Infinitely many soft photons from pushing an electron?

Question

I have been looking at some of the archives here and seen it quoted by Ron Maimon , that pushing an electron with a classical field means the electron will produce infinitely many soft photons should the universe be flat. Is this to be taken literally or it could be explained in more detail to me?

Answer 1

I will try interpreting the answer by Ron to the question since he is not allowed to talk for himself.

How-many-photons-can-an-electron-absorb-and-why

answer by Ron, broken down by concept

Unboundedly many, because the photon number is not conserved.

This is a correct general statement. The photon is a boson and the numbers are not conserved, just energy-momentum and angular momentum

Every time you push an electron with a classical field, you produce infinitely many soft photons (if the universe is flat at infinity)

Push and pull are not standard physics terminology, I suppose he means accelerates.

and conversely, any long-range field which pushes the electron has infinitely many soft photons getting absorbed in a sense, although you can't tell photons apart, so you can't distinguish the ones that were absorbed from the ones that were emitted.

Electrons in an electric field are attracted or repulsed (the field pushes the electron according to these simple-minded terms).

He is actually speaking of synchrotron radiation

The electromagnetic radiation emitted when charged particles are accelerated radially is called synchrotron radiation.

and brehmstrahlung.

Bremsstrahlung from bremsen "to brake" and Strahlung "radiation", i.e. "braking radiation" or "deceleration radiation") is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into a photon because energy is conserved. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum,

A continuous spectrum extended to infinity will have an infinite number of photons but the grand majority will be too soft to be measurable. I do not know where flat space enters in the argument.

In these semiclassical situations, the electron continually emits and absorbs photons and energy/momentum conservation is balanced up by the field.

Hope this helps.