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There is an electrostatic field around the electrically-charged particle (particle is the source of that field).

When the particle accelerates, it emits photon.

Photon travels at finite speed.

Electric field, produced by the already accelerated particle at some remote point, will be the same, until, at least, the time photon needs to travel from particle to the point at vacuum.

However, consider that photon is been absorbed by some system (an atom).

What will be at the remote point? Will it still have electric field value, that it was before the acceleration?

Maybe it propagates not through photon, and with infinite speed?

If yes, it should break the information propagation law.


Visual explanation

Figure 1

Figure 1

Consider a test particle A (electron, atom, anything that can be affected by electromagnetism), a free electron B and an atom C. On the Figure 1, some photon arrives to the free electron B.

Figure 2

Figure 2

Photon is scattered on the free electron, with the Compton scattering. As the result of scattering, as I know, there is no initial photon with some initial energy and angle, but a scattered photon with lower energy and different angle. The B electron is now accelerated.

Particle A is "waiting" for the photon from already accelerated B electron, but photon is being absorbed by an atom C, that is situated in some opposite direction, relatively to the B electron.

Not the electron B, neither the atom C will scatter (emit) photon, that will be scattered (absorbed) by particle A (just in our case).

How then, particle A knows, that B is accelerated and changed its position, how it will know, that the electric field, created by the B electron is changed at the point, where A particle is situated?

Purpose of the question

Probably scientist already thought about such question, however, I was thinking what if non-locality of the world is expressed not only in entangled particles` spins, but also in case, that I described?

According to the illustration above, what if "C" particle (system of particle) is situated somewhere near the accelerated electron "B", "A" particle or system of particles are situated somewhere far, and after scattering, we measure "C" particle state, seeing, that it absorbed (scattered) scattered photon, but we measure "C" before the photon from "B" theoretically could reach the "A" at speed $c$?

  1. Will we instantly, faster than speed of light obtain information about "A"?
  2. If yes, then the question from the top - how information of accelerated charged particle travels, if photon is absorbed?

Update

For those, who ask: "why particle A should "know" something about B"?

As I understand, Hamiltonian is used in quantum mechanics, which I refer to. Hamiltonian is full energy of the system, from which, system's each particle state (motion) can be described.

Hamiltonian is sum of kinetic and potential energy, and the last one exactly depends on particle coordinate.

So, if one particle position is changed, then it should affect energy of another one, and as I described above, it seems, that this "affection" occurs not through photons.

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – Buzz
    Commented Aug 19, 2023 at 8:08

2 Answers 2

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Let's say the particle changes position.

The fine details of the acceleration profile of the particle may be absorbed by a absorber near the particle.

But the fact the the position has changed is slowly transmitted by low frequency photons, which require a thick absorber to be absorbed.

To measure, from far away, the exact position of a particle with a small charge requires time anyway, as there is a energy-time uncertainty relation, and the energy of electric field is low far away from a small charge. So even if there is a thick absorber, it does not matter.

(What if the particle is highly charged? Well I have to think about it.)

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  • $\begingroup$ the fact the the position has changed is slowly transmitted by low frequency photons - 1) What do You mean by “slowly”? 2) What do You mean by “transmitted”, for example in the case, I described (Compton scattering)? 3) How any other photons can be emitted, besides of scattered, not violating conservation laws? 4) Why low frequency photons? How can You prove that, any links? 5) How does accelerated particle knows how many “low frequency photons” it needs to scatter in addiction to original scattered photon? 6) If there will 10^100 particles around, there will be 10^100 low-frequency photons? $\endgroup$ Commented Aug 18, 2023 at 19:19
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When the first photon scatters at particle $B$, $B$ accelerates, right? Then it will radiate, and the influence of that radiation is what "tells" $A$ of $B$'s acceleration. If you want, you can think that $B$ emits another photon and that is the photon involved in the communication, but I'd advise you against it. It's not the photon that communicates the change in electromagnetic field to far away points, but the radiation itself.

Never forget that a photon is just an idea to justify dividing in chunks the energy carried by an electromagnetic wave, and every example where the photon "flies about" scattering off things and coming at this angle and that angle is always illustrative and never too literal.

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  • $\begingroup$ Then it will radiate - what it will radiate? What do You mean by radiation? $\endgroup$ Commented Aug 18, 2023 at 18:28
  • $\begingroup$ @Stdugnd4ikbd I mean electromagnetic radiation $\endgroup$ Commented Aug 18, 2023 at 18:58
  • $\begingroup$ Electromagnetic radiation quantizes. Quants of the electromagnetic radiation are photons. Therefore, we can consider a single-photon cases, as I do in my post. As I know, single particle does not emit (scatter, if it is free particle) multiple photons. There are rare cases, when in input there is one photon, but scattered two, yes. But there are more than two particles, that can and should be affected by accelerated particle, so by Your explanation, accelerated particle should emit photon for each particle, probably in Universe, to tell it, that it has been accelerated, which is seems wrong. $\endgroup$ Commented Aug 18, 2023 at 19:11
  • $\begingroup$ @Stdugnd4ikbd I'm saying you can't consider a single photon case. Accelerating particle $B$ will generate radiation, which will have therefore some non-zero quantum associated with it. So introducing $B$ in your example forcely introduces another photon besided the one that was scattered $\endgroup$ Commented Aug 18, 2023 at 19:47
  • $\begingroup$ Why I can’t consider single photon cases? There are a lot of theories and successful experiments with single photon detection. You write that electron should emit (scatter) more than one photon, to “tell” other particles about changing of its velocity — 1) If there are $10^100$, there will be $10^100$ photons? How it doesn’t violate conservation laws? 2) How electron knows how many additional photons to emit (scatter)? $\endgroup$ Commented Aug 19, 2023 at 6:20

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