[量子电动力学的时空观-费曼(英文)] (pdf document) free file download at fliiby.com

"RI C H A R D P. FE Y N M A N The development of the space-time view of quantum electrodynamics Nobel Lecture, December 11, 1965 We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. So there isn’t any place to publish, in a dignified manner, what you actually did in order to get to do the work, although, there has been in these days, some interest in this kind of thing. Since winning the prize is a personal thing, I thought I could be excused in this particular situation, if I were to talk personally about my relationship to quantum electrodynamics, rather than to discuss the subject itself in a refined and finished fashion. Furthermore, since there are three people who have won the prize in physics, if they are all going to be talking about quantum electrodynamics itself, one might become bored with the subject. So, what I would like to tell you about today are the sequence of events, really the sequence of ideas, which occurred, and by which I finally came out the other end with an unsolved problem for which I ultimately received a prize. I realize that a truly scientific paper would be of greater value, but such a paper I could publish in regular journals. So, I shall use this Nobel Lecture as an opportunity to do something of less value, but which I cannot do elsewhere. I ask your indulgence in another manner. I shall include details of anecdotes which are of no value either scientifically, nor for understanding the development of ideas. They are included only to make the lecture more entertaining. I worked on this problem about eight years until the final publication in 1947. The beginning of the thing was at the Massachusetts Institute of Technology, when I was an undergraduate student reading about the known physics, learning slowly about all these things that people were worrying about, and realizing ultimately that the fundamental problem of the day was that the quantum theory of electricity and magnetism was not completely satisfactory. This I gathered from books like those of Heitler and Dirac. I was inspired by the remarks in these books; not by the parts in which everything was proved and demonstrated carefully and calculated, because I couldn’t 156 1965 RICHARD P. FEYNMAN understand those very well. At the young age what I could understand were the remarks about the fact that this doesn’t make any sense, and the last sentence of the book of Dirac I can still remember, « It seems that some essentially new physical ideas are here needed. » So, I had this as a challenge and an inspiration. I also had a personal feeling, that since they didn’t get a satisfactory answer to the problem I wanted to solve, I don’t have to pay a lot of attention to what they did do. I did gather from my readings, however, that two things were the source of the difficulties with the quantum electrodynamical theories. The first was an infinite energy of interaction of the electron with itself. And this difficulty existed even in the classical theory. The other difficulty came from some infinites which had to do with the infinite numbers of degrees of freedom in the field. As I understood it at the time( as nearly as I can remember) this was simply the difficulty that if you quantized the harmonic oscillators of the field (say in a box) each oscillator has a ground state energy of ( I /2) GO and there is an infinite number of modes in a box of every increasing frequency ω, and therefore there is an infinite energy in the box. I now realize that that wasn’t a completely correct statement of the central problem; it can be removed simply by changing the zero from which energy is measured. At any rate, I believed that the difficulty arose somehow from a combination of the electron acting on itself and the infinite number of degrees of freedom of the field. Well, it seemed to me quite evident that the idea that a particle acts on itself, that the electrical force acts on the same particle that generates it, is not a necessary one-it is a sort of a silly one, as a matter of fact. And, so I suggested to myself, that electrons cannot act on themselves, they can only act on other electrons. That means there is no field at all. You see, if all charges contribute to making a single common field, and if that common field acts back on all the charges, then each charge must act back on itself. Well, that was where the mistake was, there was no field. It was just that when you shook one charge, another would shake later. There was a direct interaction between charges, albeit with a delay. The law of force connecting the motion of one charge with another would just involve a delay. Shake this one, that one shakes later. The sun atom shakes; my eye electron shakes eight minutes later, because of a direct interaction across. Now, this has the attractive feature that it solves both problems at once. First, I can say immediately, I don’t let the electron act on itself, I just let this act on that, hence, no self-energy! Secondly, there is not an infinite number of degrees of freedom in the field. There is no field at all; or if you insist on SPACE-TIME VIEW OF QUANTUM ELECTRODYNAMICS 157 thinking in terms of ideas like that of a field, this field is always completely determined by the action of the particles which produce it. You shake this particle, it shakes that one, but if you want to think in a field way, the field, if it’s there, would be entirely determined by the matter which generates it, and therefore, the field does not have any independent degrees of freedom and the infinities from the degrees offreedom would then be removed. As a matter of fact, when we look out anywhere and see light, we can always « see » some matter as the source of the light. We don’t just see light (except recently some radio reception has been found with no apparent material source). You see then that my general plan was to first solve the classical problem, to get rid of the infinite self-energies in the classical theory, and to hope that when I made a quantum theory of it, everything would just be fine. That was the beginning, and the idea seemed so obvious to me and so elegant that I fell deeply in love with it. And, like falling in love with a woman, it is only possible if you do not know much about her, so you cannot see her faults. The faults will become apparent later, but after the love is strong enough to hold you to her. So, I was held to this theory, in spite of all difficulties, by my youthful enthusiasm. Then I went to graduate school and somewhere along the line I learned what was