Journal of Physics & Astronomy

Open Access Open Access  Restricted Access Subscription Access

Can Dimensional Anisotropy Satisfy Mach's Principle? A Topological Approach to Variable Dimensions of Space Using the Borsuk-Ulam Theorem


Affiliations
1 University of Debrecen, Department of Anatomy, Histology, and Embryology, United States
2 University of Manitoba, Department of Electrical and Computer Engineering and Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Canada
 

We create a model universe by insulating a compact Wave Function (WF) with an information-blocking horizon. The WF can produce entanglement independent of distance but interaction with the horizon evolves the quantum state (frequency) of the WF and the topology (curvature) of the horizon, satisfying the Borsuk-Ulam Theorem and the Page and Wootters mechanism of static time. Therefore, in an orthogonal relationship, the field curvature measures the particle’s evolution over time. Because increasing field strength accumulates pressure, whereas negative curvature creates a vacuum, their opposing dynamics give rise to poles with dimensionality transformations; pressure culminates in two-dimensional black hole horizons (infinite time), whereas vacuum gives rise to four-dimensional cosmic voids (time zero). The orthogonality of the field and the compact WF is global self-regulation that evolves and fine-tunes the cosmos’ parameters. The four-dimensional cosmic voids can produce accelerating expansion without dark energy on the one hand and pressure gives the impression of dark matter on the other. The verifiable and elegant hypothesis satisfies Mach's principle. Above alternative answer regarding the spreading of light also makes absolutely necessary to perform the above missing experiment, as a direct way that convinces anybody how light is spreading. The present article will empower big labs to perform this crucial experiment.

Keywords

Mach's Principle, GR, Borsuk-Ulam Theorem, Topolog, Page and Wootters Mechanism, Dimensional Anisotropy.
User
Notifications
Font Size

  • Laymon R. Newton's bucket experiment. J. Hist. Philos. 1978;16(4):399-413.

  • Brans CH. Mach's principle and a relativistic theory of gravitation. II. Phys. Rev. 1962;125(6):2194.

  • Brans CH. Absence of inertial induction in general relativity. Phys. Rev. Lett. 1977;39(14):856.

  • D. N. Page and Wootters W. K., PhysRevD., pp. 2885, 10.1103/27.2885., 1983.

  • Deli E. The science of consciousness: How a new understanding of space and time infers the evolution of the mind. Nadir Video; 2015.

  • Gambini R, Pullin J. The Montevideo interpretation of quantum mechanics: a short review. Entropy. 2018;20(6):413.

  • Rotondo M, Nambu Y. Clock time in quantum cosmology. Universe. 2019;5(2):66.

  • DeWitt BS. Dynamical theory of groups and fields http://www. slac. stanford. edu/spires/find/hep/www? irn= 6942989, New York USA (1965) Google Scholar BS DeWitt and G. Esposito, An introduction to quantum gravity 2008. Int. J. Geom. Meth. Mod. Phys.;5(101):0711-2445.

  • Moreva E, Gramegna M, Yurischev MA. Exploring quantum correlations from discord to entanglement. Adv. Sci. Eng. Med. 2017;9(1):46-52..

  • Wootters WK. “Time” replaced by quantum correlations. Int. j. theor. phys. 1984;23(8):701-11.

  • Foti C, Coppo A, Barni G, et al. Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states. Nat. commun. 2021;12(1):1-9.

  • Woods M. The Page-Wootters mechanism 36 years on: a consistent formulation which accounts for interacting systems. Quantum Views. 2019;3:16.

  • Smith AR, Ahmadi M. Quantizing time: interacting clocks and systems. Quantum. 2019;3:160.

  • A. Smith and M. Ahmadi. Quantizing time: Interacting clocks and systems. Quantum Physics.,2017.

  • Lobo FS, Olmo GJ, Rubiera-Garcia D. Microscopic wormholes and the geometry of entanglement. Eur. Phys. J. C. 2014;74(6):1-5.

  • van de Weygaert R. Voids and the Cosmic Web: cosmic depression & spatial complexity. Proc. Int. Astron. Union, 2014;11(S308):493-523.

  • Kravtsov AV. On the origin of the global Schmidt law of star formation. Astrophys. J. 2003;590(1):L1.

