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A bit of background helps frame this question. The question itself is in the last sentence.

For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly strange approach to explaining electron-electron interactions without using a field. Their solution was to take the everyday retarded wave solution to Maxwell's equations and mix it 50/50 with the advanced (backwards in time) solution that up until then had always been discarded as "obviously" violating temporal causality. In a series of papers they showed that this was not the case, and that the recoil of an electron when it emits a photon could self-consistently be explained as the result of an advanced photon traveling backwards in time and impacting the electron at the same instant in which the electron emits a forward-in-time photon.

While Feynman's thesis ideas deeply influenced his subsequent development of QED, e.g. in QED's backwards-in-time interpretation of antimatter electrons (positrons). Feynman in a letter to Wheeler later famously retracted (well, famously for some of us) the specific idea of paired photons traveling forwards and backwards in time. Feynman's specific reason for abandoning his thesis premise was vacuum polarization, which cannot be explained by direct electron-to-electron interactions. (Vacuum polarization is easily accommodated by QED, however.)

Feynman's abandonment of the original Feynman/Wheeler retarded/advanced photon scheme has always troubled me. The reason is this: If their original idea was completely invalid, the probability from an information correlation perspective of the idea leading to accurate predictions of how physics operates should have been vanishingly small. Instead, their oddly arbitrary 50/50 mix of real waves and hypothesized backwards-in-time waves almost works, all the way down to the minute length scales at which vacuum polarization becomes significant. One analogy is that the Feynman/Wheeler scheme behaves like a slightly broken mathematical symmetry, one that correctly describes reality over almost the entire range of phenomena to which it applies, but then breaks down at one of the extrema of its range.

My question, finally, is this: Does there exist a clear conceptual explanation, perhaps in the QED description of vacuum polarization for example, of why the Feynman/Wheeler retarded/advanced model of paired photons traveling two directions in time provides an accurate model of reality overall, despite its being incorrect when applied at very short distances?

Addendum 2012-05-30

If I've understood @RonMaimon correctly -- and I certainly still do not fully understand the S-matrix part of his answer -- his central answer to my question is both simple and highly satisfying: Feynman did not abandon the backward-forward scheme at all, but instead abandoned the experimentally incorrect idea that an electron cannot interact with itself. So, his objection to Wheeler could perhaps be paraphrased in a more upbeat form into something more like this: "Vacuum polarization shows that the electron does indeed interact with itself, so I was wrong about that. But your whole backwards-and-forwards in time idea works very well indeed -- I got a Nobel Prize for it -- so thank for pointing me in that direction!"

Answer to Ron, and my thanks.

Terry Bollinger
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    Very nice question. I've read more in detail about the Feynman-Wheeler approach in the book "Action at a Distance in Physics and Cosmology" by Fred Hoyle and Jayant Narlikar. They build up a theory of gravity in the same spirit as the Feynman-Wheeler theory. It does not seem to fit observations though. – Raskolnikov May 10 '12 at 13:05
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    (i) The idea of using half-retarded half-advanced potentials goes back to Dirac. (ii) Far from what you believe, self-interacting electrons are not experimentally proved. What we test in experiments are real electrons which do not interact with themselves. More info in my comment to @Ron. – juanrga Nov 02 '12 at 20:57
  • Carver Mead, a Feynman student, never abandonned the Feynman/Wheeler view. He calls his theory "Collective electrodynamics". – Stéphane Rollandin Jun 07 '16 at 07:59
  • This is related to Cramer's Transactional Interpretation of quantum mechanics. – PM 2Ring Jan 07 '18 at 09:25
  • @PM2Ring thanks, good ref. I've promoted a quantum-as-atemporal perspective for well over a decade (http://www.vokrugsveta.ru/telegraph/theory/754/), to the point that my elevator explanation of quantum mechanics is "Physics for which no specific history -- no external information -- has yet been assigned." I also call this ragged-edged time, since it means that even though self-observation in thermodynamic matter (e.g. us) creates sharp, crisp local definitions of "now", quantum phenomena create regions where time lags and stays undefined, possibly for very long periods of classical time. – Terry Bollinger Jan 07 '18 at 16:00
  • Google translation of above link: http://translate.google.com/translate?hl=en&sl=ru&u=http://www.vokrugsveta.ru/telegraph/theory/754/&ei=a2W0Scm4KZ3etgf-rIzDBw&sa=X&oi=translate&resnum=1&ct=result&prev=/search%3Fq%3D%25D0%2597%25D0%25B0%25D1%2588%25D0%25B8%25D1%2584%25D1%2580%25D0%25BE%25D0%25B2%25D0%25B0%25D0%25BD%25D0%25BD%25D1%258B%25D0%25B5%2B%25D1%2588%25D1%2583%25D0%25BC%25D0%25BE%25D0%25BC%26hl%3Den%26sa%3DG – Terry Bollinger Jan 07 '18 at 16:02
  • Finally, the first "rebuttal" link in this Feb 2006 Bruce Schneier information security blog describes how an atemporal view of quantum mechanics helps explain its security implications: https://www.schneier.com/blog/archives/2006/02/more_on_kishs_c.html – Terry Bollinger Jan 07 '18 at 16:10
  • Getting back to the TIQM, I've been a fan for years. But I guess it smells like teleology, which explains its lack of popularity, compared to, say, MWI. Of course, one can make it more palatable by treating it as a convenient shorthand, like your article does. – PM 2Ring Jan 08 '18 at 00:08
  • But really, it's not teleology. In QM, retarded causation is weaker than classical causation, and in TIQM retarded and advanced causation combine in a kind of complementary way. And as Ron Maimon's answer mentions, the Feynman-Wheeler absorber theory is alive and well in Feynman diagrams. IMHO, TIQM is no crazier than MWI (and it may be crazy enough to be correct ;) ). Also, it can be seen as a superset of Bohm's pilot wave approach, but with fewer problems than Bohm's interpretation. – PM 2Ring Jan 08 '18 at 00:25

