Einstein lecture by Douglas Hofstadter

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earthly lift was from a passion lien an extra stood near at cana present era felons for a lessening of mine stein fishy can ZD historia oak the beatin's cochlea creativa tank and death process and some than her fair lasting in Harlem so please welcome professor douglas hofstadter [Applause] thank you uh I guess the microphone is on so you can hear me thank you very much for the nice introduction Krista I I know that Krista and I had correspondence he wrote to me when he was whatever age he was but it was in 1986 he wrote to me and I replied to him twice we had a lovely little interchange which I had totally forgotten and which he reminded me of a couple of years ago and it was it was very sweet to reread the letters so we've in a certain sense known each other for a long time and so he invited me to give this talk and it's it's my pleasure to be in Sweden and to to be in Stockholm where I did live for a few months a long time ago 1966 and so it's always a pleasure for me to come back to Sweden well tonight's talk is something that is it was inspired by a talk that I heard in the year 2005 which was the centenary of Albert Einstein's honest me tabulous the year in which he published for absolutely revolutionary articles and I heard a talk in 2005 in Indiana University given by a physicist named John rigdon and it was the most amazing talk I think I ever heard it really inspired me and I'm going to tell you a little bit I'm in a certain sense I'm going to reconstruct professor rigged ins talk although it's my talk is somewhat different naturally I'm a different person and I have different some different ideas but but it opened my eyes to something which you will see as this lecture goes on I'll explain it anyway it was a marvelous lecture and he and I were in contact I mean I met him only on that one occasion and I I spoke with him a little bit but then I wrote him some emails and he wrote me some EO emails and we had very very nice friendly correspondence for a while in in the in the last 10 years but then when I at some point he stopped writing back and I thought he might be in ill health but I didn't hear back from him and when I was preparing this lecture I looked him up on the web and I found to my dismay that he had just died he died in fact I think it was in November of last year so just very recently so I would like to dedicate this lecture to the memory of death of John Rigden because he really inspired me and inspired me to think about Albert Einstein in all sorts of ways and that's what this lecture will show so when I was I became a graduate student in physics in roughly 1968 and I used to go to the physics colloquia and I would listen to rather difficult to colloquia with complicated topics but every once in a while a physicist would interrupt in the middle of the talk and say well now let me give you a little analogy that may help you to understand better and my eyes would brighten and I would listen and I would learn something very interesting and then they would say now let's after a minute or so they say let's get back to the serious stuff and and it was as if the analogy that they had given was somehow just fluff not important I felt that it was in fact quite the opposite that what they had just revealed to us was some secret about how they really thought how their ideas had come about and to me analogies the not only was physics interesting I was a graduate student in the subject after all but also how physicists came up with these brilliant new ideas was equally interesting and so when I finally got my PhD I actually got out of physics but let me first say that um when I did my PhD my own PhD actually was built on centrally an analogy which I'm afraid you're not going to be able to see very well I have projected this before and I think can you see anything over here at all just barely I I'm sorry I'm gonna have to improve this this image but in any case on the left side is a function that I discovered in 1919 60s when I was in mathematics doing number theory and on the right side is a is a graph that I discovered when I was doing my PhD work and in order to understand this graph I based all of my understanding on it my my understanding of the graph I had discovered in number theory about 12 years earlier and they were by no means the same thing but they were analogous phenomena and so at the core of my own PhD there was a beautiful analogy and so this once again reinforced my feeling that the discovery in physics is all about analogy making well I got out of physics because I felt I had not I didn't have the right brain for it and and I became a cognitive scientist and as I said I was always interested in the mechanisms of the mind the mechanisms of creativity how we understand the world how we can gain insights into the world and so I was a cognitive I became a cognitive scientist but I still retained my interest in physics and when I went out to Stanford which is where I grew up in 2004 a sabbatical year I was asked by the physics department if I would give a hofstadter lecture which is a lecture in memory of my father who was a physicist on the faculty at Stanford for many many years and when he died the family and that physics department Stanford set up a fund that had annual lectures in his name and so I never expected that I would be asked to give a Hofstadter lecture that was a twist and an honor and a little bit frightening to me but I took it on with pleasure and I as a cognitive scientist who had been deeply in love with physics I decided that I would talk about the role of analogy in physics and I gave it this ambitious title I don't know if this thing works very well the ubiquity can you see this red mark okay I can't see very well but anyway the ubiquity of analogy in discovery in physics and ubiquity if you don't know the word means the everywhere nasai on the presence of analogy and discovery in physics now at the time when I gave this title it was a couple of months or two or three months before I was gonna give the talk and I actually got a little bit scared and I was worried that maybe analogies were not everywhere but just a few maybe I knew of a few analogies that had been important in physics but I wasn't really I I may have overstretched you know that the validity over done it so I started looking very hard at the history of physics and trying to find what had gone on in the minds of people all the way from Galileo to Newton to people like Faraday and Maxwell and on and on and what I found was that indeed it was really ubiquitous virtually every discovery that I met that I examined was made by analogies so I found analogies by all of these people and I incorporated them in my talk it was actually kind of crazy because I had I later gave a whole course on analogy in physics and here I was trying to give the whole thing in one hour it was a bit ridiculous but nonetheless I I had a wonderful time in assembling all these beautiful deep analogies and understanding the thought processes that had led people to find such fantastically deep insights to the nature of the universe this was very exciting to me but you might wonder why isn't the name Einstein there well there is actually a reason I I was about to say a good reason but it's not a good reason there's a bad reason that Einstein wasn't there which was that I was scared that Einstein maybe was too smart maybe he didn't really use analogies because analogies sort of you know they they they seemed like again I can't see this but you can see it reminding similarity resemblance analogy almost to use a more pejorative word guesswork and I thought oh surely Einstein didn't guess at anything he just you know immediately reasoned his way to it by pure logic and so this this naive fear on my part I actually kept me from exploring Einsteins thinking processes well then Along Came John rigdon as the several years later this is five years later I went to hear John Riggins talk in the the annus mirabilis centenary year 2005 and he gave this great talk in which he talked about an analogy that Einstein had made and it opened my eyes completely to the fact that Einstein did use analogies after all and in fact he talked about a particular paper the first of the five papers that Einstein wrote that year and as Einstein said it was the most revolutionary idea that he had ever