol represents now if you put some points in here label these there's an e for this amplitude for that an amplitude for that an amplitude for that all multiplied I mean for the amplitude for this electron to go from here to here times the amplitude for the electron to go from here to here times the amplitude the electon to go from here to here times the amplitude to the photon to go from here to here time C time c those are the coupling for the junction and that bunch of junk all multiplied together has to be added for every place that this can be and and time and every place and time that that can be and when that's all done you've got piece which is supposed to be added to that piece now when you add this piece to that piece you find that the motion of this is slightly altered Its Behavior in particular in a magnetic field has changed in a magnetic field if the thing was as simple as this it turns out its polarization changes at a certain rate or it spin changes at a rate that can be measured and which we'll call one one is the result you would get for this alone if you add the this to this and figure out how the thing moves it behaves in a magnetic field slightly differently and if you just add this you get 00116 or eight or something like that if you're this time for the frun of it I'm going to write the formula it turns out that this term is proportional the contribution in the magnetic field of this is proportional to two C's c² is 1 13 46 oh sorry well I didn't the error and within the over 2 pi this time it's easy our students learn how to do this calculation in their Elementary course in Quantum electrodynamics which is a third year graduate course all right this was worked out by schwinger for the first time in 1948 the next case is to take diagrams corresponding to two of these things something like this there are other possibilities let me Erase here and write the other possibilities of this discontinuing for other possibility all of which involve four C C4 CL and there are other things that can involve four C are something like this okay there's a different kind of connection timing and finally there's nothing significant about that being straight these points it should be you know and stuff like that but I'm too lazy to draw it cck here's an interesting possibility photon is emitted makes a pair electron and positron and again if you'll just hold your moral uh criticism the electron and the positron annihilate again so that there's an electron going this way and a positron going that way and they annihilate again into a photon and that comes back it's called a closed loop it comes and it goes this involves four C's one 2 3 four also and this this and this which involve four C can all be added together and you get something proportional to C4 which by the way is fairly small being a square of 1% which is 100 one and 10,000 or so and the coefficient uh this time it's not so easy to write down it's .03 something something right at any rate this took two years to calculate after this was worked out and it took one year to find a mistake in that calculation it's true it's true it was very exciting because it was calculated very carefully by two different people they thought they were independent but they compared a little bit or something they both had it the answer was wrong and it disagreed a little bit with experiment and they improved the experiment and it disagreed and it was a showed that Quantum electrodynamics was wrong no it was an error in arithmetic so everything was all right and now uh that was two years later that brings us up to about 1950 51 and now we go on and we try to do three oh well there's you see when you have to add all these possibilities you get lots of pictures of which I'll draw one more but you can keep on going and draw a lot more they make a pair they interact by exchanging a photon and so on and I each one of these diagrams represents a definite formula and we use the diagram to represent the formula and we just make these pictures write down what they correspond to and add the amplitude a straightforward cookbook process all you got to do is write the picture and translate things and write the factors and add everything together therefore can be done by Machinery now that we have super duper computers we've got so we can compute this one C6 and by that time it's down to the millions part and all together so far up today as I told you in the very first lecture this number comes out to be when you add all this stuff together don't stop here but keep on going 59 65 2 three plus or minus 3 calculated and experimental is 24 plus or- 2 at the present time what do we got to do to make it better some of this error is at this that the computer who did this that did this calculation only did it approximately and we can do it more exactly by using more time on the computer with a little more money that'll improve the error for that however there's no use doing that until we look at number four that is C8 with four of these extra eight couplings in it and people are just beginning to see if they can estimate how big the the C8 term will be but that will be of the same order as this error in addition there's an error that comes from the fact that when we go to calculator we got to put a number in for C square and this is as accurately as it's been measured up till now and a part of this error is due to that so I have to wait to give this lecture again perhaps in a year or two in which case I'm sure I could write one more figure here and then will be smaller but the question I am not sure of of course is whether we will still agree with experiments that one never can tell until one makes the calculation more elaborately I think then that that describes the framework of the world as we see it in the first place amplitudes for every event that we add together when we expect to add probabilities and we multiply when we expect to multiply probabilities but we're not doing it with probabilities we're doing with amplitudes this me makes us philosophic difficulties uh if you wish but after a while one gets used to it one can think about these amp think about adding them one can consider these as Alternatives which you simply add as amplitude and after a while one get to be quite familiar with this uh strange language the ordinary experience of uh nature such as light going in a straight line the conservation of energy and so on are all very easily deduced from these principles and all there really is that we can find to all the phenomena that you see every day with the exception of radioactivity and gravitation is just the two three rules a photon has an amplitude to go from one point to another in space given by a special function P electron has an amplitude to go from one place to another by another function e and that there's a junction possible between a photon and two electrons which has a coefficient which is a certain number this slightly Modified by a couple of cases for polarization but no more really complicated than that represents the whole sum of a knowledge a summary a most marvelously unified theory of almost all of common experience but not all and there in lies the puzzle there are much more in the world than just electrons and photons there are the nuclei protons and neutrons and and so forth and the theory is therefore not a complete theory of the world although it is as far as we know today a very complete theory of common phenomena colors light x-ray positrons electric currents electric and magnetic field x-rays uh radio waves and so on and so on substances hard and soft chemical interchanges some sub some atoms are easy to combine with others and some are in all of this is a consequence as a result of this analysis of first fing finding the right framework which is the most exciting part of it because it's so utterly strange but after finding the framework in which to describe things namely amplitude to discover in the end only three amplitudes that you need to discuss one a simple Junction number and two function both of which by the way are really the same function in one you put one value of M and the other put the value zero so next time I'll discuss the rest of physics and also all the puzzles which are still left in this theory if you thought that was absolutely complete we still have a question or two to ask about it and I'd like to describe that and other things in physics for the next lecture on Thursday thank [Applause] you where does coherent light the light from l fit into your calculations Las has to do with the fact that watch we spoke about this situation and this situation only this time I'm going to call it Photon suppose you to have two sources or two atoms one and two which can emit a pair of photons and you want to know do you get a photon in two different carbs three and four there's two ways that that can happen but this time because it's photons we're supposed to add these two now if these atoms are in the same condition or very close then the amplitudes that we're adding are virtually equal so the amplitude for the event that the two atoms which are ready to emit produce two photons is twice as big as you would have guessed if the two photons were different different you would just get this one term because you could distinguish this case from this one but the two photons are very much the same you have to add this other amplitude which is the same thing except that instead of E's they're PS and if 0.1 and 2 are close together or in the same condition you have to add two numbers which are the same and therefore double the amplitude and multiply the rate by four so therefore the rate at which two atoms will emit light if they emit the same light is higher than if they emit different and independently so when there's a large number of atoms the same thing happens you they add all the combinations and when you have a whole lot of atoms that you're all set to emit that can possibly emit the same exactly the same kind of photon they emit much more with a greater enhancement they all cooperate to emit they emit with a much higher probability than you would otherwise expect a laser is a device for producing a large number of atoms in a corresponding physical state which are all capable of emitting a photon in a particular direction one kind of photon it corresponds to all the threes and fours being on top of each other and uh it has a therefore when they're all in the right condition to emit a whole bunch of them discharge the energy into the same Photon and that's what you call the coherent light of a laser it's a very intense light of a single frequency in a single Direction it's the reason it works has to do with this interference there another it's not very good answer but it might give you a clue does the amplitude of a photon coming out have any effect on the one going in yes what we have to do is we have to work out you remember when I cheated in the beginning when I was doing this easy I said all you do is you take the time it took the flight to get from here to here but you see that really is a sum of two times I could analyze it in two steps I could say there's a certain amount of there's an amplitude that you come out amplitude that you reach here amplitude that you reflected times amplitude that you get here now in multiplying the amplitude to go from here to here by the amplitude to go from there to there I add those two angles so I add the angle for this time to the angle for that time it's just the angle for the total time so that I can analyze this even either way I can either think of it as one Photon doing that and consider the total time it went or I get the same answer if I think of a photon went from here to here a certain change in amplitude angle then a phon new one goes from here to here that would contribute an angle two but I say to multiply them in succession when you multiply you add the Angles and that's equivalent to the total time so it comes to the same answer does the existence of a positron in involves some sort of violation of causality no the the question was that my description of the positron here involve apparently some sort of interaction and yet an electron can be all by itself that was a completely unnecessary difference there's not an essential difference I explained the the need for the positron by a kind of continuity from this diagram here to this case here which the timing is changed