wrong with the idea that an electron does not act on itself. When you accelerate an electron it radiates energy and you have to do extra work to account for that energy. The extra force against which this work is done is called the force of radiation resistance. The origin of this extra force was identified in those days, following Lorentz, as the action of the electron itself The first term of this action, of the electron on itself, gave a kind of inertia (not quite relativistically satisfactory). But that inertia-like term was infinite for a point-charge. Yet the next term in the sequence gave an energy loss rate, which for a point-charge agrees exactly with the rate you get by calculating how much energy is radiated. So, the force of radiation resistance, which is absolutely necessary for the conservation of energy would disappear if I said that a charge could not act on itself. So, I learned in the interim when I went to graduate school the glaringly obvious fault of my own theory. But, I was still in love with the original theory, and was still thinking that with it lay the solution to the difficulties of quantum electrodynamics. So, I continued to try on and off to save it somehow. I must have some action develop on a given electron when I accelerate it to account for radiation resistance. But, if I let electrons only act on other electrons the only possible source for this action is another electron in the 158 1965 R I C H A R D P . F E Y N M A N world. So, one day, when I was working for Professor Wheeler and could no longer solve the problem that he had given me, I thought about this again and I calculated the following. Suppose I have two charges-I shake the first charge, which I think of as a source and this makes the second one shake, but the second one shaking produces an effect back on the source. And so, I calculated how much that effect back on the first charge was, hoping it might add up the force of radiation resistance. It didn’t come out right, of course, but I went to Professor Wheeler and told him my ideas. He said, -yes, but the answer you get for the problem with the two charges that you just mentioned will, unfortunately, depend upon the charge and the mass of the second charge and will vary inversely as the square of the distance R, between the charges, while the force ofradiation resistance depends on none of these things. I thought, surely, he had computed it himself, but now having become a professor, I know that one can be wise enough to see immediately what some graduate student takes several weeks to develop. He also pointed out something that also bothered me, that if we had a situation with many charges all around the original source at roughly uniform density and if we added the effect of all the surrounding charges the inverse R square would be compensated by the R2 in the volume element and we would get a result proportional to the thickness of the layer, which would go to infinity. That is, one would have an infinite total effect back at the source. And, finally he said to me, and you forgot something else, when you accelerate the first charge, the second acts later, and then the reaction back here at the source would be still later. In other words, the action occurs at the wrong time. I suddenly realized what a stupid fellow I am, for what I had described and calculated was just ordinary reflected light, not radiation reaction. But, as I was stupid, so was Professor Wheeler that much more clever. For he then went on to give a lecture as though he had worked this all out before and was completely prepared, but he had not, he worked it out as he went along. First, he said, let us suppose that the return action by the charges in the absorber reaches the source by advanced waves as well as by the ordinary retarded waves of reflected light; so that the law ofinteraction acts backward in time, as well as forward in time. I was enough of a physicist at that time not to say, « Oh, no, how could that be? » For today all physicists know from studying Einstein and Bohr, that sometimes an idea which looks completely paradoxical at first, if analyzed to completion in all detail and in experimental situations, may, in fact, not be paradoxical. So, it did not bother me any more SPACE-TIME VIEW OF QUANTUM ELECTRODYNAMICS 159 than it bothered Professor Wheeler to use advance waves for the back reaction -a solution of Maxwell’s equations, which previously had not been physically used. Professor Wheeler used advanced waves to get the reaction back at the right time and then he suggested this : If there were lots of electrons in the absorber, there would be an index of refraction n, so, the retarded waves coming from the source would have their wave lengths slightly modified in going through the absorber. Now, if we shall assume that the advanced waves come back from the absorber without an index-why? I don’t know, let’s assume they come back without an index-then, there will be a gradual shifting in phase between the return and the original signal so that we would only have to figure that the contributions act as if they come from only a finite thickness, that of the first wave zone. (More specifically, up to that depth where the phase in the medium is shifted appreciably from what it would be in vacuum, a thickness proportional to I /(n - I). ) N ow, the less the number of electrons in here, the less each contributes, but the thicker will be the layer that effectively contributes because with less electrons, the index differs less from I. The higher the charges of these electrons, the more each contribute, but the thinner the effective layer, because the index would be higher. And when we estimated it, (calculated without being careful to keep the correct numerical factor) sure enough, it came out that the action back at the source was completely independent of the properties of the charges that were in the surrounding absorber. Further, it was of just the right character to represent radiation resistance, but we were unable to see if it was just exactly the right size. He sent me home with orders to figure out exactly how much advanced and how much retarded wave we need to get the thing to come out numerically right, and after that, figure out what happens to the advanced effects that you would expect if you put a test charge here close to the source? For if all charges generate advanced, as well as retarded effects, why would that test not be affected by the advanced waves from the source? I found that you get the right answer if you use half-advanced and halfretarded as the field generated by each