Lecture 1 | New Revolutions in Particle Physics: Basic Concepts

Stanford University all right so what is particle physics about particle physics is about particles it's about the question and this is a very ancient question at least I suspect about 2500 years old this nature discrete discrete meaning to say not that it's polite but that the that that matter and substances and energy they didn't think about energy but they thought about matter that matter comes in discrete units in indivisible units which of course the Greeks called atom I am told that the word atom means indivisible despite the fact that of course we break up atoms all the time nevertheless that was the origin of the word indivisible that all things in the universe are made up out of something discrete let's call them particles particles is a good name for something discrete something indivisible that idea is as I said extremely ancient the opposite idea is also ancient again I don't know precisely when it was first formulated I happen to remember a little more about the history of the atomic idea that was this matter who it is incidentally do not trust my history not because I don't know the history but I sometimes tell the history in which in which I organize things logically rather than rather than temporally so don't trust the time sequence that I tell you it often represents what I wish the time sequence was rather than what it actually was but it's good for being the presenter logic of what happened to presented in a logically compelling way rather than a strict historical way in any case are there were these characters who were the Animus and the the opposite of them the people who thought that matter material and so forth was continuously distributed continuously distributed means simply not made up out of discrete elements but I don't know what the right word is uniform continuous is the right way right word a schmear as my grandmother would have said a smear smeared out of a space in some uniform continuous kind of way and we might call that the field theory of matter fields what are fields fields are functions in space for example they could be the density of material are in in a given region of space they could be the electric and magnetic fields those are good examples electric and magnetic fields that determine how charged particles move but the fields themselves the electric and magnetic fields are things that we conceive of as being uniformly distributed in space not not in the form of particles and so perhaps matter liquids solids and so forth are also in some sense continuous just like the electromagnetic field that was the opposite idea ah the particle idea that the screen idea had words like molecules atoms and so forth collisions and particles the continuum idea continuum is the right word the continuum idea had words like Fields attached to it continuous fields of properties of various kinds which turned out to be right in some sense neither and both in some sense neither and both turned out to be right the subtleties of quantum mechanics got in the way of either of them being completely right but it also got in the way of either of them being completely wrong quantum mechanics is a subtle and difficult subject ah as are many of the preliminaries of particle physics I think I have taught all of them by now several times and they do exist on the internet the internet lectures that I've given they're out there and I advise you as I said I will try to keep it self-contained but I am going to assume to some extent the knowledge that I have taught previously in these classes it can be picked up off the internet very easily I don't know how to do it I couldn't do it for the life of me I can never access my own lectures but everybody else can do it and now the real reason is I don't like looking at myself so I never I never do open my own lectures but they're out there and they're fairly complete there are at least two courses out there on quantum mechanics I think one on classical mechanics at least one on special theory of relativity and and electromagnetism so since I put that effort in I'm now going to try to draw on it not today but in the future and use many of the things that I have lectured about okay as I said the particle physics question is where the nature is discrete or not let's just do a little bit of history which I will probably get wrong but the that's at least chronologically to my knowledge the first real evidence as again it's to my knowledge the first real evidence that matter was discrete came of course from chemistry it didn't come from physics it came from chemistry the division between chemistry and physics is a highly artificial one chemistry is simply just the basically the physics of atoms and molecules but it came from the chemist or John John Dalton John I think John Dalton who realized that the masses of chemicals the mass of a given number of molecules are given number of molecules now how he knew that he was how to deal with a given number of molecules when he might be talking on the one hand of hydrogen in other hand of a carbon dioxide of something how he knew it was a given number of molecules is itself a story Avogadro's name comes into it and so forth the word mole not the creature that lives under the ground but the the mole is Avogadro's number of molecules how they knew how many molecule they didn't know how many molecules but how they know how to compare different substances and say both of them have the same number of molecules that itself is an interesting story but it's not the story I want to tell the story I want to tell how to do with the mass of a mole of material a mass of a given number of a god rose a number of molecules that it came in discrete multiples of the mass of a mole of hydrogen now not exactly but close enough to a pretty good precision R the mass of a mole of gobbledygook is a integer multiple not three not three halves not pi not the not some other silly number but some integer times the mass of the same number of molecules of hydrogen that sort of suggested the Dalton that they were building blocks that carbon was a carbon eight carbon twelve carbon twelve had 12 units of whatever hydrogen one had hydrogen was one unit of stuff whatever that stuff was carbon twelve and whatever whatever the other numbers were so it seemed like things of being built up out of basic units which basically had the same mass as a hydrogen atom almost as though everything was made up out of units of hydrogen Dalton I think proposed something like that that they were base units and those basic units had the mass roughly of a hydrogen atom so that was the first bit of evidence and of course this was essentially right today we understand let me just tell you why that's true from today's perspective not to make a mystery out of it everything is made out of atoms and atoms are made out of protons neutrons and electrons electrons are very very light compared to protons and neutrons and in counting up the mass of an atom the electrons are not very significant an electron has about a mass of 1 mm no one yeah 1 mm 1 mm of the mass of a proton or a neutron so electrons don't come into the equation they do come into the equation but only a very very small term forget about them protons and neutrons constitute most of the mass almost all of the mass of ordinary material the other hand protons and neutrons surprisingly there's no there is a good reason for it but but at the time there was certainly no known reason in fact protons and neutrons weren't known but protons and neutrons have about the same mass as each other as I said about 2,000 times the mass of an electron and so the mass of a molecule is basically the mass of protons plus neutrons they have about the same mass and therefore the mass of a molecule is an integer multiple of the mass of a proton in Neutron on the other hand hydrogen is the nucleus of hydrogen is just one proton and so it did turn out that Dalton was right all materials have a mass which is approximately there's an approximation in their protons and neutrons don't have quite the same mass slightly different less than a percent incidentally a tenth of a percent or even less ah whereas electrons are so light that they don't come into it very much and so Dalton was right and it was the first to my knowledge the first real evidence that matter came in discrete units now molecules weren't atoms of course took a little while longer to find out that molecules were made up out of atoms and the atoms weren't just protons and neutrons or hydrogen that atoms themselves the things we now call atoms that there were about a hundred of them 100 different kinds this was of course a great triumph of chemistry of the 19th century in early 20th century to identify all of the elements that go into the periodic table up there incidentally the periodic table is not very periodic at the you know if you really look at it it it's it's a bit of a fake the periodic table it's not very periodic but nevertheless identifying all those separate atoms up there the elements the elements on some things which are composed of all the same kind you know that story they're composed of atoms and identifying the atoms and at the end of the identification of atoms roughly about a hundred of them less than 100 occurring in nature 92 of them to be precise well more than that if you include isotopes but order a hundred different kinds of atoms and everything made up out of atoms so atoms at the end of the 19th century the things we call atoms or elements were the building blocks the elementary particles of nature now of course it took another five years after the turn of the century for Einstein to do something that nailed really really nailed the molecular theory of matter it wasn't until 1905 that Einstein explained in detail how you could prove that matter was really made out of particles but the long before that chemists physicists understood for the most part that that everything was made out of these 92 elements so they were the elementary particles now sort of all hell broke loose in the beginning of the 20th century very very end of the 19th century when some discoveries were made the electron was discovered about three years I think before the turn of the century I don't I don't know exactly when it was the electron was discovered a number of other things were discovered but in