had and uh however most physicists think of the paper as being they call it they all refer to it as the photoelectric effect paper & Rigdon asked them I don't remember how he did this I mean he didn't say how many of you think of the photoelectric effect paper as the photoelectric effect paper he said it in some other way he said it's something like how many of you think of and then he described a paper in some fashion that got people to think about the right paper and then he said why did he do in this paper and everybody said he discovered the photoelectric effect or he explained he didn't discover he explained the photoelectric effect & Rigdon said no he the paper is not about the photoelectric effect that paper is about the idea that light consists of particles and it's an analogy that Einstein came up with that led him to this crazy idea and that's what this talk is about and so he he was very very adamant about the idea that physicists have the wrong impression so let me give you an example I gave a talk that was very similar to this very recently in the Max Planck Institute for quantum optics in gushing Germany now of all places an Institute for quantum optics should know where the concept of a light quantum came from I mean optics being light so here is the brochure the official brochure statement about that begins there their brochure in the late 19th century it was proven beyond doubt that light propagates through space as an electromagnetic wave yet no sooner had lights nature been understood than a whole new side emerged first Max Planck in 1900 and then Albert Einstein in 1905 concluded that light under certain conditions behaves like a shower of particles light quanta or photons I have put it in red here because this is dead wrong it was not plunk at all it was Einstein 100% who said this plunk did not have any such idea he you as you will see in the rest of this talk I don't need to anticipate it so a little bit after rigged ins talk I received an invitation to give a talk in the centenary year of the omnis mirabilis Alexandria Egypt about Einstein and I thought wow that's an honor that's a great honor and so and of course you know to go to Alexandria Egypt is an interesting thing too so I I thought okay I'll give a talk Albert Einstein analogize er extraordinaire and Alexandria Egypt so that was the nature of my talk but then I had to go look through Einstein's discoveries and he of course made many and see if I could find more analogies and I found analogies everywhere analogies lurking under every stone so once again I was gratified and you know I felt confirmed in my in my guess that analogies pervaded physics so um I discussed analogies by Einstein in such areas as relativity and these are some of the analogies I'm not going to spell them out special relativity general relativity and others and it was a great pleasure to do so in my talk I closed with a poem that Einstein wrote in honor of Newton and so I read it to you in German and then in English right so to Aaron from Isaac Newton Einstein Zita Stern added a layer and V man's old in meister aaron yellow Foulke na newton's plan AV Schrag and xena bond or in my english translation in homage to Isaac Newton a Einstein C on high each twinkling a stir teaching us to prize the master each is pulled by Newton's force ever silent on its course now so Einstein and had a great reverence for Newton and both of them thought about the nature of light and that leads me to this top of this talks topic they both thought about the nature of light and here is a picture that that captures something of the the the controversy about light in Newton's time nobody knew what light was made of now here I've - I have a picture of let's say a calm sea but with a wave in it and the wave if it were really a perfect mathematically perfect wave it would have a perfect wavelength but you can imagine that this has a very periodic behavior with a very perfect wave length and that it stretches from here to everywhere and this is the nature of a wave that it in it fills space and it it's sort of Wiggles it changes it propagates through space but it fills space and then on the other hand we have here I don't know what that is but I'll call it a buoy and anyway it's sort of a very localized phenomenon and it's sort of the opposite of a wave it's very point like and it doesn't feel space in any way shape or form and so the question was his light carried to us as waves the way sound is or is it carried to us as particles now it was a big it was a big debate and Newton took the side of the particles and there were people who were vehemently opposed to him like his colleague Robert Hooke and so these two fought it out with Annie without any conclusive result and and it's very interesting to think about this in a hundred or two hundred years later the English physicist Thomas Young made some experiments that demonstrated very clearly using a diffraction grating that in fact like was a wave and and not only that Young was able to measure the wavelength of the different colors and to find to get estimates for the wavelength of the different parts of the visible spectrum and he concluded erroneously that light was a laundry toodle wave which means like sound like it it it vibrates like this as it goes forward instead of like this as it goes forward which would be a transverse wave that was an error he made which was corrected somewhat later by his French colleague Fran el who did more experiments and determined that light was a transverse wave not a longitudinal wave and so they came to an understanding of light as a wave phenomenon that could be polarized that had all sorts of interesting properties and this was the beginning of the understanding of light as a wave I've written I put these this word wave in small small size here and larger size here just sort of to emphasize the idea that as it gets bigger it gets more and more confirmed over the years so in eighteen roughly 65 the Scottish physicist James Clerk Maxwell combined the equations that other people had found and enhanced them or augmented them with his own important additions and the equations of magnetism and of electricity and made a unified theory of electromagnetism and in his theory that showed that magnetic fields created light that created electric fields and electric fields created magnetic fields as they were changing this was a revolutionary unification of magnetism and elektra well electricity were the phenomenon electric fields all of the things that have to do with electricity and Maxwell's equations yielded a great surprise which nobody had anticipated which was that an electric field as I say if it changes it creates a magnetic field and if a magnetic field changes it creates an electric field and so that you can kind of get a back and forth reverberation and these things then propagate through space together and there is a natural velocity with which this electro magnetic wave propagates I mean today we hear the word electromagnetic and at least if you're in physics you don't even think about it but really it is electro magnetic it is two things at once and it's quite magical um and Maxwell was the first person to understand that electro magnetic waves existed and could propagate through vacuum and he could calculate their speed because there was some constants in his equations and it turned out that the speed was a natural very simple function of these constants in his equations and the constants are these mu naught and epsilon naught which I'm not going to explain they're just numbers are just constants and if you take their square root and then multiply them take their square root take the square root and divide it take the reciprocal you get a velocity which is the natural velocity of electromagnetic waves in empty space and this number 300,000 kilometers per second was a number that Maxwell knew he recognized it as being the speed of light as measured experimentally by many people and it was an overwhelmingly amazing revelation to Maxwell because he believed that he had there that he had revealed or uncovered the astonishing fact that light was something to do with electricity and magnetism which nobody would have ever suspected and this was one of the great discoveries perhaps the greatest discovery of all time and see being the speed of light and and so it confirmed the idea that light is a wave and it was transverse and