Authors: Osama Haggag
Standard Special Relativity exhibits a fundamental geometric asymmetry: while the instantaneous velocity of a worldline is strictly bounded by the invariant speed of light ( ), its proper acceleration is permitted to diverge infinitely. This unconstrained upper bound introduces severe vulnerabilities into modern field theories, manifesting as divergent particle self-energies and zero-volume coordinate singularities at causal horizons. This framework proposes an operational resolution of this asymmetry by introducing a generally covariant kinematic framework featuring an impassable, invariant upper boundary on proper acceleration ( ) deduced from first principles. By modeling a massive particle’s internal state as a localized quantum wavepacket acting as an intrinsic clock, we demonstrate that uniform acceleration compresses the local Rindler horizon to its geometric saturation limit. To preserve this invariant ceiling across multi-body compound systems, we derive a velocity-independent, non-linear acceleration composition law based on a hyperbolic group structure. By equating the Rindler horizon with the particle's Compton wavelength, we extend the equivalence principle in quantum systems, Planck’s constant is directly inserted into spacetime kinematics. Finally, this framework offers a pure kinematic reinterpretation of the partonic cross-section flattening (gluon saturation) observed at the Large Hadron Collider (LHC) as an intrinsic, structural feature of a bounded quantum vacuum.
Comments: 8 Pages. DOI: 10.5281/zenodo.20740142
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[v1] 2026-06-24 00:12:41
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