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ON THE VARIABLE FINE STRUCTURE CONSTANT, STRINGS AND MAXIMAL-ACCELERATION PHASE SPACE RELATIVITY

CARLOS CASTRO

Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, GA 30314, USA

https://doi.org/10.1142/S0217751X0301646XCited by:7 (Source: Crossref)

Abstract

We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration relativity principle in the space–time tangent bundle and in phase spaces (cotangent bundle). The maximal proper-acceleration bound is a = c²/Λ in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. The group transformation laws of this maximal-acceleration phase space relativity theory under velocity and acceleration boosts are analyzed in full detail. For pure acceleration boosts it is shown why the minimal Planck-areas (maximal string tension) are universal invariant quantities in any frame of reference. Inspired by the maximal-acceleration corrections to the Lamb shifts of one-electron atoms by Lambiase, Papini and Scarpetta, we derive the exact integral equation that governs the renormalization-group-like scaling dependence of the fractional change of the fine structure constant as a function of the cosmological redshift factor and a cutoff scale L_c, where the maximal acceleration relativistic effects are dominant. A particular physical model exists dominated entirely by the vacuum energy, when the cutoff scale is the Planck scale, with Ω_Λ = 1. The cosmological implications of this extreme case scenario are studied.

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