particular radioactivity was discovered radioactivity was the first real signal of the thing which was later that could become nuclear physics are and nuclear physics and particle physics and how only things that needed to be explained sort of there in a sort of tiny tiny little version so let me just remind you about radioactivity just for fun ah who was it a discovered radioactivity I don't even remember I know there was Marie Curie who discovered radioactivity and I think so hmm was a Becker Elle he was Becker oh yeah who's Marie Curie she what she did was lots and lots of experiments to pin it down with great but it was it was Becker Ralph and he had a chunk of lead don't ask me why he did this I do not know he had a chunk of lead and a little hole in the chunk of lead like that and some material down here radioactive is the first thing that happened was he had some radioactive material presumably radium or something like it and his laboratory and he had a photographic plate and accidentally the photographic plate happened to be near the are the material not here over here material photographic plate and the photographic plate got ruined but ruined by the presence of the radioactive material the radioactive material um just ruined you know was like light shining on it and ruined the photographic plate anybody else or not anybody else probably me would have just thrown away the rather the the plate and said that this is ruined let's find another plate and start the experiment over again but Becquerel realized he had discovered something he had discovered that radioactive materials do something to the photographic plate as if they had been illuminated by some radiation so he decided to study that radiation a little bit better and he put the source of it deep in a block of lead how he knew to use lead I do not know but lead was a good substance because it's very dense and he put it into a hole drilled into the lead and then put his photographic plate out here and wanted to see whether it would illuminate a single spot over here everything was collimated by this hole he wanted to see whether it would create a sharp little spot as if something were coming up out of this hole and indeed it did so he got the idea that a beam of some sort was being ejected or something was being ejected by this radioactive material and being collimated along a beam that was the first particle beam that was the first beam of particles I what was it he had no idea what it was but then I guess a second for delicious accident I think it was an accident again and I'm making up the history as I go along but it's close to the truth ah he happened to have a magnet in a laboratory and for some reason the magnet was in a position here where a magnetic field was created near where these particles were being ejected and what happened when he put the magnetic field when he put the magnet near this is the beam split into three separate beams three separate beams one went straight ahead just as if the magnetic field was not there one of them got deviated to the left and one of them got deviated to the right left right right left whatever one deviated more than the other in fact there were not symmetric and becker l or somebody whoever was around knew enough to realize that beams of particles trajectories of particles get bent by magnetic forces if you have a magnet and you have a charged particle the charged particle goes through the magnetic field and either bends to the right or to the left depending on the sign of the magnetic field and the charge of the particle so if the particle was a positively charged particle it would Bend one way in a magnetic field if it was a negatively charged particle it would Bend the other way in the magnetic field and what Becquerel had found is that there were three kinds of radiation one behaving as if it was composed of electrically neutral two particles which one was electrically neutral the one that wasn't deviated at all because he didn't know they were particles only knew is that some collimated effect happened that illuminated the the the detector of the screen the the photographic plate one of them got deviated to the right as if it were a negatively charged particle he called that component of the radiation he called that component beta the component that went straight ahead he called gamma and the component that deviated in the other direction as if it were positively charged he called alpha these became the three distinct kinds of radioactive effects the three distinct kinds of radioactivity beta radioactivity gamma radial gamma and alpha just again I'm not interested in making suspense here let me just tell you what they were you probably know what they were many most of you well many of you know what they were beta was electrons negatively charged particles which were just the electrons that already had been previously discovered from cathode ray tubes in that kind of thing these are electrons coming out the alpha particles we now understand and at that time there was no precedent for it that they are helium nuclei two protons and two neutrons stuck together atomic number four Dalton would have had he had he had access to helium which he didn't he would have said helium was number four on his on his integer collection of materials and gamma are photons okay electrically neutral no electricity at all and these three kinds right now um I think he did again III don't remember the history but he might have had a sufficiently dilute source that these particles arrived one at a time at their destination in that case he would not have seen a bright spot over here he would have seen blip-blip blip-blip illumination occurring or spots occurring discrete little spots occurring for the electrons and he might have said oh those are particles particles arriving one at a time illuminating a screen discreetly he would have done exactly the same thing for the alpha particles he would have found that the alpha particles arrived one at a time in other words he could have used he might have you they probably did use the screen here as a counter analogous to a Geiger counter or something whether he did or not I don't know but but it's something you can imagine that he detected the particles coming one at a time that would certainly be feasible with a Geiger counter and so evidence that whatever this radiation is it's coming in discrete little bundles that we could call particles what about gamma same thing for gamma gamma is coming one at a time but at that time becquer L had no idea neither did anybody else what gamma was it was uncharged that was all that was known and it eliminated the screen just as the others did okay that was as I said in some sense the first particle physics experiment we'll come to some later particle physics experiments soon enough let's next talk about electromagnetic radiation ordinary electromagnetic radiation oh well I said I wasn't going to make suspense gamma is photons gamma is light gamma well it's very high-energy light but gamma is in some way connected to ordinary light so let's come to light gamma was the big mystery because there were no neutral particles known at that time that could account for the gamma radiation so gamma was a mystery and that mystery persisted until fairly fairly late in the very early Senate 20th century let's put it that way fairly late in the very early 20th century was of course Planck and Einstein really Einstein who were the first to understood understand that light comes in quanta that light comes in photons but let's go back light was sort of the strong strong case for something which was not made of particles light was something which was clearly made of fields it was made of the electromagnetic field okay the electromagnetic field electric fields and magnetic fields forming waves when you shake a charge waves get given off the wave field our continuous-wave fields at least according to classical electrodynamics and they give off waves that propagate through space completely continuously and Newton of course had thought that light was was particles but Newton by that time had been completely relegated to the dustbin at least as far as a theory of light went there were many experiments some of them done by Newton himself that strongly said light is waves not particles so let's just talk about the light a little bit electromagnetic radiation if you take electromagnetic radiation it comes in waves so if there's a source of electromagnetic radiation here an antenna some form of antenna emitting could be radio waves it could be microwaves it could be infrared it could be light it could be ultraviolet an atom is a perfectly good antenna incidentally doesn't have to be a big macroscopic a tower an atom with the charge going around in a circle is an antenna antennas emit waves and those electromagnetic waves when they also fall on a photographic plate or other device which is sensitive to light or sensitive to radiation will illuminate that illuminate that and turn it white or black to the black I guess and that's in the character of light now how do we know that these things are waves how can we tell that they're also not bullets shot out of a shot out of the source here so one thing you might do is still very something very similar to what was done over here put an obstruction a little hole and see whether the light is collimated exactly as if it were bullets being shot out of a gun here those bullets you would illuminate a little spot over here now of course what happened is that you don't illuminate such a small spot you eliminate something which is fuzzier than that you only do the funny of fuzzy region but that in itself did not prove that light was waves not at all you could say well just maybe when these particles go through this opening here maybe they have little forces exerted on them by the edges of the hole here or whatever which deflect them some of them get deflected and so maybe you get a more smeary picture a more smearing image than you might have hoped for so it was not just that the beams got deflected the light beams got deflected that in itself was not enough to argue for for a particle structure to light or sorry a wave structure to light I'm sorry but you do something else which is much more sensitive to the wave character light you here's the screen over here again you open up two little holes two little