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Quantum Mechanics of a Quasi-Euclidean Space with Planck Length, Rotational Symmetry and Translational Symmetry

DOI: 10.4236/jamp.2025.131014, PP. 302-326

Keywords: Planck Length, IR Cutoff, Symmetry, Fine Structure Constant (FSC), Quantum Gravity

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Abstract:

This work is focused on a quasi-Euclidean space with UV cutoff, IR cutoff and symmetries. Mathematical analysis reveals that the UV cutoff results in the minimum structures of space. Dominated by rotational symmetry, the structure should be a local one in situ or on a sphere. Investigations show that a 10D minimum structure is a non-local one with transformability between in-situ state and spherical state due to its special topology. Based on the quantum behaviors of the 10D structure controlled by translational symmetry, IR cutoff determines two long-range interactions with dimensionless constants of ~1/137.036 and ~1/1.628E+38, respectively.

References

[1]  Eckert, M. (2014) How Sommerfeld Extended Bohr’s Model of the Atom (1913-1916). The European Physical Journal H, 39, 141-156.
https://doi.org/10.1140/epjh/e2013-40052-4
[2]  Webb, J.K., Murphy, M.T., Flambaum, V.V., Dzuba, V.A., Barrow, J.D., Churchill, C.W., et al. (2001) Further Evidence for Cosmological Evolution of the Fine Structure Constant. Physical Review Letters, 87, Article 091301.
https://doi.org/10.1103/physrevlett.87.091301
[3]  Webb, J.K., King, J.A., Murphy, M.T., Flambaum, V.V., Carswell, R.F. and Bainbridge, M.B. (2011) Indications of a Spatial Variation of the Fine Structure Constant. Physical Review Letters, 107, Article 191101.
https://doi.org/10.1103/physrevlett.107.191101
[4]  Wilczynska, M.R., Webb, J.K., Bainbridge, M., Barrow, J.D., Bosman, S.E.I., Carswell, R.F., et al. (2020) Four Direct Measurements of the Fine-Structure Constant 13 Billion Years Ago. Science Advances, 6, eaay9672.
https://doi.org/10.1126/sciadv.aay9672
[5]  Webb, J.K. and Lee, C. (2024) Convergence Properties of Fine Structure Constant Measurements Using Quasar Absorption Systems. Monthly Notices of the Royal Astronomical Society, 528, 6550-6558.
https://doi.org/10.1093/mnras/stae306
[6]  Mellen, W.R. (1975) Bulletin of the American Physical Society, 20, 492.
[7]  Yee, J. (2019) The Relationship of the Fine Structure Constant and Pi. Preprints.
https://doi.org/10.13140/RG.2.2.30832.92162
[8]  Gross, D. (2000) Millennium Madness: Physics Problems for the Next Millennium, Strings 2000 Conference at University of Michigan.
[9]  Adler, S.L. (1972) Theories of the Fine Structure Constant. Fermilab.
[10]  Sherbon, M.A. (2018) Fine-structure Constant from Golden Ratio Geometry. SSRN Electronic Journal.
https://doi.org/10.2139/ssrn.3148761
[11]  Stakhov, A. and Aranson, S. (2016) The Fine-Structure Constant as the Physical-Mathematical MILLENNIUM Problem. Physical Science International Journal, 9, 1-36.
https://doi.org/10.9734/psij/2016/21966
[12]  Craig, B.I. (2022) The Formation of 3-Dimensional Euclidean Space and the Fine Structure Constant. HAL Open Science, Preprint.
[13]  Polchinski, J. (1998) String Theory. Cambridge University Press.
https://doi.org/10.1017/cbo9780511618123
[14]  Marek-Crnjac, L. (2004) On the Unification of All Fundamental Forces in a Fundamentally Fuzzy Cantorian ε(∞) Manifold and High Energy Particle Physics. Chaos, Solitons & Fractals, 20, 669-682.
https://doi.org/10.1016/j.chaos.2003.10.013
[15]  Veselov, A.I. and Zubkov, M.A. (2004) 10D Euclidean Dynamical Triangulations. Physics Letters B, 591, 311-317.
https://doi.org/10.1016/j.physletb.2004.04.047
[16]  Sabra, W.A. and Vaughan, O. (2015) 10D to 4D Euclidean Supergravity over a Calabi-Yau Three-Fold. Classical and Quantum Gravity, 33, Article 015010.
https://doi.org/10.1088/0264-9381/33/1/015010
[17]  Mohr, P.J., Taylor, B.N. and Newell, D.B. (2008) CODATA Recommended Values of the Fundamental Physical Constants: 2006. Reviews of Modern Physics, 80, 633-730.
https://doi.org/10.1103/revmodphys.80.633
[18]  Robertson, H.P. (1929) The Uncertainty Principle. Physical Review, 34, 163-164.
https://doi.org/10.1103/physrev.34.163
[19]  Feynman, R.P. (1942) The Principle of Least Action in Quantum Mechanics. PhD Thesis, Princeton University.
[20]  Wyler, A. (1969) L’espace symetrique du groupe des equations de Maxwell. Comptes Rendus de lAcadémie des Sciences, 269, 743-745.

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