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Einstein's special relativity tells us that laws of physics are the same in all intertial frames. General relativity futher extends this by stating that reference frames that are in free fall around massive objects are inertial, but that reference frames that are stationary around massive objects are not inertial. There is no experiment that could distinguish one inertial reference frame from another, and no black-box experiment that could distinguish stationary reference frame around a massive object from one that is inside an accelerating rocket in space unless you are permitted to look out of that black box.

All charged particles in accelerating motion emit electromagnetic radiation. Because gravity is not a force, if we place a modern smartphone with accelerometer on a table, the only force the smartphone experiences is the normal force that keeps it from being in free fall. The smartphone accelerometer agrees: the 3-axis accelerometer tells that it's in accelerating motion. The reason for acceleration is that it is not traveling in a straight line through spacetime because spacetime around the earth is curved.

Let us charge the smartphone on a table with static electricity (NB: not with chemical energy stored in battery). Because it is now electrically charged, and because it is in accelerating motion, it must emit electromagnetic radiation, right? Otherwise we could distinguish a smartphone on a table from a smartphone in an accelerating rocket.

Let us also assume for the purposes of this thought experiment that we stop the rotation of the earth. The electromagnetic radiation that this electrically charged smartphone on a table emits must have some origin. It can't be the smartphone battery since for the purposes of this thought experiment, we can remove the battery. It can't be the rotation of the earth, since we assumed it has been stopped.

Since the smartphone is continuously accelerating, forever, as long as you don't destroy the test setup, it must be continuously emitting electromagnetic radiation, right? Why wouldn't it be a perpetual motion machine of the first kind then since we can extract the energy from that electromagnetic radiation and do useful work with it?

I used smartphone as an example here because smartphones have accelerometers that clearly demonstrate that a smartphone on a table is in continuous accelerating motion. Of course we can replace the smartphone with anything that can hold a charge of static electricity and that can be held stationary on a table so it won't be in free fall.

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  • $\begingroup$ The basic premise of the question: All charged particles in accelerating motion emit electromagnetic radiation is false even in flat spacetime if we consider situations with more than one point charge. EM radiation is a global phenomenon, so knowing just the local motion of a single charge is not enough to decide whether radiation is emitted. $\endgroup$
    – A.V.S.
    Commented Feb 1 at 19:21
  • $\begingroup$ I think that you are describing the paradox of radiation of charged particles in a gravitational field $\endgroup$
    – LPZ
    Commented Feb 5 at 13:59

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