and told you that this function mathematical function had to be is e function has to be of a certain form where it's completely smooth between here and here in fact the mathematical properties are that the behavior when six is later than five and six before five are very closely interconnected one can deduce one from the other that's all I wanted to say about that there's no reason why this backwards moving section can not be a long section either interacting with photons or not I gave you an illustration of one where it was a long time going interacting but it could be that this poson was made on some star 10 light years away and there been going this way in empty space unperturbed By Any photons in the neighborhood disturbing it or be picking them up or not uh like it was an electron alone in space for 10 years okay so there's no reason why positrons in fact they do they last they behave exactly the same as electrons but for the accident of the fact that the world has so many electrons the matter in the world has so many electrons in it so our laboratory walls are full of electrons and we can't make the positron not hit a wall huh if it's left alone it coasts into the wall and when it coasts into the wall it annihilate so in practice the patrons don't last very long but if you get them in a circumstance where there's no matter ah we have done so it's not left alone because of the wall but you can make them go in a circle by using a magnetic field and then you can keep them going for days going around in a circle Untouched by human hands not touching any electrons and they stay and they stay and they stay in fact we do experiments by making posit speeding up positrons going around in a circle to a very high energy and making electrons go in the circle in the opposite direction and looking at what happens when the electron and the positrons collide with each other then we have a diagram that starts out like this electron coming in positron coming in time is this way and then things happen Photon comes and then it one thing might happen is a pair of new particles might come out uh if you want to know what kinds of new could be electron and positron so interesting in coming out in the New Direction you would think that just means a collision but really what it was was an annihilation followed by a recreation but even more interesting and I will advertise the next lecture there are other particles in the world and this is one way to make them we can make particles called Neons by colle hitting electrons and positrons together and producing a pair of something else new plus and mu minus there's nothing different about a positron and electron they're all very symmetrical except history except the characteristic of our Laboratory that we have a superfluity of electron we have an excess of electron is the direction of time in your laboratory reversible then it's a very interesting subject and requires a lot of more serious disc oh his question was what about the time in your laboratory Is It reversed the order of time that is to say the order of events like this if you put hot and cold thing together then it gets lukewarm but if you take two lukewarm things in together one doesn't get hot and the other do get cold all by itself the explanation of that that direction of time has to do with the confusion of things if you would take a lot of black things and white white and black objects and then just jiggle them they get mixed up into gray if you start with gray and just jiggle them they never get black and white but each jiggle could be perfectly reversible for instance your rule could be just take a pair and flip them over take a pair and flip them over you can't tell whether I'm going forwards or backwards in time if I take a pair and flip them that is reverse them it looks exactly the same if I ran the movie picture backwards I took a pair and reversed them so therefore it turn what is interesting is it turns out that on the microscopic scale all the laws of physics are exactly reversible forwards and time backwards and time look the same but all those phenomena and there are many of course life and frying eggs are two examples which go in One Direction Only In Time have to be interpreted by the complexity of the circumstances that there are so many particles getting mixed up plus some assumption or understanding about the fact that in the past the matter in the universe is at a higher density than in the future this is a property of the Universe At Large and is not reflected in the microscopic law though it does not it turns out in spite of the fact that I draw my arrows upside down end up violating any causal principle strangely it is very interesting whenever you have shown an electron changing direction in your SpaceTime diagram it has coincided with a junction why I did that because what I really know and only thing I do know is it has an amplitude to go from 0.5 to 6 as a free particle without disturbance and then there's Junctions and then it goes to another Point as a free particle without disturbing and so I just wanted to represent functions which I've erased here by this line I mean that in the final expression you will find a factor e56 the line is only meant to indicate that fact the fact that it's straight is a convention all right it doesn't mean that the electron has to go exactly along here or anything like that all I know is that generated at five and disappears at six and it has amplitude e56 Okay I don't worry about where it actually went a disturbance has to travel from 5 to 6 then I well five and six are the places in which the photon in this particular cases coupled I have only three things it it goes from one point to another in a leap a pure leap without disturbance the amplitude to do that is that e Photon goes from one place to another without disturbance amplitude to that is the D then there's an amplitude that an electron and a photon and another electron come together at a point that's C the three rules of nature or Quantum electr dnamic if all of nature is that that would be all there was to it but that's all there is to the part that we need to do quantum electr so what I'm going to talk about in this lecture is really all of physics actually all of the known physics at the moment plus a lot that's guessed and so the lecture is going to be even more extensive than the ones before because there I was only dealing with two particles and now I have to deal with or I guess it's two dozen particles but first I I'm going to divide this talk into two parts first I'm going to talk about question that are directly related to Quantum molecular dynamics of itself supposing that that was all there was in a system electrons and photons what problems are associated with that theory alone and the second set of questions has to do with what is the relation of this stuff to the rest of physics to Nuclear Physics gravitation and so on so start with U problems of a Quantum electrodynamics which I suppose now that the theory is completely understood and you know what I'm talking about because you were here at the other three lectures most uh shocking characteristic is this crazy framework of amplitudes and if you would think about there being problems you're sure that problems must be associated with that but the physicists have been fiddling around with this now for 50 years and we've gotten very used to it a b all the new particles and all the new phenomena having to do with nuclei and higher energies etc etc always turn out to fit perfectly with every hypo every anything that you can deduce from supposing it's a framework of amplitudes whose square is probabilities and interferences and so on all appear so that the model structure of the world the framework of the world which I described has no experimental doubt about it you can have all the philosophical worries you want but there we are because it's an experimental science we have no other way to go there's another set of problems which are technical problems having to do with improving the method of calculating the sum of all the amplitudes you make all these pictures and you have to add all these numbers and you have different kinds of techniques that are available in different circumstances and of course that is what the graduate student learns how to handle and what takes so long to learn and of course since it's so technical I'm not going to discuss it that's just a continuously improving techniques for analyzing what Quantum electrodynamics really says in different circumstances but we have one additional problem that's characteristic of the theory itself that I they have a particular problem a characteristic of the theory itself which as a matter of fact was the reason why it took 20 years from the time it was first invented in 1929 till the time it was first correct satisfactorily used in 1949 and that has to do with this problem we have in our theory for example if we start with an electron here we have a certain amplitude that it gets to here which we could supposedly calculate first by it goes directly and that amplitude uh is a direct function a very precise function that comes from relativity that contains a particular number in it which I wrote last time as me and I like to write this time as M subn we put in to the theory uh we have to just put it in and then find out what results we get and F and find out what number we have to put in there to we get we with exp this is the amplitude that a particle starting at one will get to two I think I wrote it this way last time and depends on the mass of the object however the real amplitude to go a long time from position one to two oh I also told you last time that the amplitude was constant in space and you added this all together then you'd find that the amplitude to find it at a time to Simply rotated at a certain angular rate the angle would keep turning at a rate depending on the mass m but in fact there is the total amplitude to get from 0.1 to2 all so contains other possibility of which this is one that the electron could have emitted a photon and reabsorbed it and the electron could have emitted two photons a photon twice and reabsorbed it and a whole lot of other diagrams that you keep on going contribution from these various diagrams if this one for example is of order c^ s where C is a number that goes every time there's a junction or called a coupling and c^ squ was equal to one over 137.0 3599 and so on we haven't done it experimentally with not sure of this within a three plus minus that's determined also experimentally so that the predictions of the theory agree with experiment now the thing that's i' would like to emphasize is that because of the other amplitudes the real total amplitude to arrive at the time to supposing let's say that the initially it was equally equal amplitude to be everywhere in space does not revolve the phase does not turn at exactly the original value but turns it a different value because of the contributions of these other di this one would go around at this right the angle the amplitude to aride is a complex number which with time time T2 changing goes around if you've added these it's again a complex number but it doesn't it goes around faster or slower different rate now what we measure when we measure the mass of an electron is an experimental world is the rate that it goes around the mass of an electron is its energy the mass and energy equivalent as Einstein showed and uh energy is equivalent to frequency as I guess it was the BR showed and uh so I keep saying mass and energy and frequency interchangeably because I'm so used to that at any rate the frequency or the mass or the energy of the electron experiment the one that we're going to measure experimentally is not the one we put into the theory so we have another Mass which is the mass experimental which we could see would be expected to come out something like this if the C Square was small very small you want to forget it to 1% you know forget that's 1% this term is of order C4 you would say first approximation comes from this amplitude you'd get something like that and then you'd have a correction because of this thing which would have a c^ squ times it in other words some correction with 101% something like that a correction that You' compute by adding these diagrams together and then maybe see four times another correction from this and so on so on that's easy