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As an outcome of his PhD thesis work, Richard Feynman and John Wheeler wrote a series of papers on how the kickback on an electron as it emits a photon can be modeled accurately as the result of an "advanced photon" traveling backwards in time and striking the electron. In their model, this peculiar back-from-the-future impact always occurs at the same moment as when the electron emits a more conventional "retarded photon" (don't look at me, I didn't come up with these names!) that then moves forward in time in a more conventional fashion.

The advanced photon is emitted by whatever electron eventually absorbs the retarded photon. That electron may be only a few femtoseconds away in the future. However, it could just as easily be billions of years in the future, such as when you point a laser towards an especially empty void in intergalactic space.

That last point has always intrigued me, since it seems to imply that the probability of emission of the photon is dependent on the distribution of matter in the universe across all of spacetime.

Imagine for example shining a laser out into a region of space for which the probability of its photons encountering future electrons is close to zero for the entire remaining history of the universe. According to the Feynman-Wheeler advanced-retarded photon pair model, the absence of a future electron to emit the advanced photon would seem to mean that no retarded photons could be emitted in that direction, and the laser would stop working!

So my question is this:

What is the resolution to the Feynman-Wheeler empty-space laser suppression paradox?

I assume by default that Feynman-Wheeler suppression does not exist, but I also have to admit I do not know that experimentally. I assume it does not exist because quantum probabilities alls seem to be very smooth, and Feynman-Wheeler suppression would violate that smoothness. It would instead make quantum uncertainty a function of how matter is distributed throughout spacetime.

But if Feynman-Wheeler suppression does not exist, why does it not exist?

That too would seem very strange, because it would seem to imply that some very peculiar invariant is at work in the universe as a whole. Specifically, it would seem to assert that no matter what direction you look in our very stringy, very clumpy universe full of intergalactic holes, dark energy, dark matter, invisible matter, and a tiny smattering of severely-clumped radiating matter, the probability of eventually encountering an electron is always exactly the same.

Really?? That kind of smoothness just does not strike me as an obvious invariant for the universe we actually observe. About the only idea I can even think of would be that this hypothetical electron smoothness invariant might be related to the idea of a holographic universe.

So: Is there some other resolution to the Feynman-Wheeler suppression paradox that does not (a) make quantum probabilities dependent on the distribution of matter throughout spacetime, or (b) require that the angular distribution of electrons from zero to infinity, from all points in all of space, always be smooth?

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    $\begingroup$ It might also suggest that ultimately the universe is closed, and not open $\endgroup$ – user56903 Nov 18 '14 at 13:12
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    $\begingroup$ Sorry, but is your question not resolved by the fact that Feynman postulates that electrons in empty space don't radiate? I could expand a little on this if you think it may be a good answer. $\endgroup$ – Danu Dec 25 '14 at 14:06
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    $\begingroup$ Note that the Feynman-Wheeler theory talks about EM forces, not photons. It is a non-quantum theory; according to Feynman, in the talk they gave in Princeton seminar Wheeler promised another talk on the quantum version, but he never gave that talk. – $\endgroup$ – Ján Lalinský Feb 15 '15 at 13:25
  • $\begingroup$ @Danu, sorry for the slow answer, I've been away from Physics SE for a while. I may be misunderstanding, but it sounds like you are restating in omnidirectional terms the basis of my question: Photons are only emitted towards matter. So, if there is no matter other than the one electron (not possible actually), there is no emission. If you add matter elsewhere in this minimalist universe, however, a directionally biased form of emission becomes possible. $\endgroup$ – Terry Bollinger Feb 15 '15 at 23:22
  • $\begingroup$ @JánLalinský, that is fascinating, I had never encountered that story. I had noticed that Feynman seemed to make some kind of a sharp mental transition between his PhD work and QED, and the transition is centered around just that issue. I wonder if he ever discussed what changed? Also, thanks for the long answer that I have not yet looked at, but will as soon as I can. $\endgroup$ – Terry Bollinger Feb 16 '15 at 1:41
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As an outcome of his PhD thesis work, Richard Feynman and John Wheeler wrote a series of papers on how the kickback on an electron as it emits a photon can be modeled accurately as the result of an "advanced photon" traveling backwards in time and striking the electron.

No, the Feynman-Wheeler theory considers model of classical electromagnetic interaction, where electrons are mass points and interact via continuous forces characteristic for classical electromagnetic theory, not via temporally discrete events resulting in momentum change.

Feynman-Wheeler theory uses (as other similar theories of Tetrode, Fokker, Frenkel from the beginning of 20th century did) half-retarded, half-advanced solutions of Maxwell's equations with point electrons, not uni-directional photons.

It is a non-quantum theory; according to Feynman, Wheeler promised another talk on the quantum version, but he never gave that talk.

If the electron emitted a momentum-carrying body (photon), there would be no need for another such momentum-carrying body (photon from the future) to give a kick in the opposite direction to the electron. The emitted photon would do that by itself due to conservation of momentum.