2 Answers2

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The main important idea of Feynman Wheeler theory is to use propagators which are non-causal, that can go forward and backward in time. This makes no sense in the Hamiltonian framework, since the backward in time business requires a formalism that is not rigidly stepping from timestep to timestep. Once you give up on a Hamiltonian, you can also ask that the formalism be manifestly relativistically invariant. This led Feynman to the Lagrangian formalism, and the path integral.

The only reason the Feynman Wheeler idea doesn't work is simply because of the arbitrary idea that an electron doesn't act on itself, and this is silly. Why can't an electron emit and later absorb the same photon? Forbidding this is ridiculous, and creates a nonsense theory. This is why Feynman says he abandons the theory. But this was the motivating idea--- to get rid of the classical infinity by forbidding self-interaction. But the result was much deeper than the motivating idea.

Feynman never abandons the non-causal propagator, this is essential to the invariant particle picture that he creates later. But later, he makes a similar non-causal propagator for electrons, and figures out how to couple the quantum electrons to the photon without using local fields explicitly, beyond getting the classical limit right. This is a major tour-de-force, since he is essentially deriving QED from the requirement of relativistic invariance, unitarity, the spin of the photon and electron, plus gauge-invariance/minimal coupling (what we would call today the requirement of renormalizability). These arguments have been streamlined and extended since by Weiberg, you derive a quantum field theory from unitarity, relativistic invariance, plus a postulate on a small number of fundamental particles with a given spin<1.

In Feynman's full modern formalism, the propagators still go forward and backward in time just like the photon in Wheeler-Feynman, the antiparticle goes backward, and the particle forward (the photon is its own antiparticle). The original motivation for these discoveries is glossed over by Feynman a little, they come from Wheeler's focus on the S-matrix as the correct physical observable. Wheeler discovered the S-matrix in 1938, and always emphasized S-matrix centered computations. Feynman never was so gung-ho on S-matrix, and became an advocate of Schwinger style local fields, once he understood that the particle and field picture are complementary. He felt that the focus on S-matrix made him work much harder than he had to, he could have gotten the same results much easier (as Schwinger and Dyson did) using the extra physics of local fields.

So the only part of Wheeler-Feynman that Feynman abandoned is the idea that particles don't interact with themselves. Other than that, the Feynman formalism for QED is pretty much mathematically identical to the Wheeler-Feynman formalism for classical electrodynamics, except greatly expanded and correctly quantum. If Feynman hadn't started with backward in time propagation, it isn't clear the rest would have been so easy to formulate. The mathematical mucking around with non-causal propagators did produce the requisite breakthrough.

It must be noted that Schwinger also had the same non-causal propagators, which he explicitly parametrized by the particle proper time. He arrived at it by a different path, from local fields. However they were both scooped by Stueckelberg, who was the true father of the modern methods, and who was neglected for no good reason. Stueckelberg was also working with local fields. It was only Feynman, following Wheeler, who derived this essentially from a pure S-matrix picture, and the equivalence of the result to local fields made him and many others sure that S-matrix and local fields are simply two complementary ways to describe relativistic quantum physics.

This is not true, as string theory shows. There are pure S-matrix theories that are not equivalent to local quantum fields. Feynman was skeptical of strings, because they were S-matrix, and he didn't like S-matrix, having been burned by it in this way.