charge. That is, one is to use the solution of Maxwell’s equation which is symmetrical in time and that the reason we got no advanced effects at a point close to the source in spite of the fact that the source was producing an advanced field is this. Suppose the source s surrounded by a spherical absorbing wall ten light seconds away, and that the test charge is one second to the right of the source. Then the source is as much 160 1965 R I C H A R D P . F E Y N M A N as eleven seconds away from some parts of the wall and only nine seconds away from other parts. The source acting at time t= o induces motions in the wall at time + IO. Advanced effects from this can act on the test charge as early as eleven seconds earlier, or at t= - I. This is just at the time that the direct advanced waves from the source should reach the test charge, and it turns out the two effects are exactly equal and opposite and cancel out! At the later time + I effects on the test charge from the source and from the walls are again equal, but this time are of the same sign and add to convert the halfretarded wave of the source to full retarded strength. Thus, it became clear that there was the possibility that if we assume all actions are via half-advanced and half-retarded solutions of Maxwell’s equations and assume that all sources are surrounded by material absorbing all the the light which is emitted, then we could account for radiation resistance as a direct action of the charges of the absorber acting back by advanced waves on the source. Many months were devoted to checking all these points. I worked to show that everything is independent of the shape of the container, and so on, that the laws are exactly right, and that the advanced effects really cancel in every case. We always tried to increase the efficiency of our demonstrations, and to see with more and more clarity why it works. I won’t bore you by going through the details of this. Because of our using advanced waves, we also had many apparent paradoxes, which we gradually reduced one by one, and saw that there was in fact no logical difficulty with the theory. It was perfectly satisfactory. We also found that we could reformulate this thing in another way, and that is by a principle of least action. Since my original plan was to describe everything directly in terms of particle motions, it was my desire to represent this new theory without saying anything about fields. It turned out that we found a form for an action directly involving the motions of the charges only, which upon variation would give the equations of motion of these charges. The expression for this action A is A=BimiS(*;Xip)idai+& z eie~SS6(lyZ)ffi~(orOgj~(y)daidrj(I) i#j where Ij” = [Xi, (Zi) - Xi, (aj)] [X’, (Cti) - xj, th (~j)] whereX$ (ai) is the four-vector position of the i particle as a function of SPACE-TIME VIEW OF QUANTUM ELECTRODYNAMICS 161 some parameter ai, A$ (ai) is dX$ (a) / dai. The first term is the integral of proper time, the ordinary action of relativistic mechanics of free particles of mass mi. (We sum in the usual way on the repeated index µ.) The second term represents the electrical interaction of the charges. It is summed over each pair of charges (the factor 1/2 is to count each pair once, the term i=j is omitted to avoid self- action) .The interaction is a double integral over a delta function of the square of space- time interval P between two points on the paths. Thus, interaction occurs only when this interval vanishes, that is, along light cones. The fact that the interaction is exactly one- half advanced and half- retarded meant that we could write such a principle of least action, whereas interaction via retarded waves alone cannot be written in such a way. So, all of classical electrodynamics was contained in this very simple form. It looked good, and therefore, it was undoubtedly true, at least to the beginner. It automatically gave half- advanced and half-retarded effects and it was without fields. By omitting the term in the sum when i = j, I omit self-interaction and no longer have any infinite self-energy. This then was the hoped-for solution to the problem of ridding classical electrodynamics of the infinities. It turns out, of course, that you can reinstate fields if you wish to, but you have to keep track of the field produced by each particle separately. This is because to find the right field to act on a given particle, you must exclude the field that it creates itself. A single universal field to which all contribute will not do. This idea had been suggested earlier by Frenkel and so we called these Frenkel fields. This theory which allowed only particles to act on each other was equivalent to Frenkel’s fields using half- advanced and half-retarded solutions. There were several suggestions for interesting modifications of electrodynamics. We discussed lots of them, but I shall report on only one. It was to replace this delta function in the interaction by another function, say,f( I”$, which is not infinitely sharp. Instead of having the action occur only when the interval between the two charges is exactly zero, we would replace the delta function of I2 by a narrow peaked thing. Let’s say that ƒ(Ζ) is large only near Z= o width of order a 2. Interactions will now occur when T - R is of order a2 roughly where T is the time difference and R is the separation of the charges. This might look like it disagrees with experience, but if a is some small distance, like 10 cm, it says that the time delay Tin action is roughly JRZ+ u2 or approximately,-if R is much larger than a, T= R+ &/zR. This means that the deviation of time T from the ideal theoretical time R of Maxwell, gets smaller and smaller, the further the pieces are apart. Therefore, all theories 2 2 -13 162 1 9 6 5 R I C H A R D P. F E Y N M A N involving in analyzing generators, motors, etc., in fact, all of the tests of electrodynamics that were available in Maxwell’s time, would be adequately satisfied if a were 10 cm. If R is of the order of a centimeter this deviation in T is only 10 parts. So, it was possible, also, to change the theory in a simple manner and to still agree with all observations of classical electrodynamics. You have no clue of precisely what function to put in for f, but it was an interesting possibility to keep in mind when developing quantum electrodynamics. It also occurred to us that if we did that (replace δ by ƒ) we could not reinstate the term i =j in the sum because this would now r..."

You need to upgrade your Flash Player , or try to enable javascript in order see this document properly.