I think I have made an important discovery: a charge free falling in an electrostatic potential does not radiate.

The thinking that has lead me to this is profoundly similar to the key principle of General Relativity. By generalizing this principle I stipulate that a material point is always moving “freely” in the field of a conservative force and it is this field per se that affects the velocity of motion of the material point without the point itself experiencing an acceleration or being aware of its “non-uniform” motion.

In other words I am extending the key principle of General Relativity from gravity to all other fields of conservative forces. I.e. the material point free falling in a conservative force field is no different from a mass point free falling in a gravitational field in general relativity. Therefore a free falling charge does not radiate. Indeed, a free falling charge does not even accelerate either. Not according to General Relativity. So, when we say that an accelerating charge must radiate it must accelerate in some other way, e.g. by way of another force or by way of a third object involved in this interaction (which now becomes a 3-body interaction). But a free-falling charge does not accelerate and therefore it does not radiate.

Indeed, examine a charge in a state of free fall in a gravitational field. We can associate an inertial frame of reference with this charge. If the charge radiated away its energy due to acceleration that it experiences on its orbit through the gravitational field (as viewed from another frame of reference) the charge would loose velocity and thus experience a spontaneous acceleration in the inertial frame that was associated with it. According to the general theory of relativity this is absurd. It is absurd as far as our experience is concerned: a resting charge in an inertial frame does not experience a spontaneous acceleration.

I extend this argument by replacing the gravitational field with an electrostatic field (or for that matter any other field of a conservative force). Therefore a charge free falling in an electrostatic field does not radiate.

We see countless examples of this behavior everywhere. E.g. in quantum mechanics electrons are free falling on the nucleus and do not radiate. When we increase the principle quantum number and go up to Rydberg states where the electron orbit is traces an actual elliptical trajectory in a classical sense, the electron still does not radiate (here I am not talking about spontaneous emission caused by electron’s interaction with the zero-point energy field, which is a very different process; Rydberg states can be maintained indefinitely if one screens out certain zero-point energy modes responsible for the relaxation of the state).

Another example is an artificial atom or a quantum dot: we can trap an electron in an arbitrary large potential well and let it move within it without producing any radiation or loosing energy.

It is time we open up to the principle that a free-falling charge does not radiate, regardless of the nature of the conservative field the charge is free falling in. It takes special circumstances for radiation to take place, e.g. a third body has to participate in the interaction; the Larmor formula is just an approximation.

A mathematically rigorous explanation is given by the nonradiation condition of Hermann Haus, which states that a distribution of accelerated charges will radiate if and only if it has Fourier components synchronous with waves traveling at the speed of light.

Amen!

PS Alex Shenderov made an important observation that I must define a mathematical criterion of when a pairwise interaction of charges ceases to be pairwise because a third charge has entered the picture. I think that Feynman was on the right track when he proposed his absorber theory, the essential feature of which was that every photon ever emitted was necessarily absorbed by another charge and that there was no “free field”. In my Universal Ether Theory I too consider the charge interaction to be a purely pairwise process, it has to be for the interaction forces to be of conservative nature. When a third charge enters the picture the 4-dimensional vortices reconnect: an old pair is destroyed and a new pair is formed, and this process is accompanied by emission / absorption of radiation.

I think this condition should read like this: the field of the conservative force needs to be x-times stronger than the field of any interfering 3rd body for the interaction to remain pairwise.

PPS Here is another thought: what if electromagnetic radiation cannot propagate in empty space? Cosmic space is not exactly vacuum and it does contain matter (e.g. interstellar gas, etc). What if this matter is necessary for radiation to propagate in a pairwise manner from a source to the nearest receiver etc ad infinitum?