Chapter 15. Black Hole Horizons as Patternless Binary Messages and Markers of Dimensionality


Szymon Łukaszyk
Łukaszyk Patent Attorneys, Katowice, Poland

Part of the book: Future Relativity, Gravitation, Cosmology


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


[1] Braunstein S., & Pati A. (2007). Quantum Information Cannot Be Completely Hidden
in Correlations: Implications for the Black-Hole Information Paradox. Phys. Rev. Lett.
98, 080502.
[2] Wheeler J. (1989). Proceedings of the 3rd International Symposium Foundations of
Quantum Mechanics in the Light of New Technology. Phys. Soc. Japan, 434.
[3] Łukaszyk S. (2020). Four Cubes. arXiv:2007.03782 [math.GM]. 03782.
[4] Boltzmann L. (1877). Über die Beziehung zwischen dem zweiten Hauptsatze des
mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, respective den
Sätzen über das Wärmegleichgewicht [On the relationship between the second main
theorem of mechanical heat theory and the probability calculation with respect to the
results about the heat equilibrium]. Kaiserlichen Akademie der Wissenschaften,
mathematich-naturwissen Cl. LXXVI, Abt II, 373-435.
[5] Kuhn T. (1978). Black-Body Theory and the Quantum Discontinuity, 1894-1912.
University of Chicago Press. ISBN0226458008.
[6] Schlosshauer, M., Kofler, J., & Zeilinger, A. (2013). A Snapshot of Foundational
Attitudes Toward Quantum Mechanics. Studies in History and Philosophy of Science
Part B: Studies in History and Philosophy of Modern Physics, 44(3), 222–230.
[7] Teilhard de Chardin P. (1955). Le Phénomène Humain [The Phenomenon of Man].
Éditions du Seuil. ISBN006090495X.
[8] Carnap R. (1963). The Philosophy of Rudolf Carnap. Open Court Publishing.
[9] Brukner Č. (2018). A No-Go Theorem for Observer-Independent Facts. Entropy 2018,
20(5), 350.
[10] Proietti M., Pickston A., Graffitti F., Barrow P., Kundys D., Branciard C., Ringbauer M.,
& Fedrizzi A. (2019). Experimental Rejection of Observer Independence in the Quantum
World. Science Advances, Vol. 5, Issue 9.
[11] Bong K-W, Utreras-Alarcón A., Ghafari F., Liang Y-C., Tischler N., Cavalcanti E.,
Pryde G., & Wiseman H. (2019). Testing the Reality of Wigner’s Friend’s Experience.
Proceedings vol. 11200, AOS Australian Conference on Optical Fibre Technology
(ACOFT) and Australian Conference on Optics, Lasers, and Spectroscopy (ACOLS).
[12] Prigogine I., & Stengers I. (1984). Order out of Chaos: Man’s New Dialogue with
Nature. Bantam Books. ISBN0553340824.
[13] Manin Y. (2006). The Notion of Dimension in Geometry and Algebra. Bulletin of the
American Mathematical Society. 43 (2): 139–161.
[14] Hossenfelder S. (2010). Comments on and Verlinde’s paper “On the Origin of Gravity
and the Laws of Newton”. arXiv:1003.1015 [gr-qc].
[15] Hooft G. (1993). Dimensional Reduction in Quantum Gravity. arXiv:gr-qc/9310026. 10.48550/
[16] Planck M. (1900). Über Irreversible Strahlungsvorgänge [About Irreversible Radiation
Processes]. Ann. Phys., 306: 69-122.
[17] Fidkowski Ł., Hubeny V., Kleban M., & Shenker S. (2004). The Black Hole Singularity
in AdS/CFT. Journal of High Energy Physics, Vol. 2004.
[18] Gassner S., & Cafaro C. (2019). Information Geometric Complexity of Entropic Motion
on Curved Statistical Manifolds under Different Metrizations of Probability Spaces.
International Journal of Geometric Methods in Modern Physics Vol. 16, No. 06.
[19] Hirani, A. (2003). Discrete Exterior Calculus. Dissertation (Ph.D.), California Institute
of Technology.
[20] Desbrun, M., Kanso, E., & Tong, Y. (2008). Discrete Differential Forms for
Computational Modeling. In: Bobenko, A.I., Sullivan, J. M., Schröder, P., Ziegler, G.M.
(eds.) Discrete Differential Geometry. Oberwolfach Seminars, Vol. 38. Birkhäuser
[21] Bekenstein J. (1973). Black Holes and Entropy. Phys. Rev. D 7, 2333. 7.2333.
[22] Susskind L. (2008). Black Hole War: My Battle with Stephen Hawking to Make the
World Safe for Quantum Mechanics. Little, Brown and Company. ISBN
[23] Hawking S. (1974). Black Hole Explosions? Nature Vol. 248, 30–31.
[24] Łukaszyk S. (2022). Novel Recurrence Relations for Volumes and Surfaces of n-Balls,
Regular n-Simplices, and n-Orthoplices in Real Dimensions. Mathematics 2022, 10(13). math10132212.
[25] Parisi G. & Sourlas N. (1979). Random Magnetic Fields, Supersymmetry, and Negative
Dimensions. Phys. Rev. Lett. 43, 744.
[26] Verlinde E. (2010). On the Origin of Gravity and the Laws of Newton. Journal of High
Energy Physics Vol. 2011, No. 29.
[27] Brouwer M., Visser M., Dvornik A., Hoekstra H., Kuijken K., Valentijn E., Bilicki M.,
Blake C., Brough S., Buddelmeijer H., Erben T., Heymans C., Hildebrandt H., Holwerda
B., Hopkins A., Klaes D., Liske J., Loveday J., McFarland J., Nakajima R., Sifón C., &
