Richard Feynman talking with a teaching assistant after the lecture on The Dependence the creation of the HTML edition of The Feynman Lectures on Physics. Feynman Lectures On Physics Volumes 1,2,3 Feynman, Leighton And Sands Pdf . Version, [version]. Download, Stock, [quota]. Nearly fifty years have passed since Richard Feynman taught the introductory physics course at Caltech that gave rise to these three volumes, The Feynman.
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Is 'The Feynman Lectures on Physics' helpful for beginners? Feynman Lectures On Physics Volumes 1,2,3 Feynman, Leighton And Sands Pdf "The whole thing was basically an experiment," Richard Feynman said late in his career. LECTURES ON. RICHARD P. FEYNMAN. Richmond Cimor Trainiui Profesor y Toureriet PT. Cekwiv nye oy Tieckimlagy. ROBERT B. LEIGHTON. Prufif Physics. The Feynman lectures on physics, vol. I — mainly mechanics radiation, and heat, by Richard P. Feynman,. Robert B. Leighton and Matthew Sands (Reading.
However, the sleeve containing all 3 volumes was noticeably damaged, and I. Volume 1 does a bit of everything, at an introductory level, meaning a bit of. Page 1 of 1 edicao de pdf 64 bits gratis torrent Start over. The Feynman Lectures on Physics, Vol. I was so excited to see how complete these books are.
The complete picture, which. From: The Feynman Lectures on Physics. When looked at Vroni any one pair of terniinals.
All with two terminal and we manure the relation. View my complete profile. These are the lectures in physics that I gave last year and the year before to the freshman. Any right to download all or any portion of The Feynman Lectures on Physics.
Mainly mechanics, radiation and heat. Aug edraw pdf viewer 26, August 26, ebook quebec pdf epub torrent gsp at 2: 27 pm. An html5 version of Vol 1 is presently available for free from.
I, and 2 our publisher had some technical problems that delayed the publication. However, the sleeve containing all 3 volumes was noticeably damaged, and I bought this book new.
After more than 2 months, I received the books. By Richard Phillips Feynman Author. The first volume focuses on mechanics, radiation, and heat, including relativistic effects. Jan 22, If the action is of the form of the integral of a function, usually called the Lagrangian of the velocities and positions at the same time then you can start with the Lagrangian and then create a Hamiltonian and work out the quantum mechanics, more or less uniquely.
But this thing 1 involves the key variables, positions, at two different times and therefore, it was not obvious what to do to make the quantum-mechanical analogue. I tried — I would struggle in various ways. One of them was this; if I had harmonic oscillators interacting with a delay in time, I could work out what the normal modes were and guess that the quantum theory of the normal modes was the same as for simple oscillators and kind of work my way back in terms of the original variables.
I succeeded in doing that, but I hoped then to generalize to other than a harmonic oscillator, but I learned to my regret something, which many people have learned. The harmonic oscillator is too simple; very often you can work out what it should do in quantum theory without getting much of a clue as to how to generalize your results to other systems.
There was a gentleman, newly arrived from Europe Herbert Jehle who came and sat next to me. Europeans are much more serious than we are in America because they think that a good place to discuss intellectual matters is a beer party.
I will show it to you tomorrow. What is the use of that? You always want to find a use for everything! You Americans are always trying to find out how something can be used. I had then, at least, the connection between the Lagrangian and quantum mechanics, but still with wave functions and infinitesimal times. It must have been a day or so later when I was lying in bed thinking about these things, that I imagined what would happen if I wanted to calculate the wave function at a finite interval later.
In that way I found myself thinking of a large number of integrals, one after the other in sequence. In the integrand was the product of the exponentials, which, of course, was the exponential of the sum of terms like eL. We are to take the limit as e-0, of course.
Therefore, the connection between the wave function of one instant and the wave function of another instant a finite time later could be obtained by an infinite number of integrals, because e goes to zero, of course of exponential where S is the action expression 2.
At last, I had succeeded in representing quantum mechanics directly in terms of the action S. That amplitude is e to the times the action for the path. Amplitudes from various paths superpose by addition.