that it's an electromagnetic wave an Einstein in 1940 wrote an article about Maxwell's discovery and he said the following in this article in science magazine in the United States imagine Maxwell's feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarized waves and at the speed of light too few men in the world has such an experience been vouchsafed and I I would say practically nobody I can't III think that would have been the most amazing moment of Revelation that anyone could ever have so a few well a couple decades later the German physicist helps was performing some experiments to study the properties of electromagnetic waves in in his laboratory and he wanted to see if in fact the the waves that were electromagnetic agreed with all the properties of the light waves that people had studied like young and Finnell and many others and he confirmed all of the properties the speed the polar is the polarizability and so forth but um the transverse nature is there so the the experiments that he made with sparks proved this was the the final proof you could say that light was a wave in roughly eighteen eighty seven eighty eight rough roughly at that time there was one funny little thing though he had to in order to to detect the some effect of a wave he had to see a spark and he was in a room where where it was there was too much light and he couldn't see the spark very well so he closed the curtains and then he could see the sparks better but it turned out that closing the curtains also made the sparks much rarer which he had not anticipated and so he wrote a second paper about his results that simply summarized this little extra fact about these experiments that had confirmed that light that electromagnetic waves are light or that light is electromagnetic waves he wrote a little paper that just talked about this funny anomaly that he couldn't explain which well it turned out that this this little anomaly eventually spelled curtains for Maxwell's theory of light it's a great irony that the exact set of experiments that proved that light was a wave also were the foundation for the undermining of the idea that light is away very amazing so in 1905 Albert Einstein published the first of these radically revolutionary papers and I've called it a poem and it's called UBA einen de toi Gong on fervent long day's leaf despot Rettendon hora station Gazette spunked 419 in Bern and he was working as a patent office clerk technical expert at Ritter class a third-class technical expert that's what Einstein was he was not known to anyone in the world of physics at all he was just a random 26 year old patent clerk who submitted papers to the Nollan de physique and they were published because they were good papers but nobody had ever heard of him so I'm gonna tell you a little bit about this paper and I'll read you a translation of the some of the this is near the beginning of the paper it's very interesting it strikes me that the recent observations of black radiation and we'll talk about that what he today we would call it blackbody radiation but he says black radiation of photoluminescence of the production of cathode rays by ultraviolet light and of other types of phenomena that involve the production and transformation of light might better be understood through the notion that the energy carried by light is distributed discontinuously in space according to the point of view to be considered here when a light ray radiates outward from a point its energy does not spread out evenly over an ever larger volume but rather it consists of a finite number of spatially localized energy quanta which move without dividing and which can only be absorbed and produced as holes in what follows I would like to describe the thought processes and to exhibit the facts that have led me to this conclusion in the hopes that the viewpoint thus presented will prove to be useful to some researchers in their investigations and so he's he's going to tell people how he came up with this idea and that's what the majority of this paper is I'd say two-thirds to three-quarters of this paper is telling people how he came up with this nonsensical crazy idea that flew in the face of the well confirmed for a hundred years idea that light is is a wave so first let me talk about what he called black radiation de Scottish column you behind it detail he - thoughts and Halong but - - feel excited difficulty having to do with the theory of blackbody radiation now I'm going to tell you what that means so here's a picture of what physicists call a blackbody this is a container in which which is held at a certain temperature so we have to think of this body as being held at a fixed temperature and the temperature causes heat - I know how to say this exactly but it it creates electromagnetic waves inside the cavity in other words the cavity itself is has vacuum in it but but nonetheless the vacuum contains electromagnetic energy because of the temperature and and so that what electromagnetic energy means is waves of light of different frequencies and so here we have some red and some green and some orange and some blue and some other color waves propagating these arrows here means it's kind of like the waves that I showed on the ocean the wave is propagating this is a wavefront and it's like on the the pictures that I picture that I showed is propagating this way this is propagating this way etc now the question is when you hold this blackbody at a particular temperature what is the predominant wavelength or if you wish the predominant frequency of light because the wavelength times the frequency is the speed of light which is a constant so if you know the wavelength you know the frequency and vice versa so what is the predominant wavelength or frequency at a given temperature that's a very deep question that was being explored at that time and nobody could really explain it but they could measure it so here is a graph I mean I just drew it myself but it represents the flavor of the results at that time which on the x-axis here which I've labeled nu nu stands for frequency so for different frequencies you get different loops for different frequencies you get different amounts of energy in other words there's more the most light is at at this frequency and then there's less light at lower frequencies and less light at higher frequencies this is the intensity this is the intensity so there's a maximal intensity this is called the blackbody spectrum and it was a very famous mystery at the end of the 19th century because nobody could explain it people made attempts to explain it some people just tried to write down equations out of the blue that would simply reproduce that curve other people tried to derive equations that would reproduce that curve but they had great difficulty in finding an equation that would reproduce that curve so here are some results that this is the flavor of the results around 1900 so we have three people I there I wish I could see this better I guess I should point it there and then move it over okay so there was vilhelm called varna otto fritz france vin who published the the the curve that is seen here that is bluish I've color-coded it I don't know if you can tell it's blue but this is Veen here and in 1900 the English physicists Lord Rayleigh and James genes published another curve which they had derived from Maxwell's equations this curve was a parabola and it sailed up to infinity along here obviously not at all agreeing with what happened out here it agreed very well right in here and if you studied it in here it was very accurate but but but as it go further to the right and frequency higher and higher frequencies got more and more wrong infinitely wrong in fact and Max Planck in 1900 guessed a curve he guessed a formula that was close to beens curve I might say that Venus was just a guest curve also he didn't derive it but he guessed the form and wrote it down Max Planck's curve was also a guess but it coincided very accurately with the data it was five years after Veen and now Frank was very upset at the fact that he had just written down an equation without any justification and so he wanted to justify it and so he worked for months at trying to find an explanation a physical reason that this curve that he had this equation that he had written down would come out of something he finally found an idea in 1900 that came from the idea that that there were little