Taylor E. (2017). First test of Verlinde’s theory of emergent gravity using weak
gravitational lensing measurements. Monthly Notices of the Royal Astronomical Society,
Vol. 466, Issue 3, 2547–2559.
[28] Ben-Naim A. (2008). Farewell to Entropy, Statistical Thermodynamics Based on
Information. World Scientific. ISBN9812707077.
[29] Vedral V. (2010). Decoding Reality: The Universe as Quantum Information. Oxford
University Press. ISBN0199695741.
[30] Haug E. (2020). Finding the Planck Length Multiplied by the Speed of Light Without
any Knowledge of G, c, or ħ, using a Newton force spring. Journal of Physics
Communications, Vol. 4, No 7.
[31] Chaitin G. (1966). On the Length of Programs for Computing Finite Binary Sequences.
Journal of the ACM Vol. 13 Issue 4, 547–569.
[32] Landauer R. (1961). Irreversibility and Heat Generation in the Computing Process. IBM
Journal of Research and Development, Vol. 5, Issue: 3.
[33] Davidson A. (2019). From Planck Area to Graph Theory: Topologically Distinct Black
Hole Microstates. Phys. Rev. D 100, 081502(R).
[34] Scardigli F. (1995). Some Heuristic Semiclassical Derivations of the Planck Length, the
Hawking Effect and the Unruh Effect. Il Nuovo Cimento B Vol. 110, 1029–1034.
[35] Goutéraux B. (2010). Black-Hole Solutions to Einstein’s Equations in the Presence of
Matter and Modifications of Gravitation in Extra Dimensions. PhD thesis, Univ. Paris Sud. arXiv:1011.4941 [hep-th].
[36] Szostek R., Góralski P., & Szostek K. (2019). Gravitational Waves in Newton’s
Gravitation and Criticism of Gravitational Waves Resulting from the General Theory of
Relativity (LIGO). Bulletin of the Karaganda University. Physics series, No. 4 (96), 39-
56, ISSN 2518-7198. preprints201908.0050.v1.
[37] Weinstein G. (2015). Einstein’s Uniformly Rotating Disk and the Hole Argument.
arXiv:1504.03989 [physics.hist-ph].
[38] Weinberg S. (1972). Gravitation and Cosmology: Principles and Applications of the
General Theory of Relativity. Wiley. ISBN0471925675.
[39] Kanerva P. (1988). Sparse Distributed Memory. MIT Press. ISBN0262514699.
[40] Watanabe S. (1969). Knowing and Guessing: A Quantitative Study of Inference and
Information. Wiley. ISBN0471921300.
[41] Watanabe S. (1986). Epistemological Relativity – Logico-Linguistic Source of
Relativity. Annals of the Japan Association for the Philosophy of Science, 7(1), 1–14.
[42] Łukaszyk S. (2004). New Concept of Probability Metric and its Applications in
Approximation of Scattered Data Sets. Computational Mechanics Vol. 33, 299–304.
[43] Dikarev V., Preuß O., Solanki S., Krüger H.& Krivov A. (2008). Understanding the
WMAP Results: Low-Order Multipoles and Dust in the Vicinity of the Solar System.
Earth, Moon, and Planets Vol. 102, 555–561.
[44] Hansen M., Kim J., Frejsel A., Ramazanov S., Naselsky P., Zhao W., & Burigana C.
(2012). Can Residuals of the Solar System Foreground Explain Low Multipole
Anomalies of the CMB? Journal of Cosmology and Astroparticle Physics, Vol. 2012.
[45] Copi C., Huterer D., Schwarz D., & Starkman G. (2010). Large-Angle Anomalies in the
CMB, Advances in Astronomy, Vol. 2010, Article ID 847541.
[46] Kamionkowski M., & Kosowsky A. (1999). The Cosmic Microwave Background and
Particle Physics. Annual Review of Nuclear and Particle Science, Vol. 49:77-123. 49.1.77.
[47] Land K. & Magueijo J. (2005). Examination of Evidence for a Preferred Axis in the
Cosmic Radiation Anisotropy. Phys. Rev. Lett. 95, 071301.
[48] Łukaszyk S. (2020). A Short Note about Graphene and the Fine Structure Constant.
[49] Kothari D., & Singh B. (1941). Bose-Einstein Statistics and Degeneracy. Proceedings of
the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 178,
No. 973. rspa.1941.0049.
[50] Brukner Č. (2021). Qubits are not Observers – a No-Go Theorem. arXiv:2107.03513
[51] Pienaar J. (2021). A quintet of Quandaries: Five No-Go Theorems for Relational
Quantum Mechanics. Foundations of Physics Vol. 51, Article number: 97.
[52] Alsing P., & Milburn G. (2003). Teleportation with a Uniformly Accelerated Partner.
Phys. Rev. Lett. 91, 180404.
[53] Bell J. (1964). On the Einstein Podolsky Rosen Paradox. Physics Physique Fizika 1, 195.
[54] Fuchs C. (1998). Just Two Nonorthogonal Quantum States. In: Kumar, P., D’Ariano,
G.M., Hirota, O. (eds.) Quantum Communication, Computing, and Measurement 2.
Springer, Boston, MA. 10.1007/0-306-47097-7_2.
[55] Axler S., Bourdon P., & Ramey W. (2001). Harmonic Function Theory. Graduate Texts
in Mathematics, Springer.
[56] Gantumur T. (2010). Harmonic functions. McGill University, Math 140. file/114461026/harmonicpdf


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