to understand now it also now when we make a calculations of any other physical result it's much more convenient to express the answer in terms of this m which is a measured value than it is in terms of that so we have a habit of writing all the answers always imagine we might start with a number like this calculate everything and express everything in terms of the experimental mass that we measured which is the sum of all these things so all answers are calculated in terms of the experimental math now if you've understood me at all you probably don't understand why we got made such a big fuss of that because that's just a matter of convenience I it's just a question whether I put in here and compute that put it in here whether I direct put it in directly the difficulty is and the peculiarity the thing that bothers us is that this correction that you multiply c² by is infinity and the fact that it comes out Infinity because this function and the one for the this was the electron one and for the the amplitude that the photon gets from here is the same fun from here to here this point to this point actually not two to one I shouldn't have said that in here we're just going from here to here that multiplied by the same function for zero mass and then add it everywhere comes out infinity and uh that caused a lot of trouble for the first people who invented this Theory they s they saw they were getting Infinity for every answer because at every problem that they did there was something like this in it somewhere an electron going from one place to the other would always be possible to a photon every answer to every problem is infinity it was noticed by by 1949 it was 20 years later it was noticed by Beta and visce cup that if the answers were put in terms of M experimental it looked as if in spite of this being Infinity when you wrote the answers in terms of that and computed them there was no Infinity all the Infinities canceled out so that if you would Express the answer in terms of the final answer and not in terms of this one then everything would be finite it looked that way and it would took uh it was just a matter of a checking out that in fact that was true that's what was done by Sha and tomonaga and myself that got prizes for that but uh one way you could say all this is that this number is unavailable experimentally it doesn't mean anything you put into a theory let's for a moment imagine it well so that whatever this is I can always adjust this number so this comes out fin if this is infinity I put minus infinity in for that and that's one way of saying what we ultimately are doing although this looks like it comes out of infinity we put minus in uh this comes out let's say not Infinity 10 billion then we put in 9 billion 999 want to get one so if or whatever this is so uh the idea is if this is goes toward Infinity in a calculation we just say well just keep on adjusting the m so that it's to fix it back so the M comes out finite now you laugh at that because you have some kind of a feeling that's a dippy way to do mathematics and it is and this dippy way to do mathematic is the way we do this Theory because we don't never been able to straighten it out but we do know that if we do this dippy way we get results which agree with experiment if it had been that this correction were finite there would be no problem of course because the fact this would be some number and there would be another number but this fact that the corrections infin is very annoying and as a result of that it has turned out it is not possible to prove at the present time that the entire theory of the quantum El dynamics that we've written down is really self-consistent that there's not some if we calculated everything extremely accurately we wouldn't get into some difficulty in itself that the mathematical structure of the theory is self-consistent there's a nervous condition that there's something wrong with need that we start with a nice number and have to put minus infinity and play games like this that annoys us okay so that there's one problem what I have to say is that in this although the calcul this calculational scheme is quite definite and we know exactly what to do this process which is called renormalization uh we uh are not satisfied that we're that it's a mathematically legitimate process but you notice that when we compute the 10 decimal places it agrees with experiment so it may be all right and may be a real Theory another way to describe this business is the following in making all these calculations and adding over all possible places for for the in this case there's a contrib one and two was here but in our problem where I'm having trouble let's call this three and four then we would have this at four and this at three multiplied by the photon going from four to three which is the same thing at zero and and it turns out that which when four and three are very close together that these both things rise together as it gets close together but so much that when you add all the possibility you get infinity so one way of saying this is oh your whole idea that you can have two points infinitely close together is nonsense your whole thought that space can keep on going down to the last Notch and you can use geometry to the very last infinitesimal distance is wrong we stop these sums when three and four are closer than some very tiny distance let's say a distance that's shorter than any distance or any wavelength or anything we're a able to get experimentally then this correction comes out quite small well it depends if you make the distance sufficiently small then the correction gradually builds up in order to make this correction term equal to this so that this has to be zero thought of it turns out that the distances that you have to use are are absolutely well I can't even it's no use trying to describe them they're like 10 the 100 power or something like that 10us 100 cm whereas all we can do experimentally 10- 15 that means some some oh I don't know 80 90 decimal places further on than where we are so it's always possible that nature is different five or 10 decimal places down no 20 decimal faes down you don't like it 30 decimal places down it's all right the trouble is that we cannot make a model of that a real model if we stop these things at some distance then the theory that we write is in mathematically inconsistent it gives probabilities who don't add up to 100% or it gives negative energies or it gives something silly of course it gives these things with infinite pmal amounts but it's not a self-consistent theory therefore we don't know we do have this difficulty with this Theory we don't know whether if we stop the theory temporarily it makes sense or if we just go taking what we call the limit here where we use everything do the renormalization process calculate everything in terms of the experimental mass and then forget about the infinity whether that's a mathematically sound thing so I have to explain that in order to tell you the exact position of physics today that's the problem it turns out in addition there's the same kind of a problem about the C that also has a correction if you were to have started out and imagine that two electrons were interacting via a photon and they were an effective coupling C zero c0 and now you have a correction because the photon that goes along could make a pair and then that could annihilate and make another Photon and that corrects this and so on and in exactly the same way the effective coupling constant which is measured experimentally see I cheated a little bit I said it was that it isn't it comes out like this that the experimental coupling constant is equal to c0 squ plus Corrections of the order C4 see because you have two C's here and four C's here times a correction yes you guessed it that's right this correction is also infinite and causes the same nerve-wracking business but this is measured experimentally make that zero and it'll come out okay cuz 0 * Infinity is finite never mind all that if we W if we put the results in terms of the experimental constant then there's no difficulty and all the Infinities disappear so in other words we have to use the renormalization trick twice once for the masses and once for the charges uh once for charge once for the coupling constant which is called electric charge and the other for the mass of the electrons okay and when we're finished we get a coupling concept which we have to look to experiment to measure so that uh is simply a technical difficulty perhaps and maybe a real difficulty but anyway that's the slightly discomforting condition in which the theory is that's the second the second the first main problem now with regard to questions about electrodynamics if if you say I accept that that probably is okay or if it isn't okay I'll wait for some mathematician to find out for me we then have the following interesting physical problems I mentioned before where does this number come from from experiment I know but a good theory would have that this thing is equal to 1/ 2 * piun * a cubot of 3 * 6 and so on so that you know what it was if you know what I mean it it's a number that has to be put in that nature has or so to speak if you're religious you would say God has created that number but we would like to try to figure out if we can a little clue as to how he thinks to make a number like this for example Maybe that why isn't that a four there you see okay in the same way uh by the way you might ask in the same way what is the mass that is also a number yes that's also a number if you write the mass of the electron and I'm always going to put the experimental masses down it comes out a number there so and so many gram and why is it that many GRS you first have to tell me why a gram is as big as it is it's because but somebody chose a gram I think during the French Revolution or something they decided such and such is a gram and that an electron is so many grams that's therefore not a real problem but nevertheless I'll put it down here as a problem I'm not going to use Grand I'm because it's a too many zeros we have a particular unit which doesn't make any difference what it is but we call it the million electron volts it's the energy masses and energies recover that you get when you have a million volts and have one electron fall through that much difference in bage and I this mass is known many more decimal places but I'm not going to bother you anymore with these long strings of numbers so the mass of the electron is this and of course we don't know why it's that particular number that depends on why we chose the gram the size of the or the electron the volt the size it is okay and that uh so that is not by itself a serious problem but the reason I write it down is that it's going to turn out that there's large number of particles in physics not just electrons there's as I mentioned several dozen and they all have masses and they're all different and they're all the same problem where did this one get its M they're all relative to you can't play games with the grams anymore one's a ratio for example you find one is 67 times this one why so this is the mes are in general a problem which we do not to which we do not know the answer so we have no way to determine this mass now that summarizes all of the problems associated with Quantum electrodynamics the most beautiful one is the coupling constant 137 point and so on and all good theoretical physicists put that up on their wall and worry about it there is at the present time no idea of any utility for getting at that number there have been from time to time suggestions but uh they didn't turn out to be useful they would predict that the number was exactly 137 when it looked well the first idea was by Edington and experiments were very crude in those days the number looked very close to 136 so he proved by pure logic that it had to be 136 then it turned out that them experiment showed that that was a little wrong it was near 137 so he found a slight error in the logic and prove with pure logic it had to be exactly the integer 137 it's not the integer it's 13703 60 every once in a while someone comes out and they find out that if they combine Pi's and E and twos and fives with the right powers and square roots you can make that number it seems to be a fact that's not fully appreciated by people who play with arithmetic that you'd be surprised how