  • Tully RB, Courtois H, Hoffman Y, et al. The Laniakea supercluster of galaxies. Nature. 2014;513(7516):71-3.

  • Tully RB, Courtois HM, Sorce JG. COSMICFLOWS-3. Astron. J. 2016;152(2):50.

  • Tully RB, Pomarède D, Graziani R, et al. Cosmicflows-3: Cosmography of the Local Void. Astron. J. 2019;880(1):24.

  • Pycke JR, Russell E. A new statistical perspective to the cosmic void distribution. Astrophys. J. 2016;821(2):110.

  • Gregory SA, Thompson LA. The Coma/A1367 supercluster and its environs.

  • Lindner U, Einasto J, Einasto M, et al. The Structure of Supervoids--I: Void Hierarchy in the Northern Local Supervoid. arXiv preprint astro-ph/9503044. 1995.

  • Freedman RA. Universe: Stars and Galaxies+ Universe. WH Freeman; 2008.

  • Kastner RE, Kauffman S. Are dark energy and dark matter different aspects of the same physical process?. Front. Phys. 2018;6:71.

  • Narlikar JV, Appa Rao KM, Dadhich N. High energy radiation from white holes. Nature. 1974;251(5476):590-1.

  • Lightman AP, Eardley DM. Black holes in binary systems: instability of disk accretion. Astrophys. J.1974;187:L1.

  • Wald RM, Ramaswamy S. Particle production by white holes. Phys. Rev. D. 1980;21(10):2736.

  • Bianchi E, Christodoulou M, d’Ambrosio F, et al. White holes as remnants: a surprising scenario for the end of a black hole. Class. Quantum Gravity. 2018;35(22):225003.

  • Frenkel D, Warren PB. Gibbs, Boltzmann, and negative temperatures. Am. J. Phys. 2015;83(2):163-70.

  • Kovács A, García-Bellido J. Cosmic troublemakers: the Cold Spot, the Eridanus supervoid, and the Great Walls. Mon. Not. R. Astron. Soc. 2016;462(2):1882-93.

  • Farhang M, Movahed SM. CMB Cold Spot in the Planck light. Astrophys. J. 2021;906(1):41.

  • Shim J, Park C, Kim J, et al. Identification of Cosmic Voids as Massive Cluster Counterparts. Astrophys. J. 2021;908(2):211.

  • Hellwing WA, Cautun M, van de Weygaert R, et al. Caught in the cosmic web: Environmental effect on halo concentrations, shape, and spin. Phys. Rev. D. 2021;103(6):063517.

  • Lee S. A solution to the initial condition problems of inflation: NATON. Phys. Dark Universe. 2020;30:100677.

  • Vieira JP, Byrnes CT, Lewis A. Cosmology with negative absolute temperatures. J. Cosmol. Astropart. Phys. 2016;2016(08):060.

  • Lovelock D. The Einstein tensor and its generalizations. J. Math. Phys. 1971;12(3):498-501.

  • Landauer R. Irreversibility and heat generation in the computing process. IBM j. res. dev. 1961;5(3):183-91.

  • Wheeler JA, Ford K. Geons, black holes and quantum foam: a life in physics.

  • K. Borsuk, "Drei sӓtze uber di n-dimensionale euklidische sphӓre," Fund. Math. , vol. XXX. 177-196, 1933.

  • Peters JF. Computational proximity. InComputational Proximity 2016 (pp. 1-62). Springer, Cham.

  • Guadagni C, Peters JF, Ramanna S. Descriptive proximities. Properties and interplay between classical proximities and overlap. Math. Comput. Sci.. 2018;12(1):91-106.

  • Matoušek J, Björner A, Ziegler GM. Using the Borsuk-Ulam theorem: lectures on topological methods in combinatorics and geometry. Berlin: Springer; 2003.

  • J. F. Peters. Ribbon complexes and their aproximate descriptive proximities. Ribbon and vortex nerves, Betti numbers and planar divisions. Bull Allahabad Math Soc. 2020;35(1):1-14.

  • Tozzi A , Peters JV. Borsuk-Ulam Theorem Extended to Hyperbolic Spaces, in Proximity. Excursions Topol Digit Images. 2016:169-171.