holes next to each other if light was simply particles what you would expect to find here is basically two smears of the same kind just superimposed on top of each other maybe a little extra dense in the center where they overlap but just two smears one the image of this hole one the image of that hole with nothing unusual this of course is not what happens what happens is each hole emits waves you could do the same trick with water waves in fact it's not hard to do the same trick with water waves and the water waves interfere if this is the high point of a wave coming out of here and this is the low point of a wave places where the high points combine from the two holes reinforce each other places where a high point from one hole meets a low point from the other hole cancel each other and so the effect is to see when it hits the screen here too see bands the ends of positive reinforcement where the high points add missing places with no light where the high points meet low points that's an interference pattern an interference pattern is a real signal of wave-like motion of wave behavior waves up you can do this as I said with water you just to put your finger into water and wiggle two fingers and two waves from the tooling will spread out some places they'll reinforce some places they'll cancel and so rather peculiarly but not nothing terribly unusual places which were would have been illuminated by either of the two holes by themselves there's destructive interference they get canceled and places you get constructive interference and they add and you get extra intensity that is the kind of thing this interference property was the kind of thing that really nailed the wave theory of light okay so light was a wave in fact this did not occur after Newton it really occurred before Newton Huygens Huygens was a seventeenth seventeenth century Huygens must have been 17th century but previous to Newton who what yeah yeah yeah yeah yeah but but Huygens already had the basic ideas of wave propagation and that's from the 1600s sometime so this debate went back and Newton had done many experiments himself which should have been interpreted as interference occurs interference wave interference but he didn't in any case after these experiments Young's experiment others it was definitely confirmed that light is made of waves okay what kind of waves well I took Maxwell Maxwell realized that they were waves of electric and magnetic field you know what an electric and magnetic field is an electric field well I look it up if you don't know electric and magnetic fields and light is a wavy motion of electric and magnetic fields first of all light is a wave and here's a wave moving down the axis what is that wave a wave in well it's a wave of electric field here the electric field is pointing down here the way electric field is pointing up here the electric field is pointing down let's just go a line through there alternating electric field up down up down and the whole thing moves off with the speed of light the whole thing moves off with the speed of light electric field incidentally there's also a magnetic field attached to the thing it's a complicated object it has magnetic field also the magnetic field is perpendicular to the electric field and so it sticks out this way and that's what a light wave would look like if you could see if you could sample its electric and magnetic field as it went past you of course as it passes you it will constantly alternate very rapidly if it's if it's a ordinary light wave much too rapidly for you to be able to see but if it were an extremely long radio wave very very long radio wave you might be able to see the field oscillating in front of you and this is this as I said what it would look like it's a wave being a wave it will exhibit interference patterns and Maxwell had absolutely nailed the wave and the electromagnetic theory of light so let's talk about waves a little bit before we before we talk about particles let's talk a little more on our waves and the properties of waves the first property of a wave that I want to come-to is the wavelength wavelength is simply the distance along the wave before you return to before you return one full cycle to the next wave all right so you start here and you go and you come back to the same exact kind of thing as over here that's one cycle or one full wavelength and the wavelength the symbol for wavelength is lambda Greek lambda lambda for length that's the wavelength and it's measured in units of distance it's measured in meters or its measured in centimeters whatever your choice of units are ah okay so lambda equals wavelength wavelength let's just call wavelength another property is if you want to stand still and just watch the wave go past you you go ahead and go up and down and up and down and up and down it would have some frequency how many cycles per second this is not the length of the wave in space it's kind of the number of cycles per second or perhaps even something simpler the time that it takes to go through one cycle as it passes you that could we call the period of the wave period it's a time it's measured in seconds so Avera and a light wave has a very very short period up and down up and down extremely fast 10 to the minus 15 seconds or something whatever the longer the wavelength the slow of the period the shorter the wavelength the faster the shorter the shorter the wavelength is shorter the period okay what's the connection between wavelength and period yeah right so think about the wave moving past you one wavelength how long how far does it move its move distance lambda how long has it taken it's taken the period the distance that it moves divided by the time that it takes to move that distance is the velocity of the wave for light that would be the speed of light if it's not a light wave it might be moving with different speed it's a water wave it would be much smaller speed if it's a sound wave it's a smaller speed but for a light wave the wavelength divided by the period is always equal to the speed of light whatever the wavelength is the period is given in terms of the wavelength of the wavelength is given in terms of the period so that's a fundamental relation it's usually expressed a different way the inverse of the period one over the period is called the frequency it's the number of waves it's the number of oscillations per second the UH number of oscillations per unit time is called the frequency and that's equal to one over the period faster the period the shorter the frequency and so you can also write this as the wavelength times the frequency is equal to the speed of light so if I give you the wavelength you can tell me the frequency if I give you the frequency you can tell me the wavelength by solving this equation and that's the fundamental connection between wavelength and frequency now since one of the things that I really do want to teach you a little bit is the terminology the physicists use for things and they tend not to use the terminology of cycles per second for frequency they use something else it's radians per second what does that mean imagine a thing going around in a circle it's going around in a circle with a frequency F that means f times around the circle per second this is tend to use physicists and mathematicians tend to use not the number of times you go around in a second but the number of radians Radian is about 57 degrees it's an angle about that big how many radians per second and the relationship between the frequency in terms of cycles per second and the frequency in terms of radians per second is very simple in terms of radians per second we call it Omega oh man and their closely connected to each other Omega is just two pi times the frequency why two pi because there are two pi radians in a circle so frequency can be measured in either way physicists tend to use Omega except when they're writing elementary physics books for undergraduate pre-med majors in which case they use F okay we're all physicists we're all grown up we're all you know so we can use Omega like the world of physics does Omega is the frequency of light measured not in cycles per second but in radians per second you say where is the angle for a light way of going but don't worry about where the angle is just divide frequency of its multiply frequency by two pi and that defines Omega I proportional to each other and so we can also write this then as let's write it this way frequency I'm going to write a frequency is equal to C divided by lambda and now I'm going to substitute for frequency Omega divided by 2 pi and what do we get we get Omega is equal to 2 pi C over lambda fundamental equation of wave motion that the frequency measured in radians and the wave lengths are related by 2 pi times the speed of light this of course is true for any wave if you plug in the right velocity okay we will use that equation from time to time so get it down now as I said light comes in different wavelengths and those different wavelengths characterize the different kinds of radiation radio waves or very long wavelengths meters or certainly more than certainly more than microscopic lengths radio waves can be anything from what a few centimeters to 10 centimeters or something I don't remember exactly where the radio spectrum begins hmm okay go up to anything our but rarely long wavelengths are called still radio waves even though no radio could work on the basis of waves that had a wavelength of a billion light years but still they still call radio waves and where is the smaller what's the smallest radio wave I think about 10 centimeters I at small and it's a highly arbitrary division of course completely arbitrary what's smaller than radio waves smaller wavelength microwaves microwaves go from a few centimeters down to the micron micrometer or something like that micron a smaller wavelength in microwaves infrared infrared waves then from infrared waves you have light waves visible light visible light is a rather narrow range of frequencies or wavelengths and then comes a ultraviolet shorter wavelengths x-rays gamma rays gamma rays are just exactly these objects here very very short wavelength extremely short wavelength radiation and that's what the Becquerel discovered coming out of there now a trouble is that Becker L discovered discrete bumps you know discreet blips one at a time and not nice continuous