Does an electron emit radiation when falling towards Earth?

[CKH]

At least in classical theory, when an electron is accelerated it radiates energy. In GR, a free electron that is falling toward Earth is not accelerating (it's motion is inertial), so one would expect that if you dropped an electron in a vacuum tower, no radiation would be emitted. Conversely if you suspend the electron (in an electric field) so it is stationary wrt the earth, in GR the electron is accelerating so you would expect it to emit radiation.

What actually happens and why?

 

[Simon Bridge]

Well you know what actually happens - you've seen it.
"Why" is neither here nor there ... that's just the way it is.

If you mean "where is my description of the problem flawed?" then take another look at how electromagnetism works in relativity.

IRL, a relativistic description of electrons uses QFT.

 

[Dale]

This is an interesting question. I would start here

http://www.mathpages.com/home/kmath528/kmath528.htm

 

[CKH]

This is an interesting question. I would start here

http://www.mathpages.com/home/kmath528/kmath528.htm

Wow, that is an interesting can of worms. There is no date on that paper. Do you suppose that an understanding has been reached since then?

If not, then there is more to understand about physics. It seems the electron itself is not fully grokked.

BTW, the issue of relativity of acceleration is broached in that text. Has that been discussed in the forum? I ask because questions by another poster have been raised about whether Einstein's own 1916 interpretation of GR has somehow changed since then in a more modern interpretation.

 

[sardar]

In classical theory, an electron does emit radiation when it is accelerated. This is known as the Larmor formula and is a fundamental principle in classical electromagnetism. However, in the theory of general relativity, the concept of acceleration is more complex.

When an electron is falling towards Earth, it is in a state of free fall and its motion is considered inertial. In this case, according to general relativity, the electron is not accelerating and therefore would not be expected to emit radiation. This is because acceleration is defined as a change in velocity, and in free fall, the velocity of the electron does not change.

On the other hand, if the electron is suspended in an electric field and is stationary with respect to the Earth, it is considered to be accelerating in general relativity. In this case, the electron would be expected to emit radiation because it is experiencing a change in velocity.

So, the actual outcome of whether an electron emits radiation when falling towards Earth depends on its state of motion and the theory being used to describe it. In classical theory, the electron would emit radiation in both scenarios, while in general relativity, it would only emit radiation when suspended in an electric field.

The reason for this difference lies in the fundamental principles and definitions of acceleration in each theory. In classical theory, acceleration is defined as a change in velocity, while in general relativity it is defined as a change in the curvature of space-time.

In conclusion, while the concept of an electron emitting radiation when falling towards Earth may seem straightforward, the actual outcome is dependent on the theory being used to describe it. Both classical theory and general relativity have their own explanations and predictions for this scenario, highlighting the complexities of understanding the behavior of particles at a fundamental level.