  • Weeks J R, Dekker M. Chapter 14: The Hypersphere, in the shape of space: how to visualize surfaces and three-dimensional manifolds. ISBN 978-0-8247-7437-0. 1985.

  • George M. Choosing a Point from the Surface of a Sphere. Ann Math Stat. 1972;43(2):645-6.

  • D. Anosov. Diffeomorphism, in Encyclopedia of Mathematics. Kluwer Academic Publishers. 1995;155-156.

  • L. Susskind, A. Friedman. Quantum Mechanics. The Theoretical Minimum, UK: Penguin Random House ISBN 97-0-141-97781-2. 2014.

  • Martyushev LM, Shaiapin EV. From an entropic measure of time to laws of motion. Entropy. 2019;21(3):222.

  • Martyushev LM. On interrelation of time and entropy. Entropy. 2017;19(7):345.

  • Chatterjee A, Iannacchione G. Time and thermodynamics extended discussion on “Time and clocks: A thermodynamic approach”. Results Phys. 2020;17:103165.

  • Verlider E. On the origin of gravity and the laws of Newton. J. High Energ. Phys. 2011;4:29.

  • Lucia U, Grisolia G. Time and clocks: A thermodynamic approach. Results in Physics. 2020;16:102977.

  • [Google Scholar] [Crossref]

  • Lucia U, Grisolia G, Kuzemsky AL. Time, irreversibility and entropy production in nonequilibrium systems. Entropy. 2020;22(8):887.

  • Bardoux Y, Caldarelli MM, Charmousis C. Conformally coupled scalar black holes admit a flat horizon due to axionic charge. J High Energy Phys. 2012;2012(9):1-21.

  • Maldacena J. The large-N limit of superconformal field theories and supergravity. Int J Theo Phys. 1999;38(4):1113-33.

  • Almheiri A, Marolf D, Polchinski J, et al. Black holes: complementarity or firewalls? J High Energy Phys. 2013;2013(2):1-20.

  • Braun S, Ronzheimer JP, Schreiber M, et al. Negative absolute temperature for motional degrees of freedom. Science. 2013;339(6115):52-5.

  • Calabrese S, Porporato A. Origin of negative temperatures in systems interacting with external fields. Phys Lett A. 2019;383(18):2153-8.

  • B Lavenda. Do negative temperatures exist? J Phys A: Math Gen. 1999;32(23):4279.

  • F Miceli, M Baldovin, A Vulpiani. Statistical mechanics of systems with long-range interactions and negative absolute temperature. 2019;99(4-1):042152.

  • Merali Z. Quantum gas goes below absolute zero. Nature. 2013.

  • Ramsey NF. Thermodynamics and statistical mechanics at negative absolute temperatures. Phys Rev. 1956;103(1):20.

  • Abraham E, Penrose O. Physics of negative absolute temperatures. Phys Rev E. 2017;95(1):012125.

  • Baldovin M, Puglisi A, Sarracino A, et al. About thermometers and temperature. J Stat Mech Theory Exp. 2017;2017(11):113202.

  • Baldovin M. Negative Temperature Out of Equilibrium. In statistical mechanics of hamiltonian systems with bounded kinetic terms. 2020:83-97.

  • L. Onsager. Statistical Hydrodynamics, Il Nuovo Cimento. Nuovo Cim. 1949;279-287.

  • Kostic MM. The elusive nature of entropy and its physical meaning. Entropy. 2014;16(2):953-67.

  • Haji-Akbari A, Engel M, Keys AS et al. Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra. Nature. 2009;462(7274):773-7.

  • Wissner-Gross AD, Freer CE. Causal entropic forces. Phys. Rev. Lett. 2013;110(16):168702.

  • R. Weygaert. Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe the cosmic web: geometric analysis. Astrophys. 2007;1:230-239.

  • Cantalupo S, Arrigoni-Battaia F, Prochaska JX, et al. A cosmic web filament revealed in Lyman-α emission around a luminous high-redshift quasar. Nature. 2014;506(7486):63-6.

  • Wesson PS. Fundamental unsolved problems in astrophysics. Space Sci Rev. 2001;98(3):329-42.

  • Rugh SE, Zinkernagel H. The quantum vacuum and the cosmological constant problem. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics. 2002;33(4):663-705.