waves okay that then brings us to the puzzle of quantum mechanics now we're not going to go into it in any great depth certainly not tonight but let's just recount the history a little bit Einstein and Planck realized for a variety of reasons mostly thermodynamic properties of light that Einstein that light had to be thought of as being made up out of discrete indivisible elements he might have it might have been an experimental discovery in fact in some sense becquerels discovery was an experimental discovery it's just he didn't realize the thing he was seeing was electromagnetic radiation so I won't go through the actual history but let's make up a imaginary history of how the discreteness of light might have been discovered it could have been discovered this way you again shine your light on a you shine your light on the screen and you illuminate the screen and of course what you see is a nice continuous blob of light it could either be an interference pattern or it could just be a single hole in which case it would just be a blob on the screen but now you do the experiment differently here's your source of light you put an obstruction in the way the obstructions as a filter the obstruction is a not a filter but a semi-transparent the semi opaque thing which blocks out a certain percentage of the light what happens over here well blob gets dimmer okay it's not as intense you make it thicker it's even less intense you see less light arriving per unit of time and you make it even a little bit thicker and at some point all of a sudden the character of what's here changes and instead of seeing the blob you see discrete events little blips now if you wait a long time these little blips build up and they build up to something which has exactly the same pattern as the blob had so the blob in this case then is some sort of effect that has to do with lots of little blips so many little blips that you can't recognize them as being individual that's the blob but if you attenuate the light and cut it down so that the intensity coming through here is really really small what you see is blips this experiment can actually be done it was not done in those early days but you can imagine and this is what Einstein had suggested really does happen in his photoelectric paper that light comes through as absolutely discrete things the motivation for it was was thermodynamics and other things but this might have been the form of discovery discovering these individual blips on the screen and this is what really would happen so something very very confusing going on light is a wave that had already been proved in fact if we put a screen over here with two little holes in it two little holes in it we will again see light coming through bit by bit one at a time and if we leave it up there a long time the blips will sort of fill in and what they will form is an interference pattern so it became clear that there are clear but still very confusing that light is made up out of indivisible elements called photons and that the wave character of the light really represents or the wave pattern really represents the probability that the photon appears at different places in other words it's randomly arriving blips but they arrive with a probability in different locations which follows the pattern that was established by the wave theory the wave theory gives you a wave theory of probabilities that's quantum mechanics we may have to talk about we will have to talk about quantum mechanics a great deal more but this kind of experiment this kind of observation about light was the first example of a connection which is really in a sense what this course is all about the connection first of all between waves of any kind and particles they are not two different things somehow waves and particles are two manifestations of the same thing we'll have to come back to that and we'll try to explain it perhaps again later now I'm just filling in some early early facts mostly just to set the stage waves and particles at least when it came to like well it was somehow intimately connected and it didn't make sense to say light as a particle or it didn't make sense to say light as a wave but has manifestations of both all right the situation only got more complicated when electrons was studied electrons are clearly particles everybody knows electrons are particles there was no ambiguity about that no more ambiguity than there was about where the light was a wave or not it was but yet something funny well something funny also happened with electrons you could do exactly the same kind of experiment with electrons as you can today this experiment can really be done at the time it was a bit of a thought experiment but equivalent experiments you have to put the holes you have to make a screen you put the holes much closer to each other if you want to do with electrons for one reason or another and you send electrons through of course they come through one at a time everybody know electrons were little particles that came through one at a time but was totally unexpected is or would have been unexpected was that the electrons when you open two holes form an interference pattern so it wasn't just that light was funny particles were funny in general our electrons exhibited wave properties light exhibited particle properties in fact had we taken the alpha particles which are much heavier than electrons much much heavier than electrons 8,000 times heavier than an electron much harder to do these kind of experiments with but send them through to little holes like that we also would see interference patterns this has been done with objects which are much much bigger than helium nuclei namely bucky balls bucky balls have been sent through interference experiments like this and seen to form the same kind of interference pattern so everybody know what a Bucky ball is 60 carbons 60 in shape of a generalized soccer ball yeah right is it is it a rig is a regular soccer ball got six yeah like a soccer ball no it's not it's not really a soccer ball but they're well so and it's widely believed that if you did it with bowling balls well you can't really do it with bowling balls much much much too hard I understand the people who did it with buckyballs are going to try to do it with living cells viruses the prove that viruses are quantum mechanical and then they're going to ask the virus what the virus felt when it anyway good the waves and particles are somehow the same thing and if you want to penetrate that more deeply you got to learn some quantum mechanics and a place to do it is in my lectures which don't cost anything they're on the internet okay that's now let's talk about the properties of photons a little bit photons all these discrete indivisible elements of light light has energy if you absorb the sunlight it heats things obviously has energy so therefore photons have energy what do we know about the energy of a photon photons being indivisible we know the energy must come in very discrete packets now what is a photon characterized by or a light wave imagine a light wave coming in composed out of these discrete photons don't try to picture it's impossible to picture when the light wave actually falls on a screen it forms these little dots so it's particles made of particles but we see some sort of wave phenomena associated with it the wave phenomena is associated with a wavelength and therefore a frequency an angular frequency we discover that that light wave is made up out of discrete units each with an indivisible bit of energy cannot be subdivided and the energy of one photon the energy of every single photon in this light beam with a given wavelength and a given frequency is given by a number called h-bar plunks constant one of plunks many kind one of one of Planck's constant H bar times Omega in other words Omega is large when the wavelength is short the shorter the wavelength the larger the frequency larger the frequency or the shorter the wavelength the larger the energy in every photon so first lesson short wavelength photons have lots of energy long wavelength individual photons have very low energy now of course a radio wave can carry a huge amount of energy there's no question you can make radio waves with lots and lots of energy how do you make way radio waves with lots of energy you pile lots of photons up many many photons all with the same wavelength and the same frequency but there is something nevertheless some remnant of the discreteness namely the energy of such a wave is always an integer multiple this is the energy of a photon the energy of a light ray let's just call it a ray or a light wave is some integer number as an integer multiple of h-bar Omega all right so the light ray has come in indivisible units every light ray every light weight way every pulse of light with a given frequency and wave them wave wavelength an integer multiple of energy in units of h-bar Omega so this is an important equation here this equation is of absolute central importance to understanding why particle physics is the way it is in particular it's very very central to the question of why we have to build big giant machines to see smaller and smaller objects my grandson my grandson is not a kid he's 26 years old but he asked me one day how come you have to build bigger and bigger machines to see smaller and smaller things why don't you build small machines to see if there are we're going to try to answer that question but this is the central fact that the energy is proportional to the frequency of a photo of a given of a single photon alright we've been through waves and particles photons being carrying discrete units of energy I want to come to another set of concepts now this is when I we're certainly not abandoning this line of thought here but there's another line of thought that I want to remind you work mostly remind you of not quantum mechanics but the special theory of relativity special theory of relativity plays a very important role in particle physics particle physics is in a sense relativistic quantum mechanics the combination of relativity and quantum mechanics and so let me just remind you of one particular simple fact and then be clear about what that fact means most famous equation of physics equals MC squared this equation also plays a very important role in the reason for in explaining why particle physics is the way it is energy