many numbers you can make by playing with pies and twos and fives and so on and if you haven't got anything to guide you accept the answer you can always make it come out even to several decimal places by suitable jiggling about it's surprising how close you can make an arbitrary number by playing around with nice numbers like Pi I me it's a and therefore throughout the history of physics there paper after paper of people who have noticed that certain specific combinations give answers which are very close in several decimal places to experiment except that the next decimal place of experiment disagrees with it so it doesn't mean anything okay those are the problems Quantum molecular Dynamic now the next part is the con connection of quantum molecular Dynamic to physics to the rest of physics and we're going to have a good time now with the rest of the electric because I'm going to tell you all about the rest of physics and you can compare the laws of the rest of physics with the laws of quantum electrodynamics but first I must say immediately that the rest of the laws of physics are not known as well as Quantum electrodynamics and therefore what I have to say is to a logic is to a varying degrees uh uncertain uh nowhere near as certain as the electrodic so I uh first there must be a connection because there have we have to discuss one point the photon which couples to the electron also couples to the nucleus that's why the electron is AED in the nucleus so there's something inside the nucleus that couples with a photon and we sometimes say it's charged to say a particle is charged or something is electrically charged is merely a statement that it couples to a photon as photons is absorbed by or emitted by it that's what it mean anyway nuclear particles are charged so we in the beginning of the history of this thing knowing about the nucleus and puddling around looking at them it became pretty clear that it's easy to understand nuclei of of the atoms that tiny little Center where the electrons go around they're different from atom to atom and they could all be thought of as being made out of two particle a number a number of particles of which oh how do you say it in English a group of particles which are either protons and neutron like for instance a particular carbon for example is a nucleus has six protons and six neutrons in it nuclei can have uranium has 146 neutrons and 92 protons in it and so on hydrogen the simplest nucleus has just one proton in it and so it goes so out of protons and neutrons the nuclei can be made but the protons and neutrons that are in the nuclei stick together quite tightly the forces are very much very large the energies that are released when you let them jiggle around are much greater in proportion as the atomic bomb is more effective than Dynamite because the dynamite represents a rearrangement of the electron patterns and the atomic bomb represents a rearrangement of the proton neutron patterns and the relative energies are very large the particles that interact that we well when we tried to at first first guess would be that the proton is simple also and at the propagation of a proton that we make diagrams for proton same way all we have to do is put the mass of a proton in here problem first it must be that there's more than just photons involved because the forces in nuclei are stronger than electrical forces by about 100 times if we would invent some new Force we would have to have a kind of a csquare of the order one not 137 because the size of the forces needed are 100 times bigger than electric forces we call those strong forces strong forces are those which somewhere there's a constant of coupling closer to one than it is than electricity I mean it might be a quarter it might be a fifth might be two but it's not 100 not 1% in investigating this the at the beginning it was hoped that the proton was simple but the proton kept on showing that it wasn't simple at all for example there well there's many properties that indicate that it's not simple and the neutron is not simple for example the proton the electron we talked many times has a Magnetic Moment which we can start expanding like this but the proton has a Magnetic Moment 279 completely crazy and the neutron which is neutral and should have no Magnetic Moment no magnetic interaction at all if were really neutral is in fact as a magnetic interaction which is some number three three three that indicating that inside the neutron there were some charges that could interact magnetically it might be neutral but there are plus and minus or something going around in there or something so in stud to find out more about these particles which look so much more complicated than the electron you did many experiments bombarding protons on the nuclei and hitting them harder and harder first to drive the parts out of the nucleus in order to see how the nuclei were constructed but in the process they discovered going higher and higher energies that you created new particles and the names of the new particles go first they discovered pons and then muons and then lambas and chons and sigmas and C's and he ran out of the alphabet so pretty soon it was the sigma 1190 and a sigma 1386 and the Lambda 11 and so on because you just gave more numbers and those numbers were the masses of the particles and uh ultimately it is clear that is an unending number of particles there being about 400 and some odd particles at the present time which is it's a open-ended thing depends on how carefully you measured you can't go along with 400 some odd particles things get more and more complicated then it was realized that U these particles can all be understood cannot all really be we don't know because we now we're moving into partly the unknown we expect that they all can be understood as being made of others now I would like to discuss these others the So-Cal the the present guess as to the fundamental particle most of the things that are made by bombarding protons and so forth together are supposed to be made of quarks and I'll tell you about those soon those are the strongly interacting particles but in the process of the experiment some new particles were discovered which were not strongly interacting with nuclei the electron for instance does not strongly interact with the nucleus it only interacts through the photon it's a charge it's a small thing it's always got the C Square there are other particles which do not interact strongly with nuclei so what I'm going to do I'm going to divide all the particles up into two classes those which do not interact strongly and those which do right the ones which do not interact strongly they happen to be called by a horrible name leptons and the ones which do interact strongly called by an equally horrible name Barons so I start out by discussing the ones which are do not interact strongly and which are called leptons and I thought to tell you what they are well the first one in the list is put the name of the particle here and uh here we can put the mass of the particle in these nutty units me me and then uh well put down a electric coupling which will call charge the strength of the coupling to elect to the photon this is the coupling to the photon in another way but the unit I'm going to use is one for the positron so the first one is an electron and its mass in meev is 511 and it's charged to the photon is minus one by definition it's the scale in which I want to measure and I use minus because of Benjamin Franklin who chose to call the electron minus okay so we're stuck with that since 1776 no and lots of other things we're stuck with since [Music] 1776 which some of them are not so concerned as I am at any rate I now continue this list of these particles we have discovered another particle which is called the muon which has a mass of 105.6 it's 206 we know it very much more accurately than I'm writing it times that of an electron and its charge is minus one it does not have a strong interaction and your first guess would be that it propagates like an electron except that in this place where I put the mass I'm sorry after I renormalize the mass this is the renormalized mass it should just be a different number and that that's all the muon should be and that's all the muon is there's nothing different about a muon and electron that we can find except its mass it's different it has a different Mass it's just as if God wanted to try out a different number for the [Music] mass and uh for example the Magnetic Moment of a of a muan has been measured and is 01165 9 well first we calculate theoretically because it's if there was nothing have no and strong interaction no magic it's just Electro Quantum we use quantum electrodynamics same kind of diagram same game and get this number zero plus or minus one well let me get it just right it's three I think plus orus one you don't really care but the fun of it is to see how nice it works this is only the three plus or minus one that's the calculated value and the experimental value it was blah blah blah blah 90 blah is being exactly the same plus or minus three I don't want to write the one this isn't as quite as accurately calculated or measured as the electron but within the calculations and measurements they agree and this turns out to test the idea that there's nothing wrong at Short distances more accurately than the other because due to the very much higher mass that simply means that the amplitudes are changing much more rapidly by 200 times more rapidly and therefore if anything is wrong with the electrodynamics over a short distance this is 200 times more sensitive to see that there's something wrong nothing seems to be wrong so our space that's how we know from this in fact that the space is down as accurate down to distances or frequencies rates corresponding to 20,000 in these scale the electro Dynamics would be right up to 20,000 as we now know uh before there's a serious error that's kind of interesting and that produces the problem where does it come from you see now if you don't like trying to figure out where that mass comes from your problem is what what is the ratio why is this to is there another answer so to speak to some problem it's as though you had a quadratic equation that got in a book you know that has two solutions here it is with two solutions and somehow or other there's one answer and another answer but we don't know what the equation is it has those two answers I know there some of you clever kidss in algebra can cook up an equation has those two answers but if you didn't know the answer you wouldn't know how to write that equation now very recently within the last year or year or two I think it sort of gradually became apparent so it's not exactly a year or two first Clues were a little older we discovered there's another one masses this time 1860 approximately times in these units which is something like 3640 times as heavy as an electron it's twice as heavy as a proton its charge is minus one and as far as we know and we don't know much first we know it doesn't interact strongly with nuclear with doesn't interact strongly second it behaves for a few experiments but it does be everything can be understood so far by supposing it's another example of an object which obeys Quantum electrodynamics perfectly like an electron with no error but uh there is no I can't write anything down we haven't measured any magnetic moments or anything of any accuracy it's just the beginning of understanding it all right now uh obviously there's another one down here huh what you got to do is guess the rule to make these this uh lecture is to try to tell you really what we don't understand about nature we don't understand that at all that makes it very interesting to be a theoretical physicist because you have these wonderful puzzles why does she repeat herself at that 206 times and then 30640 times or whatever it is so of course you want me to write down the next one but I have no more knowledge at the present time machines are being built to try to do experiments at higher energy these are very high energies and uh they are designed to look for the another one if there's another one down here unless that's too far along if it comes out that that one should be at 10,000 we're not going to find it but if it's at 4,000 we might find it okay all right that's all that's all I can say about those particles well I say some more the