Now immediately after making a few checks on this thing, what I wanted to do, of course, was to substitute the action 1 for the other 2. The first trouble was that I could not get the thing to work with the relativistic case of spin one-half.
When the action has a delay, as it now had, and involved more than one time, I had to lose the idea of a wave function. That is, I could no longer describe the program as; given the amplitude for all positions at a certain time to compute the amplitude at another time. It just meant developing a new idea. Instead of wave functions we could talk about this; that if a source of a certain kind emits a particle, and a detector is there to receive it, we can give the amplitude that the source will emit and the detector receive.
We do this without specifying the exact instant that the source emits or the exact instant that any detector receives, without trying to specify the state of anything at any particular time in between, but by just finding the amplitude for the complete experiment. And, then we could discuss how that amplitude would change if you had a scattering sample in between, as you rotated and changed angles, and so on, without really having any wave functions.
It was also possible to discover what the old concepts of energy and momentum would mean with this generalized action. And, so I believed that I had a quantum theory of classical electrodynamics — or rather of this new classical electrodynamics described by action 1.
I made a number of checks. If I took the Frenkel field point of view, which you remember was more differential, I could convert it directly to quantum mechanics in a more conventional way. The only problem was how to specify in quantum mechanics the classical boundary conditions to use only half-advanced and half-retarded solutions. By some ingenuity in defining what that meant, I found that the quantum mechanics with Frenkel fields, plus a special boundary condition, gave me back this action, 1 in the new form of quantum mechanics with a delay.
It was also easy to guess how to modify the electrodynamics, if anybody ever wanted to modify it. I just changed the delta to an f, just as I would for the classical case.
So, it was very easy, a simple thing. To describe the old retarded theory without explicit mention of fields I would have to write probabilities, not just amplitudes. Yet, as I worked out many of these things and studied different forms and different boundary conditions.
I could not clearly identify the difficulty and in one of the short periods during which I imagined I had laid it to rest, I published a thesis and received my Ph.
I found that if one generalized the action from the nice Langrangian forms 2 to these forms 1 then the quantities which I defined as energy, and so on, would be complex. That is, if you took the probability that this would happen and that would happen — everything you could think of would happen, it would not add up to one. Another problem on which I struggled very hard, was to represent relativistic electrons with this new quantum mechanics.
I wanted to do a unique and different way — and not just by copying the operators of Dirac into some kind of an expression and using some kind of Dirac algebra instead of ordinary complex numbers. I was very much encouraged by the fact that in one space dimension, I did find a way of giving an amplitude to every path by limiting myself to paths, which only went back and forth at the speed of light.
The amplitude was simple ie to a power equal to the number of velocity reversals where I have divided the time into steps and I am allowed to reverse velocity only at such a time. Because if this is the formula for the amplitudes of path, it will not do you any good to know the total amplitude of all paths, which come into a given point to find the amplitude to reach the next point.
This is because for the next time, if it came in from the right, there is no new factor ie if it goes out to the right, whereas, if it came in from the left there was a new factor ie.
So, to continue this same information forward to the next moment, it was not sufficient information to know the total amplitude to arrive, but you had to know the amplitude to arrive from the right and the amplitude to arrive to the left, independently.
If you did, however, you could then compute both of those again independently and thus you had to carry two amplitudes to form a differential equation first order in time. And, so I dreamed that if I were clever, I would find a formula for the amplitude of a path that was beautiful and simple for three dimensions of space and one of time, which would be equivalent to the Dirac equation, and for which the four components, matrices, and all those other mathematical funny things would come out as a simple consequence — I have never succeeded in that either.
But, I did want to mention some of the unsuccessful things on which I spent almost as much effort, as on the things that did work. To summarize the situation a few years after the way, I would say, I had much experience with quantum electrodynamics, at least in the knowledge of many different ways of formulating it, in terms of path integrals of actions and in other forms.