is MC squared let's just be very clear about what it means armed in the early days of relativity people spoke of the rest mass of an object and the moving mass of an object the moving mass and the rest mass were different mass of an object was minimum when it was standing still but when it moved the mass increases you still read that in elementary physics textbooks but you never read it in any in any work of modern physics you never read that the mass of an object depends on the state of motion it's largely a change in language the change in language is such that what we now call mass is what used to be called rest mass period whenever I refer to a mass of an object I am talking about its rest mass all electrons have exactly the same rest mass all electrons have exactly the same mass period if you look up the masses of particles in a in a you know in a table of masses and so forth you will not find them called rest mass you will just qualify them called mass so from now on we will never speak about the rest mass we will speak about the mass of the electron as a number that experimental physicists measure in great detail every electron has exactly the same mass as every other electron and the mass is not something which depends on the state of motion but of course the energy is something which depends on the state of motion the faster an electron moves the more kinetic energy it has so there's something wrong with this equation yes there's something wrong with this equation this equation is no longer even though it's the most famous equation in physics it's not the right equation at least with modern terminology energy is only equal to as times z-squared for an object at rest the right way to say it is the energy of an object at rest if the object has no net motion now it could be a complicated object with all sorts of internal motions but it could be a box of gas all the molecules flying around like mad but as long as the box of gas is itself stationary then we speak of its rest mass and we can speak of its rest energy the energy of that box of gas when it's standing still and Einstein's equation says that the rest energy of an object is the rest mass or just the mass times the speed of light squared now what exactly let me imagine two experiments that you might do to confirm this just to understand precisely what it means you take a pot oh not a pot a box with molecules in it and you put it on a scale to measure its weight or its mass drum scale the molecules are cold you begin with the box of gas very very cold and you measure the mass so you measure yes you measure the mass you get some number now you feed some energy into the box you heat it up you heat up the molecules in here you increase their energy the box is still at rest the molecules are not the molecules are moving around but the box is at rest and we can ask what is the rest mass of the box of gas the answer is if you increase the energy by adding thermal energy you add a certain number of calories or a certain number of joules joules unit of energy to the box you will discover that the box is mass the box of gas its mass increases its weight increases okay now the amount that it would increase is so tiny if you increase the temperature by a thousand degrees or something it's so tiny that it would be quite unmeasurable but in principle this is the meaning of e equals mc-squared an object at rest if you add energy to it its mass increases its weight increases also its inertia increases harder to move it another example now this is the this example is not something that you can really do but the other example is something that there's no real experimental physics observational physics you start not you start with electron and a positron we haven't talked about anti particles let's just ignore the fact that we haven't talked about them for a moment two kinds of particles electrons which have negative charged positrons which have positive charge they have exactly the same mass precisely the same mass they are in every respect similar except for the fact that they have opposite electric charge because they have opposite electric charge they can combine and disappear they have plus charge and a minus charge the net charge is zero nothing prevents them from this peirong well something does the pepero prevent them from disappearing they have energy each one has an energy let's suppose suppose these two particles are at rest we bring them together each one has an energy equal to MC squared so the total energy is twice MC squared well MC squared for each particle we bring them together that energy can't disappear energy is conserved what happens to that energy that energy becomes photons photons go out you bring an electron next to a positron you let them annihilate poof out go photons the photons in some sense are energy they can be absorbed by a material and heat the material they can be converted to all forms of energy and how much energy do you get by annihilating an electron and a positron the answer is twice the mass of an electron times the speed of light squared it's a tiny amount of energy I mean if you just had one electron and positron you couldn't do much with it you need you know huge numbers of them to heat a cup of coffee but but still in principle that's what happens and of course this is this is an observational fact that's the meaning of e equals MC squared and another way to really say it which i think is the right way to say it is to say energy and mass at least for an object at rest are the same thing why do we have to have an equation really it's just a conversion of units from what we call mass units to what we call energy units and this tells you the conversion roughly like conversion from meters to the centimeters or whatever this is the conversion between energy units and mass units all right but in any case if you know the mass of an object and you want to know how much energy you would get if it disappeared you multiply by the square of the speed of light so you get a lot of energy for a small amount of yes what is the speed of light and what is Planck's constant let's write down the numerical values of the speed of light and plugs constant we need them one for here and one for here photon energy is the mass after the mechanism for the energy to be released well does it help yes it has to have a mechanism and we haven't talked about that mechanism but just let's let's stand on the outside and say look this thing happens an electron and a positron when you put them together will just disappear let's not ask what the mechanism is the one thing we know is independent of the mechanism energy should be conserved if e equals mc-squared for the electrons that energy has to show up somewheres so there are some things you say without knowing what the mechanism is conservation laws where you know that certain things are conserved you can often say important things about a system without knowing detailed mechanisms okay let's talk about numbers the speed of light is a very big number Planck's constant is a very small number how do I know it's a small number well the energy of a photon is a tiny amount of energy the frequency of a light wave is very large so it better be that h-bar is a small number try them down okay so see the speed of light that is equal to two point nine nine seven six two four five eight I'm not kidding you this is true plus of mine is something in the last digit over here times ten to the eighth meters per second units units are important it's not just two point nine nine seven six two four five eight times ten to the eighth it's that number of meters per second that's the speed of light how about Planck's constant then everybody of course will memorize this number because let's important to this class that you know that number one point same thing he'll memorize this one one point oh five four five five seven one six to eight times ten to the minus 34 very small number and what are the units anybody know what the units are I worked out the units but I think I erased them hmm energy times time right well what are the units of energy mass times velocity squared right MC squared that'll be MC squared mass times velocity s kilograms times length squared over x squared that's energy and plunks constant has another unit of length in it you know the unit of time okay so Planck's constant is measured in what's unit mass kilograms kilograms meters squared divided by seconds so why are these numbers so crazy why are they so big why are they so small why are they so odd I mean couldn't this nature playing some awful joke on us to put these that to make these numbers so awkward or are people just being foolish in using peculiar units for example the speed of light is something which depends on your choice of units if you measure it instead of measuring it in meters per second you measure it in feet per hours you'll get a different answer so there's nothing sacred about this number it depends on the choice of units length units in this case and time units you could certainly work with units in which the speed of light was a more convenient number you could work with units in which the speed of light was one the units would be light years per year for example the speed of light one light year per year or one light-second per second so it's not hard to choose the speed of light to be one you just use different units of space and time same is true a Planck's constant you can use units in which Planck's constant is equal to one but why is it that we actually use such peculiar units why don't one how come the people who invented units mister metric or whoever he was the British are worse than the metric system of cost they were really perverse 5,280 feet in a mile how many um how many stone how many pounds on a stone sixteen I don't know where they got these units from hmm I don't know it's a stone sixteen pounds again fourteen pounds even worse if sixteen is at least divisible by two four times but seven okay fourteen fourteen pound hmm that's another good one how about horsepower yeah I mean just bizarre units metric units are better but they're also very very arbitrary for example the meter had to do with how far a man's hand is from his nose why because it was using measuring lengths of rope or something so these are highly arbitrary units and have more to do with biology than they have to do with