# What is the interplay between radiation and photon creation?

While trying to provide an answer to this question, a question popped into my mind. When a charge accelerates, is there always a photon associated with that radiation, or multiple photons? For instance, suppose that a point charge is accelerated with little, and slow varying, acceleration such that the total energy radiated can be calculated by the Larmor formula $$E=\frac{\mu_0 q^2 a^2}{6\pi c}\Delta t$$ Would this always be associated with a photon of energy $$E=h f$$? Also, is the converse true, that is, does every photon have some radiation associated with it?

The emission of photons from an electron occurs in the following situations:

1. when passing through a magnetic field (Lorentz force, Hall effects), here the external magnetic field and the magnetic dipole of the electron interact.
2. during annihilation with a positron (same mass, same magnetic field and opposite electric charge), here the electric field, magnetic field and mass are completely converted into EM quanta
3. during the approach to the proton, here fields and masses are only reduced and the photon emission stops due to the asymmetry of fields and masses of the two particles.
4. during the interaction with photons (for example, a laser beam for cooling or also for accelerating electrons), shorter-wave (braking process) or longer-wave photons can be re-emitted.

Things get complicated when considering the exchange between electric or magnetic fields. Simplified, we speak of virtual photons. flippiefanus talks about the quantisation of the fields in his answer. Unfortunately, this quantisation of the electric as well as the magnetic fields is not elaborated, the constituents of these fields are simply missing.

What we are left with is the observation of how many and with which wavelengths photons are emitted in the above-mentioned processes. And there are no real rules. Sometimes more and sometimes fewer photons are emitted. There is no basic answer to your question.

A charged particle that is accelerated only radiates an electromagnetic field when the acceleration is produced by an electromagnetic force. In the case of gravitational acceleration for example, charged particle don't radiate electromagnetic fields.

At the fundamental level, the acceleration of a charge particle by the electromagnetic field therefore becomes a complicated business, because you have the exchange of photons that produces the acceleration and the radiation of photons due to acceleration. To see how the radiated photons are produced, one would have to take this entire picture into account.

In general, the quantization of electromagnetic radiation into photons is directly related to fundamental interactions that produced the photons. The reason is that the quantization properties associated with quantum mechanics comes from quantization of fields that are exchanged in such fundamental interactions.

• I find this very surprising, seeing as in classical electrodynamics the nature of acceleration in all the formulas related to radiation is never specified, I think. I suppose from the point of view of particle physics you would of course be correct, but I find it odd that a charged particle in accelerated by gravitational forces wouldn't radiate. But putting all that aside, this didn't answer my question. Suppose then that the charged particle is accelerated by an electromagnetic force. Does the radiation produced by it always have an associated photon, or multiple? Aug 20, 2023 at 13:16
• Well that depends on the specific scenario. For example, if the (de)acceleration is caused by a medium, you would see Cherenkov radiation. At the fundamental level, it is given by the process of bremsstrahlung which only radiates a single photon. But this process can happen multiple times. Aug 21, 2023 at 3:55
• Also seeking citation for the claim that a charge accelerated by, e.g., a gravitational field would not emit radiation. Aug 21, 2023 at 4:07
• @Jagerber48 That is actually quite famous because it is part of the argument that Einstein used to claim that gravitation attraction is equivalent to acceleration. Aug 21, 2023 at 4:14
• more details: en.wikipedia.org/wiki/…. I can't tell if the result holds for uniform gravitational fields only. What if the gravitational field was oscillating (like a gravitational wave)? Aug 21, 2023 at 4:35