muon is in fact unstable otherwise if it were stable you would wonder why it isn't in atoms why you can't have a proton with a muon going around it you can there is such a thing as called a mesic atom in which the Mew takes the place of an electron and its energy levels are all computable and everything by the regular way they do for electron the numbers are much bigger it's in instead of emitting light this atom emits x-rays but those are just numbers just shorter higher frequencies but the thing that's interesting is a muon oh by the way like the electron has an anti particle which is a positron with charge one that's true of all these particles everybody going for forward can go backwards in time like the electron when it turns around becomes a positron the muon is negative there's an anti- muon which is positive and presumably yes definitely an anti which is positive anyway the muan which is written as Mu minus by make it look nice disintegrates and it emits an electron H the muon sits here and in about 2 millions of a second an electron comes shooting out sometimes fast sometimes slow but the conservation of energy doesn't allow that what really turns out but careful experiments have shown that there are two additional particles coming out one of which is called an anti- neutrino e and the other one a nutrino mu so I have to tell you about neutrinos so I put those in the same list we have a thing called a neutrino or rather more precisely the electron neutrino neutrino e which I write a new e because I'm getting tired of writing the words that's just a symbol neutrino e it has a mass as nearly as we can tell a mass at rest of zero it always seems to go along at the speed of light its charge is zero so it doesn't interact with photons and it doesn't interact with nuclei it doesn't if it never interacted with anything we would never find it but we did find it so we have to learn something now it turns out there's another kind of aut nutrino there's another nutrino the nutrino mu you're not going to get tired of this because you're going to keep piling these things on until you're drugged there's so many particles I can't help it I'm trying to tell you how horribly complex apparently the world really looks and if I would give you the impression that since we solved 99% of the phenomena with electrons and phons that the other 1% of the phenomenal will take only 1% as many additional particles it turns out to explain those takes 10 times or 20 times the number of particles okay this one also has a mass zero although of course experiment can only measure to a certain accuracy and I'm not sure it might be as big as an electron or two and charge zero the towel huh what about it have another one huh Nino for the to well I put it in parenthesis things where everybody thinks are there but have not had the slightest experimental information they don't know whether there's one here and we certainly don't know whether the mass is zero but we surely know it's neutral because we Define it anyway what's in parenthesis are good guesses okay now about these neutrinos this process is understood this way by saying a muon comes along here this the present view of it well the first way and and it turns into a neutrino the new me type okay this is time going this way in and then I think maybe this is in the way you're clever all right now it's your way okay and uh at the same time is produced an electron use the square chalk I got the round chalk and an antin nutrino like let's put the arrows forward for the particles and backward for the anti particle so the anti nutrino would be coming in this way okay and the four of them come to a junction and the theory is present Theory which works nicely in predicting the the rate the properties of this reaction he said this is done by a wiggly thing like a photon hey you would say hey it's like a photon you put a photon in here and everything's all right except a photon can't change the charge of a particle if a pH The Junction that photons satisfied go between mu and mu not between mu and neutrino this has got to be a new particle and furthermore that the fact that this goes as slowly as it does means that this particle is either coupled very very weakly the coupling is extremely low or that it's coupled with some more or less reasonable strength but the mass of this is not zero like the photon it turns out that the present Theory the one that works very well made by solam and uh Weinberg is that this object which goes back and forth here which is the analog of the pro of the photon H has a very high mass and so we start another list of particles let's see I got all them here these are all the Leons and the list goes on we don't know where it goes okay now I going to make another list I guess the best place to make the other list is uh here which are called bosons or if you would like better would be the interacting particles they are the first one how do I do it I give the name the rest Mass and uh that's all I'm going to talk about here the name is the first one is the photon ah yes the photon it's rest mass is zero that means the mass that you put into the D function now this time we just have to put a different mass in for the D function so the other particle is called a w it's a horrible we haven't got a good name for that a w boson or something intermed or W intermediate Bon horrible name anyway we ought to get a nice name for this one which we have haven't got maybe we should call it a wion or something and its mass is 53,000 expected it's theoretically calculated but how much mess you have to put in here to make that rate right okay and the coupling constants in here about the same as the C over there like 38 of the SE or 1/4 of the c or something like that that is the constant is just the same kind of coupling as it is to a four but the mass is much higher and that makes that happen at a very slow rate so it takes 2 millions of a second two 1 millionth of a second that's slow because as you know the frequencies we been talking about how and millions and millions and millions hundreds of millions of millions of millions per second and this is only a million per second so uh now this particle in the particular case that I explained if you imagine the particle went from here to here has another property that I have to explain it turns out that electric charge is never lost in this particular experiment the negative electric charge on the MU appears in the electron but through the intermediary here it goes and therefore this intermediate is electrically charged so this thing is charged so if we wrote here charge on all this got the wrong thing to do is when you get stuck with the wrong colors then you have to keep remembering which hand has okay charge and a photon doesn't interact with a photon so it's got a charge of zero the charge means how does a photon interact and the answer is this has minus one oh I could use green I can use green minus one for the charge but if this thing the timing were reversed and this was a little lower than that then you would see that this would have to the thinking of it going backwards would have to have a positive charge and this the anti particle so that these W particles and their anti particles are found both with minus1 and + one and in addition it's been found that there is another W which is neutral and then they form a nice little triplet but the neutral one has a higher Mass probably about 70,000 me so we have here a in this Theory we have thing that looks exact very very similar to electrodynamic in the sense that you make the same kind of diagram in the sense that the coupling is the same order of magnitude the only differences are a rule two differences actually a rule about the charges about what you're allowed to couple to and uh the fact that you use the mass in here and one other technical detail which is very interesting and has a good history is that the coupling is not exactly the same as electr dnamic there I said in these problems that there are many polarization cases and the couplings are ones and minus ones and sometimes zero this one has half as many cases that are not zero it has many zeros where that a photon doesn't have so it's coupled just a little differently by a neutral one that means that there'll be a process like this for instance it could be that a neutrino comes along and comes out as a neutrino and hits an electron it goes out as an electron and what happens is that one of these W Rons goes across but this time it's a neutral one that has been discovered within the last five four or five years it's called neutral currents for some horrible reason but uh it caused a lot of excitement so we now un have have this other particle and what does it couple to it couples to the neutrino and the MU in other words what we have to ask is now what are the rules that tell you what kind of Junctions it makes let's take the Junctions with the wus the1 what pairs of particles can go we already know a Nutri even a square chalk a neutrino mu and a me is a pair of particles which can be on the junction of a w minus so they belong together and the other neutrino goes on a junction with the electron that's why we name them that way and it turns out of course that the town well we're guessing or not you see we believe there must be one it's some people who are very very unbalanced who might suggest that that's the same one as this but of course it's almost certainly a different one now uh it also turns out that a for instance a neutron I'm talking about a strongly interacting particle and I'm not supposed to be able to talk about that yet I'll come to that in a minute but a neutron disintegrates into a proton an electron and an anti-neutrino and that means that something in the neutrons and protons the quarks in fact can also couple to the W and so this list isn't quite finished and I'll finish it later on in the lecture these are the pairs of particles which belong which coupled to a w particle and we just have to keep making lists of those so for every particle there's a sort of pair friend or something that you get from the ones that'll couple with a W minus so for the electron resistance so it goes it's a kind of we don't understand any of this we just find this out and if you can figure out what this pattern is all about then uh you will have contributed mightily to theoretical physics that sums up all of the uh weak the oh yes one more important thing because this is charged the photon couples to it and there are diagrams which uh would be like this that uh let's say if like this is going across you can have another Gamay coming out of here Photon it could be coupled to the W and the also turns out that the theory is nice and neat if you allow a three kind of a three Junction like this in which a w not and a w+ and a w minus can all come together like that so we have this and we have that and the coupling constant is much the same therefore the possibility exists that the idea that there's one kind of thing a photon and another kind of thing 3 W is not right that there're four together somehow and so the theory of Weinberg and Salam was to try to put Electro Quantum electrodynamics with What's called the weak the general weak in Direction into one Theory and they did it but if you just look at the result that they've written you can see the glue what I mean is it's not a nice job okay there is at the present time it's a it's it's very likely that it's interconnected it's very clear that it's interconnected that they're different aspects of the same thing but at the present understanding of the knowledge it's still not possible to see them very clearly as different object case of the same thing you can make it look like the same thing but you can see the seene between the things at the present time it's not been smoothed out yet so that it becomes more beautiful and therefore probably more correct but it is uh part of our Theory today that these things belong together and the reason they and they belong together in such a way that that you can explain the connection between the coupling constant there coupling constant there but that at the present time is not explained numerically it's just has to be measured all right that's the end of the weak interactions ah we can breathe a s of relief it's a limited number of particles you're still within the possibility of un keeping this in your head but now if we