physics they have to do with biology in the sense that the real question is not why a meter is what it is why why a meter is what it is it's a question of why and why an arm has to have X number of molecules in it and there's nothing special about these numbers right given that you can ask other units are there better choices of units of the three units what do we need we have we need three units we need a length the three things that need the three kinds of units we need are length meters or feet or whatever time seconds or years or hours or something else and mass all of the other units in physics can be re-expressed in terms of ease this is a complete set of units there are three of them and we can choose them in various ways for example instead of using the kilogram we could use the mass of a proton as the basic unit of mass or the mass of the Sun or and so forth use different units of mass um certain things and astrophysics are a lot easier not easier but a lot smaller the equations are simpler they involve less constants fewer constants if you use units in which the mass of the Sun is one okay equations in nuclear physics are simply only simpler in the sense that they don't involve as many arbitrary constants if you use units in which the mass of a proton is one so you can make your equation simpler and get rid of these weird numbers and how many numbers can you get rid of how many numbers can you get rid of this well you have a choice of three units mass length and time and that means you can simplify three of the constants of nature or three of the of these type of constants here are and set them equal to one if you like so in astrophysics or in cosmology you might want to use the light year that's a much better unit than the centimeter and if you use the light year and also the year light year for distance here for time speed of light comes out one of course so we can simplify three numbers usually and what are we to the question of which numbers we simplify might depend on what kind of physics were doing if we're doing astrophysics we might want to simplify certain numbers if we're doing atomic physics we might want to simplify other numbers and in particle physics in particle physics there are basically these two constants which we can set equal to one by appropriate choices of units appropriate choices of units can set C equal to one that's easy you just use units in which time is measured or in such a way that the time and distance are measured in such a way that the distance something moves in one unit of time is one unit of distance you can also set H bar equal to one you have your choice about one other unit what's a good unit to set equal to one what's a good unit to a mass unit to set equal to one in particle physics well you could use it what about the proton or another proton why not the Higgs boson or not the why not the the MU particle or well the answer is obvious that there isn't the best there is no particularly good unit of mass which will simplify particle physics so that the at best you can at best you can set one arbitrary particle to have a mass of one and that would be foolish because there would be no particular reason to focus on any one particle what about that why do we pick the speed of light and clunks constant as well they do appear in so many equations but so does the mass of the proton or the size of the proton why okay I'll tell you why are there are two very very fundamental facts about plunks constant than the speed of light and oh the way that I'll say it is just to say the words no object in nature moves faster than the speed of light it doesn't matter what it is no matter how you try to accelerate it you can get it up closer and closer to the speed of light but you can't pass the speed of light all right for any object in nature any right so there's something Universal about the speed of light it's a universal bound Universal for all forms of matter that anything that we can make it has a certain universality all objects are constrained by the speed of light so it has some it has some reason to be thought of as something universal what about Planck's constant does Planck's constant come in to anything where you would want to say everything in the world necessarily has precisely this property it's the uncertainty principle we haven't discussed the uncertainty principle but all objects in nature the precision with which you can measure their positions and velocities and momenta are constrained by exactly the same constant the uncertainty in position times the uncertainty in momentum are always constrained to be as big or bigger than Planck's constant again everything all particles not just particles but objects of all kind are constrained by the same number so it's for that reason the specialness of these two constants that it makes a lot of sense to set them equal to one the size of the proton for example or not the size of the program let's say the size of the proton or the mass of the proton there's nothing very special about the proton the proton is one of hundreds of elementary power elementary one of hundreds of objects why didn't we set the mass of give me some weird element from up there rubidium why didn't we set the mass of a rubidium atom to one because you say rubidium is not in any way more special than for polonium okay you're learning about my chemistry knowledge there's nothing special about rubidium it's just one of many same thing is true of the proton it's just one of many the electron is one of many so there's nothing Universal about it is there a third universal quantity which is so special that we might want to set it equal to one something which everything is constrained by yeah trouble the electric charges a dimensionless quantity but yes we could do the electric charge is a fundamental constant like that gravity right what can we say we can say all objects in nature attract each other with a force which is equal to the product of the mass divided by the square of the distance between them times Newton's constant we don't make any exceptions it's not that there are some objects which do that and other objects would stomp incidentally in the case of the electric charge of course there are neutral particles so not all objects interact in the same way electrically but everything in the world interacts exactly the same way product of the masses divided by the square of the distance between them times Newton's constant so Newton's constant is one of these very universal things G I don't know what is it six point seven four nine eight three one five four I assure you it's not known to anything like that kind of precision I think it's six point seven times ten to the minus 11th and some units or other it's another thing that it makes a lot of sense to set equal to one why don't we do it in particle physics the reason is that particle physics is totally insensitive to gravity the gravitational force between objects and particle physics is absolutely negligible so gravity would be a stupid thing to set equal to one because gravity just doesn't come into the equations of particle physics particles are too light to experience significant amounts of gravity particles that we know about today they're just too light to experience any significant gravity and so it there's no particular value since none of the equations in particle physics involved gee it better to leave it alone just go away and not fix one of the unit's just leave it free it even better say that missing it what's that is it fair to say that part just misses it all the time because would be insignificant you actually don't even it's not even fair to assume that G is dismissable that in fact examining is may not be subject well of course we know that they are subject to gravity if you take enough particles they form the earth then you take another enough particle yeah so that's that's right we don't really really know what how elementary particles well no we do well we can certainly take one elementary particle and see how it behaves in the field of the earth see whether it falls and they do single particles do fall in the field of the earth but how single particles would influence each other gravitationally that of course has never been measured and so yeah it's it's possible to question whether the universal law of gravitation applies to particles I don't think many physicists do question it but the main point is a point a practical point there's no benefit gotten by setting G equal to one in particle physics because G just doesn't come into particle physics at least uh in current versions of particle physics there are other such as attraction to to electrons or the other force wouldn't it make sense bill are you thinking about gravitational attraction to set those two one with a set of G with attraction is two electrons for example electrons going to track they repel but the yeah oh yeah you can't do that but that doesn't go into your particle physics either it doesn't make you part of your visit oh right it does it does yes you you could use units and we often do in which the electric charge is equal to one the repulsion yeah is the third constant yeah you could you could you could you've heard traditionally we haven't got traditionally we haven't there's a reason that we haven't and I will eventually get to it wasn't that to fight about it like a charge the dimensionless once you sets the bar to be dimensionless the charge yeah the charge the charge is equal to one over 100 square of the charge is equal to 1 over 137 is a dimensionless measure of the charge and it's a completely dimensionless number and we'll come to it will come to what it means it you could so you can set 1 over 137 there's an obstruction to because actually when I complete this that's what they did then your third one they said Kohl's constant Hui comes with columns oh yeah you could for whatever reason historically we haven't done that and there's probably no particular benefit in it in any case we will use units in which C and H bar are equal to one quite often not always but sometimes only when I want to illustrate the size of numbers will I put C and H bar back into equations so we owe some equations come out to them simpler yeah if we set C equal to 1 then e is equal to M that's an energy in law and in energy and mass which is the same thing we had another equation over here e of a energy