resonators in the walls of the black body that could vibrate but they couldn't vibrate according to his new theory with any frequency at all they could only vibrate at certain specific frequencies now normally in physics up until then anything that could vibrate would be able to vibrate at any possible speed I mean if you imagine for example a spring for example you can make a spring go like this and you can make it go faster and faster or slower and slower or a swing if you push a child in a swing it has a natural frequency but you can make the child go at a slower frequency just by controlling it yourself or at a faster frequency anything that can do periodic behavior can go at any frequency that you wish you can drive it at any frequency you want but according to Planck's crazy idea that these resonators in the walls were not able to take on arbitrary frequencies and he didn't like this idea he thought it was a terrible idea he hated this idea but he had found it and it gave that curve and so he published it very unhappily and he did not talk about the nature of light in his paper at all he was very certain that light was a wave what he talked about only was these resonators in the walls I might make a footnote here that plunk was an opponent of the theory of atoms not in 1900 but up I don't know up until what year some years before that he did not believe in atoms and so it may be a residue of that fact that skepticism that he didn't refer to the resonators in the walls as atoms or as anything he didn't give them any name except resonators or oscillators and he didn't know what they were he just said these oscillating things that give rise to electromagnetic radiation can only oscillate at certain frequencies but the electromagnetic radiation was certainly light waves and and and with this hypothesis he was able to produce that equation that reproduced the data for the blackbody electrum precisely and it was a great triumph now Einstein was interested in light and he was also fascinated by the nature of black bodies and he felt there was more to the story than so far had been found so he was familiar with all of these attempts to explain the blackbody spectrum but of course he rejected the Rayleigh jeans explanation because it was totally wrong even though it came out of Maxwell's equations maybe in fact this may have been a clue or a cue to Einstein that there was something wrong with Maxwell's equations because ralien jeans had derived their their curve from the Maxwell equations and it didn't agree with the data so maybe this was a first clue to Einstein that something was a little bit awry he didn't like plunks ideas for some reason and I don't know why but he didn't trust plunks ideas so he ignored them totally but for some reason he did like beans ideas the old formula even though Venus formula was not as accurate it didn't reproduce the spectrum as well but Einstein was convinced that the interesting part of the mystery of the blackbody spectrum was located on the right side that place where the Rayleigh jeans formula didn't work and so he wasn't too concerned about the fact that the Veen formula was a little inaccurate on the left side of the curve it was not totally inaccurate but it wasn't pretty exactly it wasn't as good as Planck's formula but it was close enough and on the right side it was very very accurate and so Einsteins jumping-off point for thinking about the black body radiation was the formula that Veen had come up with and I'll just give you that Veen didn't call himself that long complicated name he called himself viv even as if I were publishing a paper called paper by dougie Hofstadter [Laughter] so you buddy in a ki Fateh I long in emission spectrum Anna Schwartz and kopis on the energy distribution in the spectrum of emission of a black body and so he came up with this curve which fit the data fairly well now I just want to comment a little bit on this thing I will also mention the letter H that I've put there was not in his equation that's usually what we call today Planck's constant what he had there was a combination of several other constants of nature including Boltzmann's constant and some other things maybe the speed of light I don't honestly remember but the point is that it was just a set of constants so you can just think of this oops just think of this H as being a a constant K is Boltzmann's constant by the way is another constant the T is the temperature of the blackbody and since we're holding it constant that's another constant of course that you can vary it and study it at different temperatures but it's a sort of a variable constant if you wish where has H and K are constant constants but the real variable here is is nu because that's the thing we're talking where we're trying to understand the spectrum as a function of the wavelength or as a function of the frequency so the intensity of the light at frequency nu is this formula according to beam and it just involves one variable nu cubed e to the minus H nu over KT so it's this is the formula that Veen came up with now this formula reminded Einstein and here is that those words of a very sloppy thinking reminded what a similar kind of sniffed he sniffed something it was kind of intuition it remind him of a similar formula but that that was a distribution of energies or momenta or speeds I'll come to that in a moment of molecules in an ideal gas and so let's talk a little bit about an ideal gas here's a picture of an ideal gas an ideal gas is something contained inside a container that the container is maintained at a particular volume and at a particular temperature and what I would also say is that up until the early part of the 20th century nobody knew for sure what was in an ideal gas because people many people such as machs plunk didn't believe in atoms or molecules and so what a gas was was very unclear however luckily people some people in the 19th century that even before then did suspect that a gases were made of atoms or molecules and using that gas that assumption they were able to talk about they were able to answer questions about the nature of gases and one of the key questions was you have all of these atoms bashing and this is supposed to be an atom and this is supposed to be it doesn't make any sense but it's trail behind it but I suppose that's supposed to the reason I drew it there is supposed to show its speed this is a fast one this is a slow one and there's a very slow one and so forth that's the idea of this picture the different speeds so you what you can think about of course is a two-dimensional analog that you're probably more familiar with which is a pool table and you take the cue and you push it and and the balls scatter and if you have a frictionless pool table so that the balls keep on moving forever then of course it's clear that the balls as they collide with each other and with the walls they exchange energy and momentum and so they not only change in direction but they also change in speed or in energy kinetic energy whatever you want to call it so the the the the but what you can say is as a function of the strength with which you did your first there is going to be a maximal a maximally likely speed for the balls on the table and the the very few of them are gonna go very slowly and of course none of them are gonna go at a very at the speed of light yeah you know so you're going to get a distribution of velocities and what is the nature of that distribution and Maxwell and Boltzmann Maxwell first but Boltzmann later were able to derive a formula for the distribution of kinetic energy in the balls on the table or in the gas so here is the picture of the Maxwell Boltzmann distribution and the idea being that that this is again as the the this is the peak of velocity and this this x-axis is supposed to represent the speed here or the kinetic energy whatever you want to think of it as I guess I wrote it as a function of the kinetic energy ke B and kinetic energy so this is this formula this kind of bell-shaped curve this R is the Maxwell Boltzmann distribution that tells you that there very few at a very low speed and very few at a very high speed and there is this thing here and notice the over KT which should be familiar to you and it would reminds you thanks to my telling you as it reminded on Stein of the blackbody formula that beam had come up with and so we look at these two formulas and we say my