start with the protons and the neutrons and hit them together we get this enormous number of particles and the nice thing if I would give these lecture perhaps 10 years ago I would show you all these particles and make the long list of them then my list that's starting here would have 405 objects and so forth and I'll tell you all about the properties of them and then I would explain to you that I believe that none of them are fundamental in the sense that they're propagated by one of those nice little formulas where you put a mass in because they all appear method behavior is not like them that but in the meantime in the 10 years there's been developed a theory to explain this multitude by supposing that they're made out of other simpler things called quarks simpler in the sense that their propagators are simple functions where all you do is change the mass number okay now this Theory the theory of quarks is uh what I must next describe and represents the theory of strong interaction so let's use this I see there are more particles here you see but this board doesn't go into here it goes under and we can't see it all right now here's a new piece of paper on top of the other one uh which are called which are the strongly interacting particles and I'm not going to list those but the particles that are that they're made out of which are called quarks and we're going to make a list of the quarks uh by the way uh I have to say something I I've been leaving out polarization all the time the polarization effect and I'm not going to explain it now but the electron has a different type of polarization than the photon but all these particles in this list have that type it's called spinner half is the technical language for that kind of polarization and the polarization of a photon is called spin one and the W also has spin one so this list corresponds to a kind of polarization of spin one and this list up here is spin a half and is it turns out the quarks will also spin ahead same all the same now what are these quarks what the is the story it turns out that a thing like the quarks come in a there are many different quarks just like there are many different leptons and they have names which are so bad I'm going to give them letters instead of names the names are up down strange charm Beauty and so on forget it I prefer to call U type D Type S Type C type and so on instead of giving them long names we have the following kinds of quars a u type A D type an S Type A C type A B type recently discovered and as we'll go along we'll see there must be more almost certainly and the next letter that we're sure we're going to use when we find it is T some idiot named this charm particle and this one Beauty particle and this one truth particle and I can't stand it so I have to my letters these are the the quarks and the proton for example is supposed to be made out of two U quarks and a d Quark three quarks inside going around inside three of them two use new type 1D the new Neutron is two D types and one U all right now of the 405 particles that I don't well 405 that's silly the hundreds and hundreds of particles I were talking about before they go into two classes those which when they disintegrate ultimately end up as a proton at the lowest energy and that like a neutron does for instance and those or all objects which called they're called uh barion and they have made out of three qu so some of these particles are made out of three quarks a certain class another class is called mesons of which pons are an example are made out of a quark and an antiquark and that's all we found there ain't no four Quark guys or two Quark guys or even one Quark guy what no one Quark gu that would mean that you can't get these quarks apart so you can see one so far we have been unable to get these quarks apart so you can see one you can hit those protons together as hard as you want I mean as hard as we're able to and the quarks never come out all they do is move around produce new pairs and form new groups of Threes And particles and antiparticles we can't get one separated as soon as you get one separated new pairs form in this neighborhood particle anti quark antiquark and they group up so that their Quark antiquark pairs are groups of three at any rate uh the problem is of course what holds these quarks together inside a proton and that force is large that's what's strong and that has to be done by another thing because the W's are couple weak and the photons couple weak we need something that couples strong and so I need another color for my chalk actually I need three colors for my chalk if I wouldn't play with the colors right now we have pictures of what the cork do inside a a proton for instance we would say here's a proton let's say just to make it nice no I better not do that there's a u and a u and a d Quark going along and then from time to time there's a kind of photon but it's not a real phot it's a different thing it's called a gluon you can imagine the level at which the physicist who can call that truth they can't what is they call it glue CU it's a particle Like Glue holding these things together so it's a gluon and the gluons go across and do various things in here in the complete analogy to the way the electrons have photons go between them in an atom and the gluons then are the next particle and why the colors are shifting here I'm not quite sure but there are gluons okay and they have a rest Mass zero like photon and the zero charge but they couple strongly I should put down here couples to electron or couples to charge this one couples to those pairs and this one couples the quarts all right the particle has the same polarization characters the photon and so on we just repeated it just looks like I've just repeated Quantum electrodynamics at a different scale with a stronger coupling it's almost that it's very close to that it's almost exactly the same as electrodynamics on a different scale I would now yeah I think I don't know whether it's worth describing exactly the difference it's rather curious and interesting and uh I see I have a little time so I'm going to do that before I do that I have to finish with two remarks one we still have to ask how does something like this happen and the answer is it's the quarks which are doing it it's the uark which can turn to a d quark and electron and nutral so that inside here I'm sorry I got it backwards D turns to a u so that the ddu comes to the U surprising but you only have to change one of them to do that because they they're moving around so the D turns to U so really this is not the fundamental rule but the fundament damn this excuse me Square J is is that the D partic Quark can turn into a u Quark plus an electron plus a neutrino and that that's pictured by supposing that on that line that we can have the following diagram let's see I got for some dumb reason I've caught myself by making all the quarks blue and so on it's terrible I don't mean anything by these colors but this is to remind you it's a quark this is a de Quark turning into a UK quar with the emission of a green thing a w Meson and then going into I got myself into a pickle okay I should have anticipated that I get this difficult the colors are just to keep cack out the different types of particles to help you a little bit electron neutrino I get the sign wrong yes I got the sign wrong it's neutrino electron oh yes in this diam it's an anti nutrino that just means this arrow is up there that's all right you can that's clever you know how to turn that up there and this is a core coming in here so we have to say in addition that the uh W particles couple not only to these pairs but also to other Pairs and another pair it involves the quarks for example here would be that it was H the U Quark coupling to the D all right this is not quite right I'll put that there to remind you not quite right uh this turns out that the C qu couples to the S not quite right and nobody knows what the heck goes on Beyond what's not quite right is well I have I say one more thing that tells us how the W's couple to the quarks almost there's a slight fixing I have to do now I Al also say that the photons coupled to the quarks we know that because we know the proton is electrically charged and if it's going to be made out of quarks then the quarks have to be electrically charged electrical charge means that the photon couples to it now the electrical charge in this case has to add up to one the electrical charge in this case has to add up to zero and the difference between these two must be one in order for that to work any when you get finished you find that the Ed have to have a charge of plus 2/3 in other words the the charge of these particles goes like this plus 2/3 for the U and- 1/3 for the D and - 1/3 for the S and plus 2/3 for the C and let's see the B the B is probably minus A3 but now we don't have too much it's a good guess so we haven't checked it but the others have much better understood and so of course the t is no doubt plus 2/3 but that's waiting to be found now with regard to the mass I cannot really give an answer there's no way to define the mass because you can't get the particle out separate and so we have technical arguments as to different ways of defining a m and everybody who defines the mass differently comes to different numbers here so the numbers I'm going to write here are not accepted by everybody and I wouldn't accept them myself on another lecture when I redefine the way I Define it but the main feature I'll Define it somehow and put some particular way of defining it this is 400 and this is 42 and this one is 500 roughly and this one is uh 1,800 or, 1900 no no no 1600 and this is 4500 when they get heavy everybody agrees with the definition but when they get light the problem is the interaction energies are so big that you can't tell how much is due to mass and how much is due to coupling in his heart of the fire the feature that we do know is that these two are the same and this is more and then when they get heavy we got the numbers okay these are lighter so that the lightest of all of the strongly interacting particles are made of un and D quarks heavier ones involve sometimes an S for many years we thought the only kind of quarks we would have were the ud ands by the way the names of these different you want to say different kinds of quot you say different flavor quot the flavors that we had for many years are just these three and in 1974 we found a particle called the P Meson which could not be made made out of these quarks and there was also a very good theoretical argument that there had to be a fourth Quark having to do with that theory over there the wiber inste and that's called the sequar that one belongs with this number and uh that checks out and very very recently within a year or so ago we found another funny particle which means that it has to be another qu another flavor all right and so that putting down these charge numbers and telling you what pairs coupled to the W and Ming all these pictures tells you almost the whole Theory the only thing that's not quite right is this it turns out that the U which I drew here let's say the U is connected to a d the U can also be connected to an S and in fact when the U goes through like this it turns into a d or an S one amplitude for D another amplitude for an S so that what really happens here is that combination some amplitude for D and also some amplitude for S and in here it's a it's a big amplitude for d and a small amplitude for S here's the other way a small amplitude for S and a big amplitude for S and a little amplitude for D it is very likely that there's some amplitude for B in here also in fact there's pretty good evidence that there's a very small amplitude for B so I could put that in but it's not known very well why it chooses these proportions for those two amplitudes is utterly unknown so I got everything out it's terrible mixup and youd say the Hopeless Mass physics has got itself worked into it has always looked like this it's always looks like a horrible mess but as we go along we see patterns and we push them back down so that uh we put theories together we combine this stuff and pretty a certain Clarity comes and it gets simpler it's a lot better than the terrible mess I would have made with a 405 particles a few years ago the qu the thing that I would finish with uh I would I think it's just as