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Abstract: Relativistic kinematics is usually considered only as a manifestation ofpseudo-Euclidean Lorentzian geometry of space-time. However, as it isexplicitly stated in General Relativity, the geometry itself depends ondynamics, specifically, on the energy-momentum tensor. We discuss a fewexamples, which illustrate the dynamical aspect of the length-contractioneffect within the framework of Special Relativity. We show some pitfallsassociated with direct application of the length contraction formula in caseswhen an extended object is accelerated. Our analysis reveals intimateconnections between length contraction and the dynamics of internal forceswithin the accelerated system.The developed approach is used to analyze the correlation between twocongruent disks - one stationary and one rotating the Ehrenfest paradox.Specifically, we consider the transition of a disk from the state of rest to aspinning state under the applied forces. It reveals the underlying physicalmechanism in the corresponding transition from Euclidean geometry of stationarydisk to Lobachevsky-s hyperbolic geometry of the spinning disk in the processof its rotational boost. A conclusion is made that the rest mass of a spinningdisk or ring of a fixed radius must contain an additional term representing thepotential energy of non-Euclidean circumferential deformation of its material.Possible experimentally observable manifestations of Lobachevsky-s geometry ofrotating systems are discussed.



Author: Moses Fayngold

Source: https://arxiv.org/







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