One of the important by-products, for example, of much experience in these simple forms, was that it was easy to see how to combine together what was in those days called the longitudinal and transverse fields, and in general, to see clearly the relativistic invariance of the theory. Because of the need to do things differentially there had been, in the standard quantum electrodynamics, a complete split of the field into two parts, one of which is called the longitudinal part and the other mediated by the photons, or transverse waves.
This separation depended upon the relativistic tilt of your axes in spacetime. People moving at different velocities would separate the same field into longitudinal and transverse fields in a different way.
Furthermore, the entire formulation of quantum mechanics insisting, as it did, on the wave function at a given time, was hard to analyze relativistically. Somebody else in a different coordinate system would calculate the succession of events in terms of wave functions on differently cut slices of space-time, and with a different separation of longitudinal and transverse parts.
The Hamiltonian theory did not look relativistically invariant, although, of course, it was. One of the great advantages of the overall point of view, was that you could see the relativistic invariance right away — or as Schwinger would say — the covariance was manifest. I had the advantage, therefore, of having a manifestedly covariant form for quantum electrodynamics with suggestions for modifications and so on.
I had the disadvantage that if I took it too seriously — I mean, if I took it seriously at all in this form, — I got into trouble with these complex energies and the failure of adding probabilities to one and so on. I was unsuccessfully struggling with that. So, he forced the quantum electrodynamics of the day to give him an answer to the separation of these two levels.
He pointed out that the self-energy of an electron itself is infinite, so that the calculated energy of a bound electron should also come out infinite. But, when you calculated the separation of the two energy levels in terms of the corrected mass instead of the old mass, it would turn out, he thought, that the theory would give convergent finite answers.
He made an estimate of the splitting that way and found out that it was still divergent, but he guessed that was probably due to the fact that he used an unrelativistic theory of the matter. Assuming it would be convergent if relativistically treated, he estimated he would get about a thousand megacycles for the Lamb-shift, and thus, made the most important discovery in the history of the theory of quantum electrodynamics. Returning to Cornell, he gave a lecture on the subject, which I attended.
He explained that it gets very confusing to figure out exactly which infinite term corresponds to what in trying to make the correction for the infinite change in mass. If there were any modifications whatever, he said, even though not physically correct, that is not necessarily the way nature actually works but any modification whatever at high frequencies, which would make this correction finite, then there would be no problem at all to figuring out how to keep track of everything.
If, in addition, this method were relativistically invariant, then we would be absolutely sure how to do it without destroying relativistically invariant. I want you to see an interesting point. I did not take the advice of Professor Jehle to find out how it was useful. I never used all that machinery which I had cooked up to solve a single relativistic problem.
But now I went to Professor Bethe, who explained to me on the blackboard, as we worked together, how to calculate the self-energy of an electron. Up to that time when you did the integrals they had been logarithmically divergent. I told him how to make the relativistically invariant modifications that I thought would make everything all right.
We set up the integral which then diverged at the sixth power of the frequency instead of logarithmically! I became more and more interested and finally realized I had to learn how to make a calculation.
So, ultimately, I taught myself how to calculate the self-energy of an electron working my patient way through the terrible confusion of those days of negative energy states and holes and longitudinal contributions and so on. When I finally found out how to do it and did it with the modifications I wanted to suggest, it turned out that it was nicely convergent and finite, just as I had expected.
Professor Bethe and I have never been able to discover what we did wrong on that blackboard two months before, but apparently we just went off somewhere and we have never been able to figure out where. It turned out, that what I had proposed, if we had carried it out without making a mistake would have been all right and would have given a finite correction. Anyway, it forced me to go back over all this and to convince myself physically that nothing can go wrong.
At any rate, the correction to mass was now finite, proportional to where a is the width of that function f which was substituted for d. If you wanted an unmodified electrodynamics, you would have to take a equal to zero, getting an infinite mass correction.
Keeping a finite, I simply followed the program outlined by Professor Bethe and showed how to calculate all the various things, the scatterings of electrons from atoms without radiation, the shifts of levels and so forth, calculating everything in terms of the experimental mass, and noting that the results as Bethe suggested, were not sensitive to a in this form and even had a definite limit as ag0.
