2014/04/10 by Viktor T. Toth, Toth, Viktor T.
Computer Science · Mathematics · #Advanced Mathematical Theories #Computability, Logic, AI Algorithms #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.1404.2801
openalex publication_date 2014/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compare the behavior of a charged particle in a gravitational field and empty space. We resolve the apparent conflict between the Lorentz-Dirac equation and Larmor's formula of radiation by noting that the former describes an electron that is itself accelerated by an electromagnetic field. If instead, a hypothetical particle is considered that is accelerated by a non-electromagnetic force, Larmor's formula is found to be consistent with the accelerating particle's equation of motion. We consider the consequences concerning the equivalence principle and find that it is indeed violated if one demands that the same electromagnetic field be present in both the gravitational and accelerating cases; however, if one allows for the external electromagnetic fields to be different, the validity of the equivalence principle is restored. In either case, the basic idea behind the equivalence principle, which leads to a geometrized theory of gravity, remains unaffected.