Freely falling observer and a static charge - Unruh radiation does not exist

Let us treat a problem that we left open in the blog post about the Larmor formula and Unruh radiation. If we have an electron that is statically supported on Earth using static electromagnetic forces, does it appear to radiate to a freely falling observer?

It does not radiate to another static observer, because there is no source of energy for the radiation.

From the point of view of a freely falling observer, the static electron is being accelerated by a huge spaceship, namely Earth.

Suppose that the freely falling observer would see radiation, that is, a wave packet. According to Claim 7 of our previous blog post, then a static observer would see a chirp.

Since the static observer does not see chirps or any other type of radiation, the freely falling observer cannot see either.

Let us conjecture an equivalence principle:

Equivalence principle 1. If we have an electron that is supported with static electromagnetic forces in an accelerating rocket and an inertial observer, then the electron will behave in the same way as a similarly supported static electron in a gravitational field to a freely falling observer.


Equivalence principle 1 implies:

Theorem 2. An inertial observer will not see any Unruh radiation from an electron that is supported with static electromagnetic forces in an accelerating rocket. QED.


Why did we resort to equivalence principles and did not study directly the radiation from an accelerating rocket in space? That is because the author of this blog is not aware of generally accepted methods of studying complex systems like a rocket in quantum field theory. If we have an electron supported in the rocket, what kind of quantum field interactions might happen between the electron, the frame of the rocket, and the propulsion system? There will be vibrations, phonons, in the frame. It looks like the vibrations cannot produce Unruh-like radiation, but it is hard to prove that.

Summary

In our blog posts April 5, 2018 and April 15, 2018 we have shown that Unruh radiation does not exist if two equivalence principles hold and a claim about photons in an accelerating frame holds.

On the other hand, if an electron is accelerated with laser or impinging other electrons, there will be radiation. Some of that radiation could be interpreted as Unruh radiation.

Our blog posts about the Larmor formula and Unruh radiation have a common message: radiation is a result of dynamical interaction between charges or photons. It is not the acceleration itself that produces any radiation, as can be seen from our treatment of electrons that are supported with static electromagnetic forces.

We have left open the question if a varying gravitational field might produce electromagnetic radiation. Does Hawking radiation exist? The next blog post will be dedicated to studying that question.