The "action from future" (use of advanced fields) was invented partially because retarded EM field of point particle is symmetrically distributed around the radiating charged point particle, thus being insufficient to explain expected reaction on its motion. Difference of advanced and retarded field of the particle has non-symmetrical limit at the position of the particle that can be used to express the Lorentz-Abraham results for radiation reaction force, so Feynman and Wheeler saw "action from future" as a possible replacement for their previous approach.

Imagine for example shining a laser out into a region of space for which the probability of its photons encountering future electrons is close to zero for the entire remaining history of the universe. According to the Feynman-Wheeler advanced-retarded photon pair model, the absence of a future electron to emit the advanced photon would seem to mean that no retarded photons could be emitted in that direction, and the laser would stop working!

So my question is this:

What is the resolution to the Feynman-Wheeler empty-space laser suppression paradox?

Laser ( or any directional light source) is a macroscopic device constructed in such a way that its macroscopic EM field in the form of unidirectional light ray consists (in microscopic theory like the F-W theory) of immense number (~$10^{24}$ and more) of individual particle fields. The device is constructed in such a way (usually adding an absorber with appropriately sized hole suffices) that the elementary fields cancel each other in most directions.

According to the Feynman-Wheeler advanced-retarded photon pair model, the absence of a future electron to emit the advanced photon would seem to mean that no retarded photons could be emitted in that direction

If I express this idea in the classical framework of the Feynman-Wheeler theory (thus changing it, as it has to be), you are saying that

if there are no distant particles ever interacting with retarded field of a charged particle of the laser within certain solid angle viewed from the laser particle, there is no action of these distant particles back on the particle of the laser and thus the laser particle cannot radiate retarded field in this direction at all.

The bold part is not a valid conclusion based on Feynman-Wheeler theory, because in Feynman-Wheeler theory retarded fields are given by retarded solutions of Maxwell's equations which (although decaying to zero with increasing distance) are never exactly zero in any direction.

Remarks: Feynman-Wheeler theory postulates that total field vanishes exactly outside the perfect absorber (so it can be shown that difference of total retarded and total advanced field vanishes everywhere), but the individual fields are not assumed to vanish in any direction.

How this is accomplished (how could the perfect absorber work) was not specified and that is one of the two weakest points of the whole theory:

  • what good reason is there to believe that point particles cancel each other's fields exactly (which implies total advanced field and total retarded field are the same everywhere) ?

  • why should we in addition believe that fields are half-retarded, half-advanced when together with the above belief this leads to Lorentz-Abraham equation for point particles, which is unphysical for them and was derived more convincingly by Lorentz as an approximate equation for extended charged bodies ?

The really convincing part of the Feynman-Wheeler work is that radiation reaction on charged bodies can be explained as action of the EM forces due to other charged bodies; self-interaction is not necessary. This works even without the other Feynman-Wheeler assumptions, as total field in macroscopic theory is able to explain radiation damping already and microscopically this can be explained simply by correlation of individual microscopic fields of particles without any self-interaction.

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  • $\begingroup$ Jan Lalinsky, that is fascinating and consistent with the odd transition Feynman made when he went from his PhD work to QED. Perhaps his efforts to quantize his PhD work led him simply to abandon the oddly complicated half-retarded, half-advanced framework and move to the conceptually far simpler electron photon interactions of QED? I'm pretty sure I've seen comments by Feynman where he was assuming a photon-based interpretation of the half-and-half model, but that's a lot different from producing the actual model. $\endgroup$ – Terry Bollinger Feb 16 '15 at 1:55
  • $\begingroup$ I hope others will look at and weigh in on Jan Lalinsky's answer! It is a interesting one, and it provides a route for resolving my question that is, at least for me, nicely unexpected. $\endgroup$ – Terry Bollinger Feb 16 '15 at 2:01
  • $\begingroup$ "Perhaps his efforts to quantize his PhD work led him simply to abandon the oddly complicated half-retarded, half-advanced framework and move to the conceptually far simpler electron photon interactions of QED?" He changed focus after his PhD, but as he told the story, his work on the classical theory lead him to all the other things he was praised for - his method of diagrams and other things in quantum electrodynamics. $\endgroup$ – Ján Lalinský Feb 16 '15 at 8:12
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Perhaps this almost ventures into the realm of philosophy, but the original premise oddly treats the photon differently from the electron. The only reason we think of it this way is because it is more common to observe the photon being created, since it is a boson. But quantum electrodynamics dictates that as a photon is traveling along at a great distance, then it must also, with some probability, split into an electron and a positron on its own for a brief moment. If we at first imagine this as a discrete event, then the photon traveling through empty space would eventually transform into its own interaction partners to satisfy the advanced photon condition. Thus we can see there should be no laser suppression.

But I think a proper perspective should have us look a little deeper and realize that in the absence of specific attempts to interact with these electron/positron splitting events (i.e., "measuring them"), they will not happen discretely. Instead they will exist on a continuous probabilistic continuum along the photon's trajectory. In other words, even if we take the advanced photon model as the best solution to the kickback problem, a full treatment should end up with something closer to a path integral of advanced photons with pieces contributing from all along the trajectory.

We could consider this complicated picture as if the photon carries with it its own integrated ability to push off of things. And perhaps we could call this momentum.

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