  • Sánchez-Monroy JA, Quimbay CJ. Cosmological constant in a quantum fluid model. Int. J. Mod. Phys. D. 2011;20(13):2497-506.

  • Maccone L. A fundamental problem in quantizing general relativity. Found. Phys. 2019;49(12):1394-403.

  • Lambas DG, Lares M, Ceccarelli L, et al. The sparkling Universe: the coherent motions of cosmic voids. Mon. Not. R. Astron. Soc.: Lett.,2015;455(1):L99-103.

  • Saulnier L, Champougny L, Bastien G, et al. A study of generation and rupture of soap films. Soft Matter. 2014;10(16):2899-906.

  • Peters JF, Tozzi A. Quantum entanglement on a hypersphere. Int. J. Theor. Phys. 2016;55(8):3689-96.

  • Pontzen A, Slosar A, Roth N, et al. Inverted initial conditions: exploring the growth of cosmic structure and voids. Phys. Rev. D. 2016;93(10):103519.

  • Hooft GT. Dimensional reduction in quantum gravity. arXiv preprint gr-qc/9310026. 1993.

  • Noid DW, Gray SK, Rice SA. Fractal behavior in classical collisional energy transfer. J. chem. phys. 1986;84(5):2649-52.

  • Y. Zeldovich, G. Barenblatt, V. Librovich, et al. The Mathematical Theory of Combustion and Explosions., New York: Plenum, 1985.

  • S. Wolfram, A new kind of Science, Wolfram Research , 2002.

  • Hohensee MA, Leefer N, Budker D, et al. Limits on violations of Lorentz symmetry and the Einstein equivalence principle using radio-frequency spectroscopy of atomic dysprosium. Phys. Rev. Lett. 2013;111(5):050401.

  • Peck SK, Kim DK, Stein D, et al. Limits on local Lorentz invariance in mercury and cesium. Phys. Rev. A. 2012;86(1):012109.

  • Santiago J, Visser M. Tolman temperature gradients in a gravitational field. Eur. J. Phys. 2019;40(2):025604.

  • Tolman RC. On the weight of heat and thermal equilibrium in general relativity. Phys. Rev. 1930;35(8):904.

  • Frenk CS, White SD. Dark matter and cosmic structure. Ann. Phys. 2012;524(9‐10):507-34.

  • Ahmadi B, Salimi S, Khorashad AS. Irreversible Work, Maxwell’s Demon and Quantum Thermodynamic Force. arXiv preprint arXiv:1809.00611 v2. 2018.


Abstract Views: 100

PDF Views: 0




  • Can Dimensional Anisotropy Satisfy Mach's Principle? A Topological Approach to Variable Dimensions of Space Using the Borsuk-Ulam Theorem

Abstract Views: 100  |  PDF Views: 0

Authors

Eva Deli
University of Debrecen, Department of Anatomy, Histology, and Embryology, United States
James F. Peters
University of Manitoba, Department of Electrical and Computer Engineering and Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Canada

Abstract


We create a model universe by insulating a compact Wave Function (WF) with an information-blocking horizon. The WF can produce entanglement independent of distance but interaction with the horizon evolves the quantum state (frequency) of the WF and the topology (curvature) of the horizon, satisfying the Borsuk-Ulam Theorem and the Page and Wootters mechanism of static time. Therefore, in an orthogonal relationship, the field curvature measures the particle’s evolution over time. Because increasing field strength accumulates pressure, whereas negative curvature creates a vacuum, their opposing dynamics give rise to poles with dimensionality transformations; pressure culminates in two-dimensional black hole horizons (infinite time), whereas vacuum gives rise to four-dimensional cosmic voids (time zero). The orthogonality of the field and the compact WF is global self-regulation that evolves and fine-tunes the cosmos’ parameters. The four-dimensional cosmic voids can produce accelerating expansion without dark energy on the one hand and pressure gives the impression of dark matter on the other. The verifiable and elegant hypothesis satisfies Mach's principle. Above alternative answer regarding the spreading of light also makes absolutely necessary to perform the above missing experiment, as a direct way that convinces anybody how light is spreading. The present article will empower big labs to perform this crucial experiment.

Keywords


Mach's Principle, GR, Borsuk-Ulam Theorem, Topolog, Page and Wootters Mechanism, Dimensional Anisotropy.

References