goodness there's quite a similarity here isn't there and I mean if you if you look at it there's really only one major difference I mean here we have the new up here and some constant and then over KT here we have the kinetic energy over KT and here we have the new cubed and here we have just kinetic energy not cubed but other than that these formulas are very similar Einstein thought Wow there is something worth exploring here so he hears that word again similar so resemblance again I'm just trying to bring out using this green these green words these green sloppy thinking words nothing to do with logic only to do with intuition trying to bring out the fact that Einstein was led by intuition and sniffing things intuitively so he wanted to deepen this analogy and he turned to thermodynamics which was his he believed in thermodynamics more than in any other part of physics for some reason now if I can read this molecular theory Toronto Zoo they're a panna cotta and Hopi from Gaza on four don't lose the one from four lumen molecular theoretical investigation of the dependence or dependency on of the entropy of gases and and thin solutions from dependence dependency on the volume so this is what he started to to explore was what if you have a if you have a gas and so I here is a here is a gas filling up a container a volume V and the particles are going like that now he's asking himself the curious question what if all the molecules in the gas come to occupy a very different a smaller volume so I you know the famous question you may have heard some time you know what if all the gas molecules of air came to on one side of this room just half of this room what's the chance of that very small that they would all do so the chance that any one of them would be on this side of the room is a half the chance that two of them is a half squared chance for three of them is a half cubed and so forth and the half comes from the fact that we're taking devolve the volume of this half of the room is half of the volume of the whole room so this is the chance of this happening is very slim but it's still possible and that he calculated this difference in entropy s now entropy is an abstract concept I'm not going to talk about it too much but this was something that belonged to thermodynamics and that Einstein was very familiar with and you will see here that what we have here is a a formula that basically depends on the ratio of the two volumes it's saying we take the ratio of the volumes which is like the one-half that I just told you to and we put it to a high power that is we imagine that all the particles in the gas move to one side so it's that ratio that ratio of volumes to the nth power just like I said you know 1/2 times 1/2 times 1/2 times 1/2 we'd have to do it for the enormous number of molecules in this room the chance would be obviously infinitesimal so this was the formula for the difference in entropy between the two situations occupying the full volume occupying a partial volume now he did the same calculation which I'm not going to describe in any way not the same but the analogous computation for electromagnetic waves in a in a and a container and this is the title of the heading of his article UBA the enthalpy def column on the entropy of the radiation and he came up with this formula now this was the formula a bit applied to the black body and the other one above it is the formula that applies to the ideal gas now if you look at these two formulas you see there's a remarkable similarity we have everything is the same Boltzmann's constant in the front logarithm a ratio of two volumes to some power and that's it the only thing that's different is that here we have the number of particles in the black in the ideal gas and here we have a ratio of two energies I'll say something more about this in just a moment again the letter H was not used in his formula it was a combination of other constants but it turns out to be equivalent to Planck's constant so it's easier to write it that way I should point out I didn't say this this is applying to radiation of a particular wavelength not not to the entire radiation in inside the black body but to the radiation of wavelength lambda or well of frequency nu given new this is the difference in entropy now so what is this telling us it's suggesting that there are two things that are analogous that this thing is analogous to that the number of particles in an ideal gas is analogous to this ratio of two energies by the way H times nu H has certain units attached to it and nu is a frequency and it turns out that when you multiply frequency times that number H you get an energy and so when you divide an energy by an energy you get a pure number and this pure number was analogous to the number of particles in an ideal gas and the Einsteins eyes must have lit up at that point and he said my goodness it seems as if the radiation inside the blackbody is behaving like the particles that not everybody believes in in an ideal gas but I believe in them and he did Einstein was a confirmed believer in atoms and he felt that he was sort of seeing evidence of what some people eventually even called atoms of light a quaint term so here was the section of his paper in templates yonder our stalkers filled up a kite and Hopey the moon accommodation column from four lumen not dim boats mansion Prince EEP whatever that means and and so the idea is the hidden meaning is that not only is there an analogy here but that it is saying that the number of particles is given by this ratio of energies you take the total energy at that wavelength you divide by this little teeny amount of energy I said wavelength I should say frequency you divide by the little teeny amount of energy determined by that frequency and that's saying it's measuring the entire energy in terms of little energies it's saying these there's little energies chunks of energy of size H nu H can remember being a constant chunks of energy of that size are populating the container that is filled with electromagnetic radiation so it's as if this radiation which we know is waves consists of little particles bouncing around and so that was his crazy conclusion and he I say undermined maybe that's too strong but he has challenged at least Maxwell's discovery that light is electromagnetic waves by using Maxwell's own spectral distribution for the velocities or kinetic energies of particles in an ideal gas so once again we have these ironies where Maxwell is used to under law under undermine Maxwell very curious things so Einstein says and I will spare you the German if monochromatic radiation of sufficiently low density acts like a discontinuous medium meaning particles in terms of its entropy as a function of the volume then the next logical step would be to investigate whether the laws governing the production and transformation of light are structured as if light were made up of such energy quanta in what follows we wish to take up this matter so at this point we're about three-quarters of the way through the paper and we get into what I call it's not called by Einstein but I call an appendix to the paper because what he does is as it says here he sort of offers weapons to any skeptics to test this idea which is a very radical idea he says look there are three phenomena in physics that I've thought of where maybe the supposed or alleged particulate nature or corpuscular nature of light might manifest itself and he gives three examples of phenomena that have not been explored very much as of yet in 1905 and I'm not going to talk about two of them just one of them the second of which was called the photoelectric effect which was the effect that hi Nora shouts had discovered this anomaly in 1887 and this is the section of the paper called you buddy it's all gone from Katahdin Stalin Jewish belief song Festa Copa on the production of cathode rays by Billie Jean how do you say that radiation or of something illumination of solid bodies okay so here was the here was the picture you have light striking a plate and if the light is according to Einstein's view if it's if it's frequency is low it's going to have very low energy light quanta and they won't be sufficient to dislodge anything from the plate but if their frequency grows higher they become more energetic H times nu is the size of energy of the particle the quantum and as nu grows H nu grows and so this particle that contains