Let us imagine a pair of bodies free-falling from the Pisa's tower (suppose we can neglect the air resistance). Let us assume that Body A is electrically charged, while body B is not. Observing from the Earth surface and according to classical electrodynamics, A will radiate electromagnetic (EM) waves (because of its accelerated motion) that will carry energy away in the surrounding space. This "dissipated" energy will be presumably taken by the kinetic energy of A during its accelerated motion, thus it is reasonable to expect that A will touch the ground slightly after body B, as if it had been braked by a sort of "friction".
The question is how can this fact be reconciled with the Einstein's Equivalence Principle (EP) ? Indeed, in the reference frame centered with body B, the other body will be seen to slightly accelerate upwards, while if the two bodies were in space, far from any gravitational field, the situation would not be equivalent (there, they would remain at rest with one another), thus violating the EP. Where is the mistake in my reasoning?
There is no error in your analysis that the charge will radiate and simulate friction wheras the electrically neutral body will be a little bit faster. Quantitatively the effect is ridiculously small, however. Einstein's Equivalence Principle is a heuristic principle that takes only gravity into account (which is not a flaw of this principle). A useful method to clarify things is to exaggerate them: consider two uncharged bodies and one of them has a massive obstacle in its way. Can EP be made resonsible if the obstacle changes the trajectory of one of the particles? Different situations are allowed to cause different phenomena.
Dear Ulrich, thank you for your answer but see http://arxiv.org/abs/gr-qc/0006037
Let a magnet roll down a slope. If the slope is electrically conducting, the magnet will move much slower than if the slope is an electric insulator. In processes like this not ontly the total energy (field+particle) is conserved, but also the total (field+particle) linear momentum, the total (field+particle) angular momentum and the total (fied+particle) boost momentum are conserved. These conserved quantities (in all 10) deteremines the kinetic properties of the magnet. A similar experiment can be made with an electrically charged particle with analogous results.
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