Szymon Łukaszyk
Łukaszyk Patent Attorneys, Katowice, Poland

Part of the book: Future Relativity, Gravitation, Cosmology

Abstract

This study aims to reconcile quantum theory with the universality of the speed of light in vacuum and its implications on relativity through an information-theoretic approach. We introduce the concepts of a holographic sphere and variational potential. Entropy variation expressed in terms of the information capacity of this sphere results in the concept of binary potential in units of negative, squared speed of light in vacuum. Accordingly, the event horizon is a fundamental holographic sphere in thermodynamic equilibrium with only one exterior side: a noncompressible binary message that maximizes Shannon entropy. Therefore, the Jordan–Brouwer separation theorem and generalized Stokes theorem do not hold for black holes. We introduce the concept of inertial potential and demonstrate its equivalence to the variational potential, which ensures that any inertial acceleration represents a nonequilibrium thermodynamic condition. We introduce the concept of the complementary time period and relate it with the classical time period through integral powers of the imaginary unit to formulate the notions of unobservable velocity and acceleration, which are perpendicular and tangential to the holographic sphere, respectively, and bounded with the observable velocity and acceleration based on Pythagorean relations. We further discuss certain dynamics scenarios between the two masses. The concept of black hole informationless emission is introduced as a complement to informationless Bekenstein absorption and extended to arbitrary wavelengths. Black hole quantum statistics with degeneracy interpreted as the number of Planck areas on the event horizon are discussed. The study concludes that holographic screens and equipotential surfaces are spherical equivalents, and every observer is a sphere in nonequilibrium thermodynamic condition. Lastly, we propose a solution to the black hole information paradox.

Keywords: entropic gravity, black hole information paradox, Shannon entropy, Landauer’s
principle, Axis of Evil (cosmology), black hole quantum statistics, exotic ℝ4 , imaginary time, no-hiding theorem

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