this energy it grows in its energy and it can maybe reach a threshold energy at which depp's at which it can dislodge electrons and then as it grows even shorter in wavelength higher in frequency blue in this case it can dislodge electrons much more forcibly and so they go out with higher energy so this idea is that the the higher the frequency the higher the energy of the electrons that are ejected and it basically Einstein showed in a very simple calculation that the energy of the electrons that were ejected was a linear function just a multiple of the energy of the light of the frequency of the light that was hitting the plate it's a very simple derivation coming from a very very radical hypothesis but it gave a very simple prediction for what the photoelectric effect would be if people stunts were to study it and he says he modestly adds as far as I can tell our interpretation does not conflict with the properties of the photoelectric effect as observed by mr. Lonard now Lonard was a physicist who had studied the photoelectric effect but had not studied it in great detail he had some results and as Einstein says here they did not conflict with his theory but they did you know they didn't confirm his theory either so he's simply saying let's see I'm proposing this as the subject of experiments for the future so this was an analogy that he made between black bodies and ideal gases a hypothesis that light consists of particles and this appendix and they were published in an island of physique Max Planck was the editor now Planck was a very honest person he didn't like these ideas at all but he couldn't find any errors in them and so he published them and that was to his great credit who believed in these ideas I will give you a list there is the list that's the list of the people who believed in this site these ideas for the next almost 20 years that was the entire list okay very interesting in 1907 Einstein made a new analogy that was correlated to what he had done and what Max Planck had done in 1900 he took the idea that periodic phenomena whether they were resonators in the walls of the black body or whether they were the waving things in electromagnetic radiation that periodic phenomena should all be quantized mean meaning restricted to certain specific frequencies as opposed to taking on any frequencies arbitrarily that was Einstein's jump a leap of intuition he based on two cases the plunk case and his own case and he decided that for vibrating atoms in crystals when they when you heated something up that they that the the vibrations of the atoms could not go at arbitrary frequencies they were limited to certain restricted frequencies just like the resonators in plunks about blackbody walls and and so that was the that was his analogy his gas and I came from these places now it happened that there was a lot of famous law the law of Doolin p'tee about the about the specific heat that is I'm not going to go into the details here but the specific heat of solids as a function of temperature do Lauren Pattie had shown many many decades earlier by a very reasonable argument that the specific heat of all solids should be the same and should be the same at all temperatures and many solids obeyed this but Dimond had been seen to be anomalous and in fact the specific heat of diamond fell rapidly towards zero as you got toward very low temperatures and nobody could explain this but Einstein's idea about the vibrations of the atoms in a in a crystal did explain it Einstein was able to derive this is this picture here shows the actual data the dots going down here and Einsteins curve which agreed really remarkably well and so it confirmed something that had been it explains something that had been bothering physicists for a long time so the the the strange thing is that the reactions after this paper in 1907 was published the reactions to Einstein's sound quantum hypothesis which is what I would call it were positive but reactions to the light quantum hypothesis even though it was an ingredient in the sound quantum hypothesis were negative and Max Planck himself who was a big supporter of Einstein he wanted to be nominated Einstein to membership in the Prussian Academy of Sciences which was the most prestigious Academy of Sciences in all of Europe and here was what he said in Minh has nominated er about Einstein that he may occasionally have gone a bit overboard in his speculations as for instance in his hypothesis of light quanta should not be held to much against him for even in the exact science as if one never takes any risks no genuine innovation can be accomplished now plunk knew that very well because of his own work but here he was saying basically Einstein is he's a little bit nutty sometimes he comes up with crazy ideas like light quanta but I forget it it's ok he's he's basically a good guy hmm so no so I might say yeah ok plunk can accept his crate his own crazy idea of discrete levels of energy of resonators but light particles having zero mass no way ok Millikan robert millikan was a very famous physicist who had already done very important work and he took on on took it upon himself to study the photoelectric effect and he studied it for several years very very very greatly in detail and came up with a set of results that were so long that eventually he published a whole book about them but this that was a couple of years after this but in 1914 in an article he published about it he wrote the following we are confronted by the astonishing situation that these facts that the photoelectric effect straight line that Einstein had predicted that these facts were correctly and exactly predicted nine years ago by a form of quantum theory which has now been pretty much abandoned meaning the form of quantum theory meaning idea that light consists of particles so that's what Milliken said even though he had confirmed Einstein's prediction I didn't believe in light quanta in any way at all then in his book he wrote this this is the book two years later this is quite interesting despite then the apparently complete success of the Einstein equation the physical theory of which it was designed to be the symbolic expression is so untenable that Einstein himself no longer holds to it which is not true we are thus in the position of having built a very perfect structure and then having entirely knocked out the underpinning without causing the building to fall it stands complete and apparently well tested but without any visible means of support in other words my curve my straight line curve confirms the idea that Einstein said but Einsteins justification like quanta there's that's nonsense so there's no explanation supports must obviously exist and the most fascinating problem of modern physics is to find them experiment has outrun theory or more precisely put experiment guided by erroneous Theory has discovered relationships that seem to be of the greatest interest and importance but the reasons behind them are as yet not at all understood guided by erroneous theory very interesting niels bohr i don't know when he wrote this were i to receive a telegram from albert einstein confirming the existence of light quanta i would point out to him that the telegram itself transmitted by electromagnetic waves was proof against them okay now einstein was awarded the Nobel Prize in 1921 here is the citation in English for his services to theoretical physics and especially for his discovery the law of the photoelectric effect where is a mention of light quanta nowhere why does he get a Nobel Prize for writing us saying that there's a straight line the straight line came from somewhere it came from the idea of light quanta that was the whole beauty of the thing and yet they didn't award him the Nobel Prize for that so I am likening this to them michl on the give me signing three stars to the restaurant that I'll call Shea's albear so here's their ranking how they explained why they gave the Shea's about three stars for serving edible food and especially for garnishing each dish with dainty parsley stems that's about the equivalent of the Nobel Citation the way I see it okay so Niels Bohr won the Nobel Prize in 1922 and for some reason he saw fit to criticize Einstein in his Nobel lecture so let's read what he said I don't know why he did but he did Einstein was led to the formulation of the so-called hypothesis of light quanta according to which the radiant