The rest of my work was simply to improve the techniques then available for calculations, making diagrams to help analyze perturbation theory quicker. I just took my guesses from the forms that I had worked out using path integrals for nonrelativistic matter, but relativistic light.
It was easy to develop rules of what to substitute to get the relativistic case. I was very surprised to discover that it was not known at that time, that every one of the formulas that had been worked out so patiently by separating longitudinal and transverse waves could be obtained from the formula for the transverse waves alone, if instead of summing over only the two perpendicular polarization directions you would sum over all four possible directions of polarization.
It was so obvious from the action 1 that I thought it was general knowledge and would do it all the time. This was one of the amusing advantages of the method. In addition, I included diagrams for the various terms of the perturbation series, improved notations to be used, worked out easy ways to evaluate integrals, which occurred in these problems, and so on, and made a kind of handbook on how to do quantum electrodynamics.
But one step of importance that was physically new was involved with the negative energy sea of Dirac, which caused me so much logical difficulty. Therefore, in the time dependent perturbation theory that was usual for getting self-energy, I simply supposed that for a while we could go backward in the time, and looked at what terms I got by running the time variables backward.
They were the same as the terms that other people got when they did the problem a more complicated way, using holes in the sea, except, possibly, for some signs. These, I, at first, determined empirically by inventing and trying some rules. I have tried to explain that all the improvements of relativistic theory were at first more or less straightforward, semi-empirical shenanigans.
Each time I would discover something, however, I would go back and I would check it so many ways, compare it to every problem that had been done previously in electrodynamics and later, in weak coupling meson theory to see if it would always agree, and so on, until I was absolutely convinced of the truth of the various rules and regulations which I concocted to simplify all the work.
During this time, people had been developing meson theory, a subject I had not studied in any detail. I became interested in the possible application of my methods to perturbation calculations in meson theory.
But, what was meson theory? All I knew was that meson theory was something analogous to electrodynamics, except that particles corresponding to the photon had a mass. Next, there were different kind of mesons — the one in closest analogy to photons, coupled via , are called vector mesons — there were also scalar mesons. Therefore, I had to find as many opportunities as possible to test whether I guessed right as to what the various theories were. One day a dispute arose at a Physical Society meeting as to the correctness of a calculation by Slotnick of the interaction of an electron with a neutron using pseudo scalar theory with pseudo vector coupling and also, pseudo scalar theory with pseudo scalar coupling.
He had found that the answers were not the same, in fact, by one theory, the result was divergent, although convergent with the other. Some people believed that the two theories must give the same answer for the problem. This was a welcome opportunity to test my guesses as to whether I really did understand what these two couplings were.
So, I went home, and during the evening I worked out the electron neutron scattering for the pseudo scalar and pseudo vector coupling, saw they were not equal and subtracted them, and worked out the difference in detail.
I got a different answer for each coupling — but, I would like to check in detail with you because I want to make sure of my methods. But, it took him six months to do the case of zero momentum transfer, whereas, during one evening I had done the finite and arbitrary momentum transfer.
That was a thrilling moment for me, like receiving the Nobel Prize, because that convinced me, at last, I did have some kind of method and technique and understood how to do something that other people did not know how to do.
That was my moment of triumph in which I realized I really had succeeded in working out something worthwhile. At this stage, I was urged to publish this because everybody said it looks like an easy way to make calculations, and wanted to know how to do it. I had to publish it, missing two things; one was proof of every statement in a mathematically conventional sense. But, I did know from experience, from fooling around, that everything was, in fact, equivalent to the regular electrodynamics and had partial proofs of many pieces, although, I never really sat down, like Euclid did for the geometers of Greece, and made sure that you could get it all from a single simple set of axioms.
Because no simple clear proof of the formula or idea presents itself, it is necessary to do an unusually great amount of checking and rechecking for consistency and correctness in terms of what is known, by comparing to other analogous examples, limiting cases, etc. In the face of the lack of direct mathematical demonstration, one must be careful and thorough to make sure of the point, and one should make a perpetual attempt to demonstrate as much of the formula as possible.