Ron Maimon
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    This answer could be improved vastly if you could add references in the style of user Qmechanic. – Physiks lover May 11 '12 at 14:20
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    @Physikslover: I think the above point of view is my own, first expressed here in this answer. Feynman never says this, because he wants to distance himself from the S-matrix (maybe because it smells like Heisenberg who got too close to Nazis, maybe just because he learned to appreciate local fields, and didn't like Wheeler's positivism, who knows). Wheeler never looks backwards. The forward-backward business in Wheeler-Feynman is somewhat different from Feynman's QED propagator, but only in that the virtual photons make an additional part which gives the Coulomb law. Refs r Feynman papers. – Ron Maimon May 11 '12 at 14:41
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    Ron, I think @Physikslover was interested in your answer, not trying to disparage it. You have a lot of concepts and thoughts in it, many of them far from trivial. – Terry Bollinger May 12 '12 at 00:49
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    @TerryBollinger: I get touchy, sorry. I don't know a good reference for this, it's the sense I get from reading Feynman and Wheeler, although with Wheeler, it's harder to know the exact philosophy. Wheeler is not an S-matrix guy exactly, that's more Mandelstam and Gell-Mann (later), and Feynman is vehemently anti-S-matrix by the late 1960s (you find this out in Most of the Good Stuff). This is probably because he believed there are local fields inside hadrons, and of course, he's right. He heckles Heisenberg in later life (perhaps because of the Nazi business, perhaps on content, hard to say) – Ron Maimon May 12 '12 at 00:53
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    The anti-S-matrix business is echoed in Weinberg, who starts out gung-ho on S-matrix (as does Feynman--- he famously considered Chew's 1960s talk on S-matrix and hadronic bootstraps to be one of the great lectures in science), but Weinberg also eventually concluded that S-matrix just leads to field theory. Veneziano did S-matrix, but eventually concluded it was large-N. The only people who kept going with S-matrix were John Schwarz, Joel Scherk, David Olive, Pierre Ramond, Tamiaki Yoneya, and a handful of others, and Scherk dies early. The S-matrix program comes straight from Feynman's work. – Ron Maimon May 12 '12 at 00:57
  • Thanks Ron, it's OK, been there done that. BTW, I just looked it up in Lawrence Krauss' Quantum Man: Yes indeed, Ernst Stuckelberg came up with Feynman diagrams and methods eight years before Feynman did. There's no indication that Feynman knew about his work -- I can't say that for some other named physics effects -- but other-person naming happens so often in physics that someone created a name for the effect -- and used the name of someone else to identify it... :) – Terry Bollinger May 12 '12 at 01:10
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    @TerryBollinger: It is impossible for Feynman to have been cribbing, because Stueckelberg does it Schwinger's way, while Feynman derives everything from unitarity, and is not sure he is doing field theory! It was only when Feynman met Schwinger and compared notes that he realized his stuff was equivalent to local fields, and even then, he wasn't comfortable fully with local fields until the mid 1950s. Stueckelberg's work was recognized early by Pauli, and Einstein named Pauli his successor on his death in 1955, but Pauli dies a few years later, and this shakes Schwinger deeply. Schwinger quits – Ron Maimon May 12 '12 at 05:45
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    smoking, starts exercising, loses weight (and lives til his 70s). Schwinger might have read Stueckelberg. Stueckelberg continues to make insanely advanced contributions that are ripped off left and right--- he discovers affine Higgs mechanism (years before Brout and Englert, but abelian), the renormalization group (but it's Gell-Mann and Low that isolate the essential scaling part--- and cite him), and more. He dies extremely depressed from neglect, and borderline insane. It's a terrible story, and it happens again and again in physics. Hopefully the internet will put an end to this nonsense. – Ron Maimon May 12 '12 at 17:28
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    I'd like to add the Stueckelberg's renormalization program is proposed (and rejected) in 1941, about 8 years before Bethe's calculation, but Stueckelberg's covariant perturbation theory (the closest match to Schwinger and Feynman) dates to 1934 or so, 15 years before Schwinger/Feynman. Feynman does get one thing from Stueckelberg (indirectly, through Wheeler)--- namely the idea tha positrons are electrons going backwards in time, which Stueckelberg realized in 1938 or so. There is no bad faith from Feynman, and his methods are so original and fruitful (in S-matrix) that it doesn't matter. – Ron Maimon May 12 '12 at 17:28
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    Ron, I've been off on other things for a while. I looked again at S-matrices and they were pretty much as I recalled them. I do not claim to understand them in huge depth and may very well be missing something more profound about them, but to me they come over more a convenient method of calculation that is actually explained better by Dyson's interpretation of the Feynman's path integrals, but I could be wrong on that. The question of "why does reaching far into the past and far into the future almost work?" is closer to what my concern is. – Terry Bollinger May 29 '12 at 02:32
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    @TerryBollinger: I can't make sense of the previous comment--- S-matrix is a definition, it's not a method of calculation. Dyson doesn't have an interpretation of Feynman path integrals (do you mean Dyson's derivation of Feynman diagrams?) The question "why does reaching into the far past and far-future almost work" is nonsensical--- it doesn't almost work, it does work, fully and completely, this is Feynman diagrams. The thing that almost works is classical half-advanced half-retarded propagators and no self-interaction. The reason it almost works is because it is almost Feynman diagrams. – Ron Maimon May 29 '12 at 03:53
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    Ron, thanks, those last two sentences are a lot clearer to me as to your intent than the earlier discussion. By "Dyson's" yes, I meant his translation of Feynman's highly visual approach into precise classes of equations. S-matrix is a definition, yes, but as with most physics definitions it also unavoidably implies a broad class of calculation approaches and ways of analyzing the problem. – Terry Bollinger May 29 '12 at 12:04