energy in contradiction to Maxwell's electromagnetic theory of light would not be propagated as electromagnetic waves but rather as concrete light atoms there's that phrase Bohr uses it this concept led Einstein to his well known theory of the photoelectric effect the predictions of Einstein's theory have received exact experimental confirmation in recent years namely Millican in spite of its heuristic value however the hypothesis of light quanta which is quite irreconcilable with so called interference phenomena is not able to throw light on the nature of radiation 1922 Niels Bohr okay that's how many years later seventeen years later what would I have thought now of course I would on Albert Einstein side I would have been so so deeply insightful and I would have been his one pal all of you well I don't know but I certainly would have been on his side and why would I have been on his side well because I was born in 1945 long after all these phenomena or her confirmed and so I grew up knowing the concept of Photon and it wasn't as if I really would as if this the genetic material that created this person would have created a person who believed in Einstein's ideas I'm sure I would have fallen into the trap that all of the other colleagues did too had I really been born at at back at that time it's very easy to think oh my goodness they were so silly but actually you know it's it's really quite interesting to think what made Einstein believe in it and what made all of them be so skeptical I mean he was very smart people very interesting well Along Came in 1923 the Compton effect which was in effect by which light would hit atoms and dislodge an electron from its orbit sending the electron off scattering the electron off somewhere and the light changed wavelength which was not supposed to happen Maxwell's equations didn't have light scattering off of things and changing wavelengths and it did change its wavelength and not only did it change its wavelength but if you calculated what Einstein theory of light quanta would predict them to do they it changed its wavelength in exactly the way that his theory had said it would all of a sudden people started thinking maybe he was right and the world of physics never from that point never was sceptical any longer about this idea and in 1926 the American chemist Gilbert Lewis coined the catchy word Photon and that became a very important concept of course as we all know so in the end is light a particle or is light a wave well there's the answer read it as you wish okay light is a all right and finally Einstein still was mystified by the nature of light even until the end of his life in a letter that he wrote to his child Walt not childhood but his young student hood pal Micaela best so he wrote all these years of v conscious 50 years of conscious brooding have not brought me any closer to answering the question what are light quanta today of course every rascal thinks he knows the answer but he is deluding himself so I will conclude with a poem that I wrote since I first gave this lecture in Germany I wrote it in German and then I translated it to English so here it is least in shorts and cope on pasta Einstein's pas - Prix de Alta Tyson Nam of our elite Eva vel endure I see Einstein watched black bodies glowing in them glimpsing God all-knowing he suspects not waves in light such spectacular insight thank you [Applause] thank you so much dog let me ask you I mean the question of particles or waves is obviously still a mystery because because light presents itself in both ways do you think that we ever will have intuitive interpretation of what it actually is because it can't be both at the same time intuitively intuitive intuitively it can't be both at the same time but in fact it can be both at the same time so I think my guess is that we won't ever have an understanding that is any better but of you know what do I know I I have the feeling that we won't ever come to understand I couldn't it be some kind of couldn't we find an analogy or or a sort of metaphor or how you describe it that sort of souls to conflict solves the duality that we just don't realize yet is that impossible you think well you know I I couldn't possibly tell you that but I I sort of feel as if the nature of quantum mechanics is something that is fundamentally mysterious I I kind of agree with Fineman who says if you think you understand quantum mechanics well you're you don't or line Stein says you're fooling yourself I I sort of feel as if the fundamental nature of quantum mechanics is is not accessible to creatures at our level at our size and that what we have to do is make do with I don't know how to phrase it exactly sort of an intuition about oh I think it'll behave more like a wave in this circumstance and more like a particle in that circumstance and and then just see if that's the case I I just somehow fundamentally think that we're not able we're not going to be able to I mean maybe I it's almost a romantic hope I don't know almost as if to say this is something that's beyond us in some intrinsic fashion okay but let me ask you this done you you you you talk here about the power of analogy in creative thinking and could it be could you see a situation where the opposite holds what I mean is that you you you create an analogy and you think in terms of that analogy so much so you get constrained by it you get limited by it you see what I mean oh yes well I mean I think that you know we do that all the time in life I mean stereotypes of people we we we we we we we categorize people very rapidly in terms of in surface level terms and we may be misled by those analogies that we are making and in politics it happens all the time too I mean there is a book that was written about the analogies that guided the American that were written the the the rival analogies during the Vietnam War that were raging in the government all sorts of different people in the nineteen mid-1960s advocated different things and made different analogies to various different situations in the world in world history you know some they're talking about the Vietnam War and some would liken it to things that had happened in the the capitulation by Chamberlain to to Germany and other people would talk about analogy of the domino effect and other people would talk about this and not there were many many different analogies and each analogy was convincing deeply convincing to person who held it and and they wouldn't budge from that analogy and and we're all trapped by our categorizations and analogies we're all trapped by that many analogies are our misleading there's no reason that analogies are should always be good they're just the nature of our thinking and and many of them are going to carry us down false pathways I'm thinking of Einstein's as you know Einstein never accepted the quantum physics in the modern expression of it until his death he never accepted it is that it can't be like that yeah and he uses his famous analogy when he says God does not play dice yes even though he was not religious as a lot of people think but but he uses that metaphorically so in a sense I'm Stein was trapped by that analogy that the universe should be deterministic and logical sort of so to speak yes and no he was trapped by it in that in the sense that he didn't like the many aspects of the quantum mechanics that had come out in the 1920s but aside from having created the idea that light is a quantum phenomena quantum phenomenon he had also in about nineteen sixteen or seventeen created the first probabilistic theory of of subatomic phenomena which had to do with what was called induced emission and spontaneous emission and I don't want to try to go into the details but the the point is that in that in those papers he posited that nature behaved probabilistically intrinsically now just like Planck had not liked his own theory in 1900 that said resonators could only vibrate at certain frequencies and plunk didn't like that Einstein did not like or did not believe in his papers in nineteen sixteen and seventeen but he published them nonetheless because he knew that they explained some phenomena that nobody had been able to explain before and he thought maybe just as plunk thought maybe this ideas as provisional we'll replace it with something else but for the time being I'll publish this paper that'll be a step along the way but as it turned out the the ideas of