well that I finish a summary rather than to describe in more detail how these gluons work it turns out there are eight different kinds and so on but I'm not going to complicate that the thing I would like to emphasize though is this that all these theories are very similar to Quantum electrodynamics they have little quicklet changes little small counting changes but they're very similar they all involveed the interaction of a spin 1/2 type object with a B on of spin one type object uh one case is obscure because it has a mass but as a matter of fact all the masses are obscure so now let me talk now about the Grand Problem the character of the theories forget about the masses for a minute the character of the theories certainly indicates well looks like they're the same somehow they're very very similar but remember something we have not yet checked quantitatively this Theory with the gluons it might be wrong we have only got a few experiments to check W boson that might be wrong on the other hand why does it look like it could be the same thing being repeated there are several possibilities one a limited imagination of man when he sees a certain Theory and he sees a new phenomenon he tries to fit it with that theory and until he's made enough experiments he doesn't know that it doesn't work and so when he gives a lecture in 1979 in New Zealand he thinks it works and he says this is the way it works and it's look how wonderfully similar they are it's not because they're similar really it's because all we've been able to think of is the same damn thing over and over again another possibility is that as a matter of fact it is the same damn thing over and over again and uh that nature has only one way to do it so to speak and she keeps repeating her story from time to time and there's a third possibility and that is they look very similar because they are different aspects of the same thing that there's some larger picture from which is to be understood that the thing breaks down into what looks like different things but they're different cases of the same thing not different cases uh well it's very hard since I haven't got The Right theory I can't exactly explain myself but I'll try the best to say that there is one large object which has supposedly a first approximation well has a whole lot of fingers and these are the different fingers but they all belong on the same hand they all got the same characteristics and the reason therefore that they repeat the pattern of having the same kind of interacting part and the same kind of coupled particles is that they have the same they really come from the same thing and so there are many people of course working trying to get the grand picture which puts all this together in one super duper model and I have promised you in these lectures not to talk about speculations but things that have a reasonable experimental check none of the speculators agree with any of the other speculators as to what the grand picture is throughout this entire story however there remains one un satisfactory feature and that is the mass numbers there is no really satisfactory theory of the origin of these masses we can write this stuff down and we see the pattern but we don't know where these numbers come from there are theories which suppose that there's still another kind of particle which generates Mass it has a different kind of polarization you'll like that one it has only one kind of polarization not two like a electron or Photon it's called spin zero there proposals that there are spin zero particles in the world and various theories to show how they might produce numbers of masses but not one of those theories really produces the numbers that we see in a satisfactory way it just says maybe they will come out maybe it'll do this and maybe it'll do that and the more you look at it the unless it turns out to be the case that it really does what you want it to do so we do not have any understanding of the masses and I believe that from the fundamental point of view that is probably a very Ser a very interesting and serious problem the particular work that I do is work on is this it turns out that this theory of the gluons and the quarks is a very definite precise Theory it has only one constant in it plus those masses the coupling constant the coupling constant however is large and the method that we use to make calculations for electrodynamics work successful easy calculations in which we approximate by first tying out the diagram with the least number of of these things and then more and more because the more you put in the smaller the contribution because of the 1% when the coupling is Big the diagrams with many of these and the diagrams with few of them are both are all important and the problem is to add together in some other order not just by starting out with no gluons and then putting in one gluon it'll never work it is true that at very high energy and very high energy collisions it does appear as if it is right to make start with an approximation in which youed have the minimum number of gluons and make a correction for one more gluon and so on and in those experiments you can calculate or predict certain Trends which ought to occur and those Trends do occur in experiment which is the only evidence we have that this theory is on the right track because at the present time although we have a definite Theory we have a situation that's never before existed in the history of physics we haven't been able to calculate anything from the theory therefore we can't compare it to experiment it isn't that there aren't experiments there are hundreds of experiments with the strongly interacting particle all kinds of experimental accuracy in detail it's just that we can't calculate anything with this Theory and that's not because the theory is indefinite we have a definite proposal and a definite results let's compare the theory to experiment the usual thing you're supposed to do it tells you in books science is very simple you make a theory compareed to experiment and if the theory doesn't work they throw it away take then make a new theory compare it to experiment throw it away well here's a theory compare it to experiment we don't know how so we're boxed temporarily in making a method of calculation to compare it to exper uh so I'm trying amongst other people also trying to figure out how to improve our methods of analysis so we can make it a re a reasonable mathematic analysis gra in all this I disregarded I didn't discuss gravitation the reason I didn't discuss gravitation is this uh the gravitational influence between objects is extremely tiny so tiny it holds you in your seats wait between microscopic particles between electrons for example or between two Neons or protons and so on the my gravitational force is very small as you know the force between two electrons varies inversely is the square of the distance and the product of the charges that's electric force and there all gravitational force is the prod the masses and invers is the square of the distance and one varies the same way as the other and one is very much smaller than the other in fact the gravitational force if you don't like big numbers before you're going to get them now is weaker than the electrical force between two electrons by one followed by I mean the fractor is one followed by 40 zeros and 41 zeros perhaps and that's so tiny that it you'd say oh I will never see gravity at all the difference is that gravity is like attract whereas in electricity unlik likes repel and so forth so when you have a lot of objects you have a large number of particles the gravity keeps adding and adding and adding and adding but the electricity cancels the plus and minus so what we end up is all electrical forces which are so enormous between the electrons and the protons simply hold the electrons and the protons in a terribly intimate mixture of matter matter is a fine mixture of plus and minus charges so Fally all cancel each other out so on a large distance there's not much left but gravity keeps on adding and adding and adding and so at last when we get to these ponderously large masses that we are we begin to measure the effect of gravity on planets on ourselves and so on because of this from an experimental point of view it is impossible at the present time to get any experiment in which any Quantum question about gravity is involved in order to produce a gravitational influence you have to have so much matter so many gravitons if there were any that the quantum approximation is unnecessary of course it is not possible in the world to have this framework of amplitudes on part of the world and not the rest of the world so it is not a satisfactory situation to say that when the matter is big enough I'm going to make this approximation forget it when the question does come up is there a Quantum picture for Gravity yes there is a Quantum picture for gravity and there the same kind of business a thing goes across we have to have a different color chalk for that and it's called a graviton and it would be appear in this list except its polarization quality is a little bit different than a photon it's called spin 2 and the gravitons go back this picture has it that the gravitons go back and forth but in any practical situation there is so many of them that we can use the FI Theory without thinking about the quantum theory it's also true that the quantum theory of gravity has Infinities like the electromagnetic Theory but they seem to be a little bit more difficult to get rid of anyway that summarizes all that is known by man as far as I knew when I left Caltech before I started to give these Lees it is always possible that somebody has figured something out in the meantime or measured something in the meantime that I haven't yet heard of about down here in the southern hemisphere which I enjoying by the way very much and uh I hope you've enjoyed this talk and I'm open the situation to the lecture the questions I guess I'll let you ask me questions I'm done with this [Applause] lecture could you tell us something about a possible relationship between Quantum electrodynamics and gravitation no I don't see it I this they' got a long history you see at the time when Einstein worked out his theory of gravitation he paid it's not the quantum theory it's the What's called the classical approximation field Theory the other important theory in the world at that time was the theory of electrodynamics also a field Theory not with the amplitude and so at that time time the problem was to put the was always the problem of physics of put everything together so at that time the problem was to put electrodynamics and gravity together all right but the electrodynamics and the gravity were both wrong there should have been quantum theory and in addition we find many other things in the meantime the problem is to put everything together there's nothing special about trying to put electrodynamics and gravity together any better than putting Quark Theory and gravity together or what the only one that I know how to that there's some real advance in understanding how to go together so far is this W mezon and Photon that's electrodynamics and weak interaction the problem is to put them all together ultimately and that is the problem I was discussing and how far we've gotten is not very far but I would not choose for historical reasons to think it's more important to put gravity with electricity than to put any other combination together do the correction factors which you mentioned at the beginning of the lecture and which operate at very short distances imply that space is quantized yes that leads to a lot of possibilities it could be that space is quantized and so on and so on but all the experiments you see are in agreement with supposing that distance is virtually zero and we don't know where it is it's certainly Way Beyond the experimental range which corresponds to 10-5 CM it doesn't mean that it could be quantized at 10 20 cent but this is a interesting feature I forget the question I forgot to repeat the question the interesting feature is uh that if people try when people have tried to make a theory that space is quantized they get into difficulties they have nobody has made up a nice theory that space is quanti that agrees with observation it's not so easy to make up these theories what one does all the time is fall into one or another