Nevertheless, a very great deal more truth can become known than can be proven. It must be clearly understood that in all this work, I was representing the conventional electrodynamics with retarded interaction, and not my half-advanced and half-retarded theory corresponding to 1. I merely use 1 to guess at forms. And, one of the forms I guessed at corresponded to changing d to a function f of width a2, so that I could calculate finite results for all of the problems.
This brings me to the second thing that was missing when I published the paper, an unresolved difficulty. The deviation from unity was very small, in practice, if a was very small.
In the limit that I took a very tiny, it might not make any difference. And, so the process of the renormalization could be made, you could calculate everything in terms of the experimental mass and then take the limit and the apparent difficulty that the unitary is violated temporarily seems to disappear.
I was unable to demonstrate that, as a matter of fact, it does. It is lucky that I did not wait to straighten out that point, for as far as I know, nobody has yet been able to resolve this question. Experience with meson theories with stronger couplings and with strongly coupled vector photons, although not proving anything, convinces me that if the coupling were stronger, or if you went to a higher order th order of perturbation theory for electrodynamics , this difficulty would remain in the limit and there would be real trouble.
Therefore, I think that the renormalization theory is simply a way to sweep the difficulties of the divergences of electrodynamics under the rug.
I am, of course, not sure of that. This completes the story of the development of the space-time view of quantum electrodynamics.
I wonder if anything can be learned from it. I doubt it.
It is most striking that most of the ideas developed in the course of this research were not ultimately used in the final result. For example, the half-advanced and half-retarded potential was not finally used, the action expression 1 was not used, the idea that charges do not act on themselves was abandoned.
The path-integral formulation of quantum mechanics was useful for guessing at final expressions and at formulating the general theory of electrodynamics in new ways — although, strictly it was not absolutely necessary. The same goes for the idea of the positron being a backward moving electron, it was very convenient, but not strictly necessary for the theory because it is exactly equivalent to the negative energy sea point of view.
We are struck by the very large number of different physical viewpoints and widely different mathematical formulations that are all equivalent to one another. The method used here, of reasoning in physical terms, therefore, appears to be extremely inefficient. On looking back over the work, I can only feel a kind of regret for the enormous amount of physical reasoning and mathematically re-expression which ends by merely re-expressing what was previously known, although in a form which is much more efficient for the calculation of specific problems.
Would it not have been much easier to simply work entirely in the mathematical framework to elaborate a more efficient expression? This would certainly seem to be the case, but it must be remarked that although the problem actually solved was only such a reformulation, the problem originally tackled was the possibly still unsolved problem of avoidance of the infinities of the usual theory.
Therefore, a new theory was sought, not just a modification of the old. Although the quest was unsuccessful, we should look at the question of the value of physical ideas in developing a new theory.
Many different physical ideas can describe the same physical reality. Thus, classical electrodynamics can be described by a field view, or an action at a distance view, etc. Originally, Maxwell filled space with idler wheels, and Faraday with fields lines, but somehow the Maxwell equations themselves are pristine and independent of the elaboration of words attempting a physical description.
The only true physical description is that describing the experimental meaning of the quantities in the equation — or better, the way the equations are to be used in describing experimental observations. This being the case perhaps the best way to proceed is to try to guess equations, and disregard physical models or descriptions.
For example, McCullough guessed the correct equations for light propagation in a crystal long before his colleagues using elastic models could make head or tail of the phenomena, or again, Dirac obtained his equation for the description of the electron by an almost purely mathematical proposition.
A simple physical view by which all the contents of this equation can be seen is still lacking. Therefore, I think equation guessing might be the best method to proceed to obtain the laws for the part of physics which is presently unknown. Yet, when I was much younger, I tried this equation guessing and I have seen many students try this, but it is very easy to go off in wildly incorrect and impossible directions.
I think the problem is not to find the best or most efficient method to proceed to a discovery, but to find any method at all. Physical reasoning does help some people to generate suggestions as to how the unknown may be related to the known.