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    @TerryBollinger: Ok, I get your previous comment better now, but it's still not the best way to think about it--- you're saying that the Dyson series explains what the S-matrix methods are all about. This is not so--- the Dyson series just describes how to get diagrams from field hamiltonians. The best way to see what the S-matrix method is all about is to read an S-matrix theory book from the 1960s, like Frautschi's. This stuff is not explained well anywhere, it is a field which is quietly buried. The "profound thing" is that the S-matrix is the fundamental quantity, not local fields. – Ron Maimon May 29 '12 at 16:25
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    ... the local fields are operators that can be defined at a point, you can measure them will little local sources, and when you do, you find that they fluctuate violently, and they require renormalization etc, etc. The S-matrix is a one-step quantity from the past to the future that doesn't respect space-time causality. It allows you to introduce a particle picture, and follow particle proper time. It allows you to introduce a string picture, and follow strings backwards and forwards in time. Particles are equivalent to fields, but strings aren't. – Ron Maimon May 29 '12 at 16:29
  • I do not believe that "silly" was a technical term, but I know that those self-interacting electrons are bare electrons, which are unphysical and have infinite masses and charges. The electrons that we detect in experiments are dressed electrons and those real electrons never interact with themselves. Feynman & Wheeler idea was not so "silly" as you claim, simply Feynman lacked the skills to develop QED in more rigorous terms and used the unphysical bare particles. – juanrga Nov 02 '12 at 21:02
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    @juanrga: That's not true. Both dressed and bare electrons interact with their own self field, this cannot be removed in a quantum theory, because you need to include loops where the electron emits a photon, emits a second photon, and absorbs the first photon (only the k-independent part of this is absorbed in the charge renormalization, which is the only difference between bare and dressed). There is no way to forbid electrons from absorbing their own photons, because the photons don't come with a label saying which electron emitted them. It's not consistent, and it's silly. – Ron Maimon Nov 02 '12 at 21:08
  • ... Feynman dealt with both dressed and bare electrons in the 1950s, since he understood how to reorganize the perturbation expansion in terms of the physical mass and charge. He didn't lack the skills, but by then, he had long ago abandoned the idea that electrons only interact with the photons emitted by other electrons. – Ron Maimon Nov 02 '12 at 21:10
  • @RonMaimon: Dressing eliminates any self-interaction. Dressing is not "charge renormalization". The dressed interaction satisfies $V^\mathrm{dress} a^\dagger |0\rangle = 0$ and, evidently, forbids "electrons from absorbing their own photons", which is good because they are nonphysical processes leading to divergences. In fact, I can say more: there is not non-trivial evolution in both the vacuum and the one-particle sector. – juanrga Nov 03 '12 at 12:20
  • @RonMaimon: Of course, Feynman considered both dressed and bare electrons in the 1950s. You misunderstood me completely. What I emphasized is that Feynman was forced to use the nonphysical concept of self-interaction (which he had abandoned previously) because he started with a nonphysical bare-particle quantum model. Latter he was forced to use renormalization to recover a physical S-matrix. But if he had started from a dressed-particle model he would not needed self-interactions neither renormalization. – juanrga Nov 03 '12 at 12:24
  • @juanrga: You are assuming the dressed electron is alone. The dressed electron in the presence of another dressed electron will emit and absorb its own photons. You are saying nonsense, I didn't misunderstand you. – Ron Maimon Nov 03 '12 at 13:44
  • @RonMaimon: I am not assuming that the dressed electron is alone. I wrote electrons (plural) in my posts. Once again you misunderstand what I am saying. – juanrga Nov 03 '12 at 20:19
  • @juanrga: I am not misunderstanding--- when you have dressed electrons, they interact with their own radiation, period. A dressed electron can emit then absorb the same photon, it contributes to the scattering of two electrons. – Ron Maimon Nov 03 '12 at 20:43
  • @RonMaimon: I wrote before that "Dressing eliminates any self-interaction". Dressed electrons do not interact with their own radiation, because the field degrees of freedom are properly eliminated via proper dressing and we obtain a direct-particle-action theory in the spirit of Wheeler Feynman theory. Thus Feynman was not "silly", as you pretend but go ahead your understanding. – juanrga Nov 03 '12 at 21:03
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    @juanrga: That is what you said, and this is just plain incorrect. For example, if you produce an electron and a positron, they are the "same electron", yet they repel. What is true is that you can integrate out the electromagnetic field (because it is free) and produce a theory of nonlocally interacting electrons. But these electrons still interact with themselves at past times. There is no way to make "electrons interact only with themselves" work, it has no analog in QED, and please ask it as a question if you want a proper answer. – Ron Maimon Nov 03 '12 at 23:29
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    @RonMaimon: The electromagnetic field is not free, but interacting with matter through the well-known term. The resulting theory is as local as the field theory. The rest of your comment is a repetition of misunderstandings corrected before. – juanrga Nov 04 '12 at 12:50
  • @juanrga: The information situation here is not symmetrical, as I know what I am talking about (but I said electrons and positrons repel, go figure). The electromagnetic field is free meaning has no self-interaction (at least not in the usual gauges) and can be integrated out, leaving a nonlocal electron theory. This was Feynman's 1950s method of doing a quantum analog of Wheeler-Feynman. It reappears in the Feynman-Vernon theory of decoherence, which is now called the Caldera-Leggett theory of decoherence (it's the same idea). This is what is true--- you can integrate out the photon field. – Ron Maimon Nov 04 '12 at 13:32
  • @TerryBollinger You're thinking of Stigler's law of eponymy – PM 2Ring Jan 07 '18 at 09:29
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Drawing from Feynman's and Wheeler's memoirs:

  1. Feynman was originally motivated to produce a theory of EM without the infinities of self-interaction, but he then needed a mechanism to reproduce radiation reaction, the loss of energy of an accelerating electron. He thought that a nearby electron could back-react to achieve the effect, but his advisor Wheeler pointed out the problems with that idea (time delay, attenuation, etc.)

  2. However, Wheeler suggested that, if the advanced as well as the retarded wave solutions of Maxwell's equations were taken seriously, one must then take account of "the presence in the universe of a nearly infinite number of other objects containing electric charge, all of which can participate in a grand symphony of absorption and reemission of signals going both forward and backward in time." (You can tell that's Wheeler's prose, right?)

So,

  • the original shaking electron produces retarded and advanced waves, which
  • shake every other charged particle in the universe, both later and earlier than the original shake.
  • All those other shaken particles in turn radiate advanced and retarded waves.
  • The advanced waves from the "later" shakes, and the retarded waves from the "earlier" shakes arrive back at the original source electron exactly at the time of its shaking, and sum to exactly the right amplitude to produce the radiation reaction, and no other observable effects. (Taking their word for it, although I can see how the distance attenuation could be compensated by the increasing number of particles with distance.)

I think Wheeler would say that it's "oddly arbitrary" to only include the retarded solutions: since advanced waves are also perfectly good solutions of the equations, a 50/50 split is the natural choice.

[I'm puzzled that Wheeler was pursuing a theory without fields (no EM degrees of freedom), yet still working with Maxwell's equations. Feynman, on the other hand, only mentions losing the infinite self-interactions as motivation.]

Art Brown
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  • Art, that's a good summary. On your last point, Feynman really, really wanted to solve the electron infinite self-energy problem, and decided quite early to approach it by assuming that particles only interacted directly: never with themselves, and never through fields. Wheeler then helped him, including pointing out that Feynman's first attempt was ordinary reflection! It as Wheeler (who else?) who came up with the amazing and truly weird time interpretation. And that to me is the deep mystery: It doesn't sound like something that should even come close to reality -- yet it does, almost. – Terry Bollinger May 29 '12 at 02:17
  • @TerryBollinger: Thank you. You are of course right (re ditching the fields). I've since read Feynman's nobel lecture, where he said as much. I think he shared your appreciation of the deep mystery that apparently completely different approaches to a problem can give the same result. – Art Brown May 30 '12 at 16:37