pit either you come that the sum of the probabilities is not 100 of all events is not 100% or it turns out that you can get states of lower and low more and more negative energy that would be very useful because what we could do is we could take some object and send it into an energy is conserved the total energy in the world is concerned but suppose I had this object I can put it into a place where it has negative energy and get some positive out because I start saying with zero you want more put it in a more negative energy get more on so it's obviously unstable universe if we can have states of negative energy of ever larger possibility these are the kind of things that happen to a poor individual who tries to make up a theory with some arbitrary thing like a lattice in space or something he gets into that type of difficulty there are very few self-consistent theories and that's uh the only ones we really know how to write are ones in which we suppose Point like space time and these propagators with some masses and one or another of the various kind of polarization systems these are what we call spin zero spin a half spin zero we don't have knowledge that there are any fundamental particles spin a half all these spin one the photon W and the gluon spin two is there is possibility in principle of spin three heads but we know of no fundamental particle with that spin two is a graviton thought by the way there are uh it's not the answer to your question I finished your question but I must remark that there are many interesting theories which try to put the gravity electrodynamic but they always invent a lot new other particles that have to go along with it such as spin three half fundamental particles and so on but at the present time the biggest of them is not able to com to include the particles we do find and invent a lot of particles we don't find why have gluons not been observed yet I didn't completely describe uh the Glon Theory and I don't be afraid I'm not going to but just like there were three of these coming together so in the gluon theory there's also three of these coming together I I say that not in answer to your question but to make a something I had forgotten to say uh this uh is the place that smokes out as clearly as possible that we don't know how to calc the most simple thing in this Theory the simplest thing would be what is the interaction energy between a pair of quarks as you pull them further and further apart in the case of electricity the energy it takes to pull a pair of particles apart the force it takes the force it takes goes down fast enough that it takes a certain amount of work and you can get them apart the question is whether in this Theory as you pull the quarks apart the force decreases fast enough so that you can do it if the force stayed constant no matter how far you pulled them you could never never get them apart it is believed hoped is a better word that if we really could analyze this thing that would turn out to be the case now the first thing you try is to suppose it's the other way and you find no there's something there are terms in here that look funny it's hard to calculate it's not so easy to show that the force goes to zero when they get far enough apart therefore it could be that the force doesn't go to zero as it get far enough apart all I'm saying is the theory is complicated enough that we can't at the moment can't tell that's why I'm so anxious to figure out how to calculate something even the simplest qualitative question as to whether the force increases or keeps Falls with distance fast enough or not is not at the present time been analyzed yet from this Theory it's a something I think that theoretical physicists should be ashamed of when you think of how much money is put into doing these experiments and the big apparatus and so forth and here we just sit around with a beautiful Theory and Mumble about it and can't calculate any numbers we shouldn't get our salaries I think well maybe they should be raised we'd work faster I don't [Music] know I'm still worried isn't your theory really still a wave theory he's worrying about a wave particle duality that I described in lectures 1 and two and says effectively that I convinced him that it's particles in lecture one and then I did a lot of calculations of amplitudes which seemed to him to be nothing but the analysis of waves which the same kind of calculations that we do for waves and why don't I admit that it's a wave theory you that I'm really using and I Tred to explain that in uh two features about it I chose to say talk about amplitude to go from one place to another directly as a given answer it is also possible to analyze that by saying and I did say this that you could think about the amplitude to go from here to here and then the amplitude to go from there to there and in that method of analysis you can write it as differential equations if you want a mathematical form that look that the same mathematically when you're dealing with a single Photon as the max will equations for the wave there are two differences first let's take the case of a single Photon in which it turns out that the calculation of my amplitudes is precisely the same mathematically as the calculation of the electric field according to Maxwell's equations which is a wave theory the difference is in the interpretation of the answer the square of the electric field for example in that theory is supposed to be the energy density in Space the square of the wave function although mathematically determined by exactly the same equation is the probability of finding a photon so another way to answer it for the case of single photons is to say this we calculate as if the light is a wave but we interpret the intensity of the wave what used to be called the energy density of the wave not as the intensity of the light as but as the probability of finding a photon it's that duality of interpretation which produces the difficulty because if this were really a wave coming in we couldn't understand how the photon counter would acquire enough energy to go off sometimes immediately when you turn it on no you see if for example a wave is shining on a a surface a metal surface we find the following that if you shine light on a surface and you shine a lot of light a lot of electrons come out with a certain each one with a certain energy if you decrease the intensity of the light that is weaken the waves you would have thought that the wave would kick the electron less and so you get a lot of electrons out with less energy that's not what happen you get fewer electrons with the same energy and when your wave has gotten so weak it could hardly Shake an electron at all you still see an electron come out with a full jab of energy only once in a great while and that Paradox has to be described by not Chang you see it would be a miracle if the mathematics would change because nobody was going to play around with this wave theory that long if it didn't agree with experiment so there's something right about those equations the behavior of the amplitudes they were describing it wasn't interpreted right first second I've talked about out not sufficiently and this is a difficulty that many people I answered somebody else this way have with this wave particle business and these quantum mechanics is that they're always the first thing to do when you're giving a lecture is to take the simplest example and the simplest example is always one particle but suppose the same way we take two particles two photons I've talked about amplitudes for two photons to come to two points now the amplitude if you thought of it as a differential equation is an amplitude defined let's take electrons or have two electrons the amplitude defined if you understand it I'm wrri it mathematically because you were asking me a mathematical question the amplitude to find one particle at a position in space I'll call X1 it's a vector position it's a thre Dimension and the other particle at a position X2 that's a function of time when there's only one particle it's a function of X the position of that one particle and time now it's characteristic of electric fields of fields in general that the functions of position and time but when there are two electrons or more the amplitude is the amplitud to find just like the probability to find two electron one here one there at the time T this kind of a function is not away it's a function of two positions in space and time that's a new one when there's only one particle it's a function of one position in time then it's like a w when there several particles the functions or the amplitudes we have to talk about are functions of several positions in space and time and that's not a wave in a normal sense so knowing that that's the case I emphasize with a slightly different attitude and I don't I know I'm talking about wavs if I was talking about one particle but not if I'm talking about more okay you haven't told us very much about quarks and gluons uh it's true that I left out an important thing because of the shortage of time in a to make a complete disc description of these things I'll just say it that the quarks of each flavor like the U type Quark really comes in three varieties there's a we call them colors a red one a green one and a blue one they not they have all the properties the same they're all the same charge and mat they're all exactly the same it's just red green and blue that's three different kinds what are the three quarks that form a proton has one red one one green one and one blue one always always a three different on the way the gluons work just to make a quick thing I be done in a minute let's suppose that now I'm going to change the color system and draw pictures with the right colors for the quarks you see red green or blue so we would if I would say I have a a green deco okay and it could turn into a red UK for instance and in doing so it emits a glue on which I've been drawing as orange but it's a special kind of a gluon it's a gluon which has a went out a green in it and anti- red it has it's like if to draw it correctly I should draw colors for it green and red going the other way and what happens is if you draw these things the colors always check out for for example this could connect to a red let's say it could be a connection between another quot let's say a red D would then turn into a green U or something like that or a green s or something no I'm sorry it don't change the type I'm sorry it has to with the glue on it keep the the flavor fixed so this is say a u a u and a d interacting but the colors get exchanged what the gluons do is they carry colors back and forth and the reason why there's a three thing is that gluons coupled to any kind of color business so if you have a gluon which is the the green an the red one say you can connect it to a green an anti- green blue one for instance if you emitted a anti- red blue one so the quarks the glue on have colors and since there are three colors and you have every kind of combination you would expect three * three or nine different kinds of gluons actually there are only eight different kinds of color combinations the particular combination which has an equal amplitude to be red antire red blue anti-blue and green anti-green doesn't exist and that describes the theory much more completely than I did before that with that game with the colors uh we have a pretty good understanding of why it's only that three particles come together or a quark and antiquark only colorless combinations combinations which are symmetrical in color that don't have any bias in color are the low energy State any other states presumably take infinite energy to make or something can't be made so you need a red green and a blue you need three okay thank you all very much and thank uh Rob for the opportunity to give these lectures often thought I've never been able to figure out how to explain electrodynamics and Quantum electrodynamic and I thought that this was a opportunity to try on a poor unhappy audience to see whether it was at all possible to explain this subject in a finite number of lectures and I chose to come to a part of the world as far distance as possible for my [Music] home so that if I were not quite successful I wouldn't have supper so directly thank you very much for the opportunity and for your patience in coming all the time to the link [Applause]