probability remained and so Einstein was actually the very first person to introduce probability into quantum mechanics so in a funny sense I'm Stein did he was the pioneer of the idea of non determinism in quantum mechanics he was the first person to suggest it but he was also one of the last to you know to cling to the opposite it'sit'sit's and to accept the consequences he couldn't really accept the consequence because you can tell this better but I think he even created a Gedanken experiment and the EPR experiment saying that if you were right with your quantum physics then this experiment would have these absurd results yes so it can't be right yes and now we have made that experiment and it has these that's right that's right can you explain that better than I did now because well I don't know I mean I can talk about the EPR paradox a little bit but I don't I'm not an expert by any means but I can just simply say that the idea would be that if you have let's say a decay phenomenon in which two particles are produced simultaneously and and one of them is going to be like a photon is going to be polarized in a certain direction and the other one is going to has to be polarized in the other direction in order to conserve angular momentum so you know that these two photons are going to go away from each other at the speed of light by definition and one of them is going to be polarized in the opposite way to the other okay so they go away for a year and one of them is very far away and you measure its polarization and you find out what it is and at that moment the other ones polarization is determined and must be the opposite in order to conserve angular momentum as I said but it it [Music] it's as if the information spread instantaneously across two light-years of distance when in fact nothing can you know you can't go fast in the speed of light and this is going way faster than speed of light is going instantaneously he's what he called spoky action action at a distance is what Einstein that's right spooky action at a they would call it entanglement and today we call it entanglement that's correct and and yeah it's it's it's a very mysterious thing and and and at the heart of the most mysterious qualities of characteristics of quantum mechanics and once again it underlines the the the mysterious nature that I don't think we're ever going to be able to understand as what I would call classical creatures creatures that exist at a level that so much higher than the size at which quantum effects really take place that we can't we have no intuition for them hmm tell me the the idea of gravitational we I mean when I when I started when I went to school when I was a kid I learned that gravity gravity gravitational gravity is a force but as I understand it according to Einstein's theory gravitational gravity is not a force right it's a curvature of yeah I think that you know when you say something is or isn't a force it's a little tricky I mean it's it's like what I mean it's not like this strong or weak electromagnetic force it's it's a curvature of space what I'm trying to get to yeah okay we are trapped by this analogy we're talking about it as a force and then maybe we limit our way to think well gravity yeah I mean in that sense that was Ines another of Einstein's great analogies the so-called equivalence principle which led him to the idea that what looked like a force might not actually be a force might actually be something quite explain the equivalence yeah well okay if you have electric charges that attract or repel each other the strength of the force is proportional to how how much charge they have and and so there's a this quality this quantity II or whatever letter you want to use to represent charge in the equation well there's something very similar in gravity which is the formula for the gravitational attraction between two bodies looks almost exactly the same as the formula for the repulsion or attraction of two charges to each other the difference is that where there are two charges multiplied the two objects together in the numerator in in the in the formula for gravitational attraction which comes from Newton it's two masses that are multiplied together so the gravity of an object is proportional to its mass well Einstein noticed that this was curious because it meant that according to Newton's laws F equals MA force equals mass times acceleration that M there was the same M as in the other formula the mass the two masses multiplied so if you put one force on one side of the equation and the on the other side of the equation the two M's cancelled and what it meant was that if you put a bunch of bodies in the same gravitational field they would all fall at the same rate which is of course new Galileo's yeah idea but Einstein was seeing this in a new way he was saying that gee everything all falling at the same rate that remind me of something that I studied in my mechanics class which was things called fictitious forces and a fictitious force is something like centrifugal force where you're on a merry-go-round or something that's turning and and in that frame of reference if you were to throw off a ball a tennis ball or a golf ball or a bowling ball or whatever all of the balls that you threw off would follow the same pathway because it would turn out that the centrifugal force that would be seeming to affect them would would be independent of their mass and that facts Einsteins that force independent of that is the back the behavior is independent of the mass that's just like a fictitious force and and so all of a sudden and fictitious forces came about in accelerating reference frames like when you're going around in a merry-go-round that's called an accelerating reference frame it's I guess it's the same thing as if you if you imagine that you stand on a plate in space there's no way for you to tell if it's gravity that pulls you down on the plate or if you're actually accelerating correct that was the I the idea of the the equivalence principle was that gravitational forces are indistinguishable from accelerations Einstein came to this idea through a series of connections mental connections of analogies and that let he called it the happiest thought of his life yeah and I mean it's the same as we're the relative speed if you sit on a train and you look at the window and see the other train you don't know if it is you who are started to move or if it's the other trains oh it's related sorry to use that word in this context but yeah yeah but when you're talking about is is actually Galilean relativity which is a predecessor of special relativity which it's offices predecessor of general relativity yeah yeah that's why Einstein says today to the ticket man on the train excuse me is Chicago stopping by this train yes yes okay we have to end very soon let me just ask you a few things now we talked about Einstein for a long time now I want to talk about you a little bit the first time you were in Sweden was when you were 16 years old right right that's a week out for about three days three days you came with your father yeah who was awarded the Nobel Prize in Physics that's correct 1961 correct and then you mentioned that it was in this wonderful city not this time of year but almost I mean December and and it was so romantic that it gave me a feeling that Stockholm was infinitely romantic yeah and it made me want to come back in a winter that's why I came back for three months to absolve because I wanted to be in Sweden in the deepest darkest coldest winter yes you've been here now for two months and you mentioned you were in Sweden for six months fifty years ago yeah fifty-two years ago they could aha holy for lasting and post rains come and they screw you I had the hawk who knew it yeah via two namely not too young a tan sprock raquel scary italians Leticia nice calories a cup emollient svenska but four liters okay they rule it say a machine or yeah ie image comedy protest in NZ schedule your honor - letís they mostly oh so now you're devoted hurry three mana diverticulum strands winter oh the rocket your yatta Chrome's went Covington can you say okay okay tax ahem Smith yeah [Applause] [Music]

Channel: Fri Tanke

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Keywords: albert einstein, willy wien, douglas hofstadter, christer sturmark

Id: NXdQfPrU64g

Length: 90min 56sec (5456 seconds)

Published: Sun Feb 04 2018