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Relativistic Dynamics of Accelerating Particles Derived from Field Equations

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Abstract

In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein’s celebrated energy-mass relation E=mc 2 is commonly derived from that fact. By contrast, in Newtonian mechanics the mass is introduced for an accelerated motion as a measure of inertia. In this paper we rigorously derive the relativistic point mechanics and Einstein’s energy-mass relation using our recently introduced neoclassical field theory where a charge is not a point but a distribution. We show that both the approaches to the definition of mass are complementary within the framework of our field theory. This theory also predicts a small difference between the electron rest mass relevant to the Penning trap experiments and its mass relevant to spectroscopic measurements.

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Acknowledgement

The research was supported through Dr. A. Nachman of the U.S. Air Force Office of Scientific Research (AFOSR), under grant number FA9550-11-1-0163.

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Correspondence to Alexander Figotin.

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Babin, A., Figotin, A. Relativistic Dynamics of Accelerating Particles Derived from Field Equations. Found Phys 42, 996–1014 (2012). https://doi.org/10.1007/s10701-012-9642-z

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