for a photon this is the energy of a massive particle which has some rest mass energy of a photon is equal to H bar Omega now the equation simplifies if we set H H bar equal to 1 energy is just equal to frequency so that that's just an illustration of the use of what's that no well yes yes yes yes yes but not for a photon photons have no mass don't forget this is okay there's a difference between these two the meaning of e in these equations in this equation its rest mass and rest energy but photons can never be brought to rest nevertheless they do have energy but it's not rest energy it's the N it's basically kinetic energy photons have kinetic energy energy of motion so this is just plain energy whatever the energy is and it's equal to their frequency so they're two different yeah well mass and rest mass rest energy or so for this thing because what is zero what is rest it has to be relative to something yeah you know just just forget the word rest now let's forget the way rush you just different use it to differentiate them quick you know what is mass at rest in the universe where would it be not in the universe it's in the laboratory we're talking about yeah relative to the laboratory energies are measured relative to the laboratory energies are different depending on the state of motion of the observer if you have a photon or anything else and two different observers observing it they see two different energies obviously even even in Newtonian physics that's true if I have an object here and I see it I say it has no kinetic energy you're running by at 100 miles an hour you look at it and you see that it has kinetic energy so energy is something both sigh young energy is something that depends on the state of motion of an object it makes sense to ask what the energy of this cup of coffee is when it's at rest then it's just the internal motion of the molecules and so forth and no no overall kinetic energy that's the thing which is the M when you write energy is equal to mass on setting is the the counter that sitting on is not address what's a key in the universe accounted sitting on mat it okay if it's it rest then its rest relative to something else if on the point is that energy is measured relative to a given frame of reference energy is not a universal thing that everybody will agree on its relative to a particular frame of reference so relative to my frame of reference the energy of this cup of coffee what it's standing still relative to me is equal to its mass okay maybe things constant yeah didn't like frequency cycles per second you said physicists use Omega 2 pi so much think that's a historical factor my question is it seems to me - pi nu 0:57 whatever 2 times that is more complicated than a complete idea hmm I really like why would one use something that is be more complex than the single person good question engineering that yeah yeah I mean there's some mathematical simplicity to radians that the I I think the answer is you look at all the equations you write down you write them in both in terms of frequencies and you write them in terms of omegas and you see in which form you'll encounter fewer factors of 2 pi I'm not sure what the answer to that is Omega he related for sure practically speaking is it possible to accelerate particles fast enough with energy that they will interact gravitational force will certainly be very far from it very very far from it no of course it depends on what you mean by a particle I don't think you'd want to call the earth a particle but well what's elementary yeah yeah but what this is also posted on what it was a source of positron where is the source of particle high-energy collisions that's the only way to do it you need it yeah you need a you need a collision terror to create positrons okay now look we apostasy we used to hook leave the cage sometimes your puzzle comes we use the planks cost plank at time and plank distance and things like that when we're not doing at plumb time and plunk distance correspond to setting G equal to one yeah so we're not doing that now one of the reasons that we might not want to do that is once you set three of these equal to one let's say then you have a natural unit of length the natural unit of time and natural unit of mass the natural unit of length when you set G equal to one and all of them equal to one this called the Planck length and it's very very much smaller than anything that comes up in normal particle physics so you would not want to measure particle sizes particle radii and so forth in units of the Planck man a clock length it's just too small it's much smaller than anything that occurs in so that's the reason for not doing it you use like in black holes or call them all of years yeah anything that really involves gravity and quantum mechanics together and relativity it makes sense to put all three of them to one but if only two of them are important you may only want to set two of the constants equal to one okay let's see I want to go a little bit further yeah let's go a little bit further with the basic concepts that will draw on over and over I mean today I'm just listing basically the preliminary concepts practically establishing language energy mass particles waves Fields let's talk about another concept that comes up over and over in particle physics in fact it comes up over and over and over cell physics momentum momentum if you take an object and it's at rest it has no momentum at all it may have energy it has equals mc-squared energy but it has no momentum an object at rest if it's moving it typically has momentum momentum is conserved just like energy when two objects it could hit each other the net amount of momentum doesn't change and so momentum is a conserved quantity and because it's a conserved quantity it has an importance anything that's conserved is important momentum is a combination of the mass of an object or better yet that's rest its energy its energy and its direction of motion its mass its velocity in its direction of motion it's a vector quantity it's a vector quantity and as a rule it's proportional or as a vector quantity it points along the direction of motion of an object points along its velocity for a non relativistic object an object moving with much slower than the speed of light the momentum of course is equal to the mass times the velocity the arrow on top means that it's a vector quantity it has a direction okay so mass times velocity is momentum in non relativistic physics but it's not quite the right expression for in relativistic physics and in particular it's not quite the right thing for things moving with the speed of light so let's talk about light does light have first of all does light have energy yes a beam of light shining on something heats it does light have momentum now ordinary light if it hits you in the chest or something doesn't give you much of a push why it's because and the light so dilute and it just doesn't have much of a kick okay but if you got hit by this laser beam that they make in where is it in across the bay on the other side what's that place um Livermore yeah they got this great big laser and laser shines it's light and when it hits a piece of material it just implodes it what is it that's imploding it it's the momentum of the light just pure sheer momentum and it can be huge so yes light has momentum and a pulse of light moving along let's imagine a pulse of light moving along the x-axis every pulse of light moving along a given direction now of course real light might have some dispersion it might some of it might go out some parts of the light wave may go one way some parts may call it the other way but if the light is very collimated so it's moving along a particular axis then the right formula now I'm not going to prove this I'm not going to prove it I'm just going to tell you the right formula for a light beam is that it is the energy of the light beam divided by the speed of light let me just compare it with this or another way to write it is the energy is C times P but let's leave it in this form here now let me just compare these two things momentum is mass times velocity momentum is energy divided by velocity just a simple question are they dimensionally the same other dimensionally same so to inquire literally dimensionally the same all you have to remember is that the dimensions of energy am mass times the speed of light squared so just in terms of units energy is like MC squared divided by C just tells you that the momentum of a beam of light is its mass times its velocity not really it's mass its mass the rest of the mass of the light beam is really zero it has no mass rest mass but in terms of units it's equal to an energy times C squared sorry mass times C squared divided by C you get the point it's just a question of units this doesn't look like this in terms of units one has a velocity upstairs one has a velocity downstairs but it is the same in units when you remember that e equals mc-squared okay so this is the formula for the momentum or the relationship between the momentum and the energy of a light beam and it points in the direction along this data along the motion that's right that's right how to write this let's just say the magnitude of points along the direction of the light beam but the magnitude of the momentum is equal to the energy divided by C the magnitude of the momentum the direction is along the direction of axis of the light beam along the state of along the direction of motion of the light beam but the magnitude of the momentum the size of it is equal to the energy of the light beam divided by the speed of light C okay you can see now momentum is energy divided by C that's why that's why the momentum is so small you can detect the energy of a light beam sure you can it heats up but heats up a little bit of water it heats up it evaporates water and so far it's not hard to detect the energy but it's quite hard to detect the momentum of the light beam and that's because this is this C in the denominator here momentum of a light beam is very small typically cause if you as I said if you pump up the light beam enough they can give quite a kick all right so that oh-oh let's let's do one little exercise all right let's just um yeah the momentum of a light beam is its energy divided by the speed of light now we have a formula remember the formula for the energy of a photon let's take