Volume 120, Number 4, November 2017
|Number of page(s)||7|
|Published online||08 February 2018|
On the equivalence principle and electrodynamics of moving bodies
M. Smoluchowski Institute of Physics, Jagiellonian University - Łojasiewicza, St. 11, 30-348 Kraków, Poland, NORDITA - Roslagstullsbacken 23, 106 91 Stockholm, Sweden and Department of Mathematics, Royal Institute of Technology, KTH - 100 44 Stockholm, Sweden
Received: 17 September 2017
Accepted: 19 January 2018
We consider a certain extension of Einstein's elevator thought experiment by assuming that the elevator is charged and falls into an electromagnetic field. We argue, on grounds of the equivalence principle, that an observer-dependent metric should exist, for which the geodesics coincide with the trajectories of the charged body in the electromagnetic field. We give a solution to this problem by finding such a metric and hence we are able to recover the Lorentz force law. Recovery of the leading terms of the radiation reaction force is also possible with this approach.
PACS: 04.20.-q – Classical general relativity / 03.50.De – Classical electromagnetism, Maxwell equations
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