one photon now one photon is an example of a light beam let's figure out what the momentum of a photon is so it is equal to its energy divided by the speed of light but what's the energy of a photon h-bar Omega so the momentum in magnitude is equal to H bar Omega divided by the speed of light now do you remember the relationship between frequency wavelength and the speed of light we had that before that yeah what was it the freak frequency times wavelength is equal to C right frequency times wavelength and now for you if I put Omega here Omega times lambda is what 2 pi times C or 2 pi divided by C 2 pi times C right 2 pi times C no 2 pi C over 2 pi C over 2 pi good C over 2 pi is that right we're makin is bigger than 4f Omega is bigger than F right all right yeah right so wait a minute I don't believe you I don't believe you I got to do it myself okay we have frequency times lambda equals C right so therefore yeah so now wait Omega is equal to 2pi times frequency right so frequency is omega over 2 pi so this is omega over 2 pi and I say that Omega times lambda is 2 pi times C I was right right Omega times lambda is 2 pi C so let's get rid of the Omega here and write Omega is equal to 2 pi C over lambda I've just divided by lambda let's just see what we get we get momentum of a photon is h-bar divided by C and now times Omega and Omega is 2 PI over lambda times C the C's cancel out that's good because I know they C should cancel out now what do we find we find the momentum of a photon it's 2 pi H bar that's a number divided by the wavelength what what's that yeah yeah 2 pi H bar equals H right right we could that's right right so right so P is also equal to just old-fashioned H divided by lambda there's an example where we did it was possibly not so smart to use H bar right okay look the two PI's are gonna get you one way or another someplace they're gonna get you the PI's always come up somewhere you can't get rid of them okay what does this say this says the shorter the wavelength the larger the momentum of a photon Oh sing --gel photon of a radio wave has a very very small momentum a single photon of a gamma ray a gamma ray is a very very short wavelength photon as a good kick to it one photon it won't hit the it's still a pretty small kick but what this is telling you is that the momentum is related to the wavelength the shorter the wavelength the bigger the momentum that is extremely important lesson that the shorter the wavelength the bigger the momentum and also of course the bigger the energy the energy and the momentum are related or proportional to each other so if you try to make very short wavelength photons the result will be that you have to spend a lot of energy to make them now it becomes clear why physicists have to build bigger and bigger machines to see smaller and smaller things the reason is if you want to see a small thing you have to use short wavelengths if you try to take a picture of me with radio waves I would look like a blur if you wanted to see any sort of distinctness to my features you would have to use wavelengths which are shorter than the size of my head if you wanted to see a little hair on my head you will have to use wavelengths which are as small as the thickness of the hair on my head the smaller the object that you want to see in a microscope the shorter the wavelength of light that you have to use okay if you want to see an atom literally see what's going on in an atom you'll have to illuminate it with radiation whose wavelength is as short as the size of the atom but that means the short of the wavelength the all of the object you want to see the larger the momentum of the photons that you would have to use to see it so if you want to see really small things you have to use very make very high energy particles very high energy photons or very high energy particles of different types how do you make high energy particles you accelerate them in bigger and bigger accelerators you have to pump more and more energy into them to make very high energy particles so this equation and it's near relative what is it's near relative e equals H bar Omega these two equations are sort of the central theme of particle physics that particle physics progresses by making higher and higher energy particles because the higher and higher energy particles have shorter and shorter wavelengths that allow you to see smaller and smaller structures that's the pattern that has held sway over basically a century of particle physics or almost a century of particle physics the striving for smaller and smaller distances that's obviously what you want to do you want to see smaller and smaller things and at the same time the striving for shorter and shorter wavelengths which means the higher and higher momentum or higher and higher energy particles yeah we think there is well yes and no yes in some sense yes we think when you get down to the plunk length something new begins to happen and we can talk about that at some point in these lectures where it may bottom out but we're very far from the place where it bottoms out if it bottoms out it probably bottoms out at the plunk length which is you know 17 orders of magnitude smaller scale than what we're trying to see at the LHC so we've got a long ways to go a very long ways to go even if it does bottom out alright those are the basic facts that I wanted to to get out in front of you they sort of determine largely how particle physics is progressed and as I said it has progressed by going at every stage the shorter and shorter wavelengths larger and larger momentum and energy and smaller and smaller objects would there be any heuristic saying that the wavelength or the size of the particle you want to look at is inversely related to the size of the site left on your building realize it's ridiculous ratio but is that sort of you need one wrong speaker roughly speaking yes that's correct roughly speaking that's right um if you have a given capacity to accelerate now what determines your capacity to accelerate the size of the electric and the magnetic fields that you can create so let's suppose you take the largest fields that you can create then a magnet made of steel this big and that determines that determines your ability to accelerate ability to accelerate means the energy that you can pump into something per meter even a meter of accelerator how much energy can you pump in all right so to double the amount of energy that slack produces it would have to be twice as long or round but there that that's right but the round gives you another problem the problem that round gives you is that when particles move in circular orbits they radiate and when they radiate they lose energy so let's take the case of a linear accelerator the longer the linear accelerator is the higher the energy that you can pump the particles to and pretty much linearly linearly proportional to the size of the accelerator and it's going to get the double resolution yeah so basically resolution time size is it costly or rough yeah yeah so if you wanted to get to this Planck length how big an accelerator would you have to have well as I said 17 orders of magnitude longer than the CERN accelerator no no I think it's more like the galaxies yeah I call it the Gedanken I'm right higher I mean the highest cosmic ray energy of 10 to the 21 electron volts or something like that which is a 21-9 is what quick 21 minus 9 12 10 to the 12 GeV whereas the accelerator in well no it actually doesn't work at the highest energy cosmic rays a 10 to the 12 GeV but but the problem is you see the problem is cosmic rays they may have this huge energy but they hit stationary targets whereas in the accelerated CERN they're going to be colliding targets and so you get more bang for your buck from the colliding particles but still still cosmic rays have much more energy than effective energy than the accelerators the problem with them is in order to really do good experiments you have to have a few huge flux of particles you can't do an experiment with one high-energy particle it will probably miss your target or it probably won't be a good dead-on head-on collision learn anything from that you learn very little from that so what you want is enough flux of particles so that so that you have a good chance of having a significant number of head-on collisions that takes a lot of particles when the targets are small so I told you how big an accelerator you would have to make now I would tell you how many particles have to collide in order to see something interesting and I once worked out how much energy it would take to fuel this accelerator in order that you could do experiments and a reasonable amount of time and then I got something like a hundred trillion barrels of oil a second so you need the accelerator as big as the galaxy being fueled by some time I think it was a hundred trillion barrels of oil a second and it's going to be a while till we do experiments like that yeah but these are but these are real distance scales I mean they really do come in to physics and the puzzle and the question is how to probe them how to get at them without being able to spend the hundred billion barrels of oil and build a galactic sized accelerator so is it hopeful in what sense in what sense would you ask your people compared to this it's not comfortable to the 10 to the 12 GeV from no when you have a particle hitting a stationary target take that 10 to the 12 and take its square root that's 10 to the 6th it's like having 10 to the sixth GeV in colliding particles each one colliding so if you have two particles colliding each one with 10 to the sixth GeV it's like having one particle with 10 to the 12 filling a stationary particle now 10 to the 6 that's a million GeV that's a thousand TeV so we're still very low compared to what to what the cosmic rays can do but if you have a handful of cosmic rays coming in the chances are that it's going to do an interesting collision or negligible for more please visit us at stanford.edu

Channel: Stanford

Views: 487,924

Rating: 4.8849015 out of 5

Keywords: science, physics, particle, quantum field theory, molecule, Planck's constant, mass, atom, electron, gamma, light, photon, quanta, electromagnetic wave, field, electric, magnetic, momentum, frequency, magnitude, Newton, Einstein

Id: 2eFvVzNF24g

Length: 114min 10sec (6850 seconds)

Published: Fri Jan 15 2010