Clifford Algebra as a Way to Quantum Gravity

Authors

  • B.I. Lev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe70.6.361

Keywords:

Clifford algebra, wave function, test particle, space-time manifold

Abstract

This article puts forward a novel hypothesis for a solution to the problem of quantization of gravity. The objective of this study is to demonstrate that the geometric representation of the wave function can be considered as a characteristic of the space-time manifold. In this approach, it is shown that the Dirac theory for the hydrogen atom and the Kepler dynamics for the planetary system describe analogous phenomena in the space-time. The states of these systems possess parameters that correspond to the permitted dynamic states of the space-time, thereby maintaining information regarding the corpuscular and wave nature. The proposed approach sheds a new light on the potential resolution of the problems of quantum gravity.

References

1. J. Oppenheim. A postquantum theory of classical gravity. Phys.l Rev. X 13, 041040 (2023).

https://doi.org/10.1103/PhysRevX.13.041040

2. B.J. Wolk. Quantum gravity through geometric algebra. J. Phys. A: Math. Theor. 57, 015402 (2024).

https://doi.org/10.1088/1751-8121/ad0ee7

3. M. Hatifi. Quantum gravity without metric quantization: From hidden variables to hidden spacetime curvatures. arXiv:2502.08421v1 [gr-qc] 12 Feb 2025.

4. D. Hestenes. Clifford algebra and the interpretation of quantum mechanics. In: Clifford Algebras and Their Applications in Mathematical Physics. Edited by J.S.R. Chisholm, A.K. Commons (Reidel, 1986).

https://doi.org/10.1007/978-94-009-4728-3_27

5. D. Hestenes. Spacetime physics with geometric algebra. American J. Phys. 71, 691 (2003).

https://doi.org/10.1119/1.1571836

6. B.F. Schutz. Geometrical Methods of Mathematical Physics (Cambridge University Press, 1982).

7. A. Harvey-Tremblay. The observer, defined as a measure space of halting programs. Is a complete and constructive formulation of physics. scholar.archive.org, (2022).

8. M. Novello. Spinor theory of gravity. arXiv.gr-qc/0609033 (gr-qc).

9. M. Novello, E. Bittencourt. Metric relativity and the dynamical bridge: Highlights of Riemannian geometry in physics. Brazilian J. Phys. 45, 756 (2015).

https://doi.org/10.1007/s13538-015-0362-7

10. B.I. Lev. Geometric interpretation of the origin of the universe. J. Modern Phys. 13, 89 (2022).

https://doi.org/10.4236/jmp.2022.132007

11. B.I. Lev. Application of Clifford algebra to describe the early universe. Mathematics 12, 3396 (2024).

https://doi.org/10.3390/math12213396

12. C. Doran, A. Lasenby. Geometric Algebra for Physicists (Cambridge University Press, 2003).

https://doi.org/10.1017/CBO9780511807497

13. M. Arminjon, F. Reifler. Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations. Brazilian J. Phys. 43, 64 (2013).

https://doi.org/10.1007/s13538-012-0111-0

14. G. Horton, C. Dewdney, A. Nesteruk. Time-like owns of energy-momentum and particle trajectories for the Klein-Gordon equation. J. Phys. A: Math. Gen. 33, 7337 (2000).

https://doi.org/10.1088/0305-4470/33/41/306

15. A. Soiguine. The Geometric Algebra Lift of Qubits and Beyond (LAMBERT Academic Publishing, 2020).

16. I.M. Benn, R.W. Tucker. Clifford analysis of exterior forms and Fermi-Bose symmetry. J. Phys. A: Math. Gen. 16, 4147 (1999).

https://doi.org/10.1088/0305-4470/16/17/029

17. B.I. Lev. A probable approach to the geometrization of interaction. Mod. Phys. Lett. A 3 (10), 1025 (1988), ib. 4, erratum, (1989).

https://doi.org/10.1142/S0217732388001203

18. B.I. Lev. Research and Applications Towards Mathematics and Computer Science. Vol. 4, Chap. 11 [ISBN: 978-81-19491-72-8].

19. C. Daviau, J. Bertrand. New Insights in the Standard Model of Quantum Physics in Clifford Algebra HAL Id: hal-00907848 (2013).

20. A.D. Sakharov. Vacuum quantum fluctuations n curved space and the theory of gravitations. Dok. Akad. Nauk. SSSR 177, 70 (1967) [Sov. Phys. Dokl. 12, 1040 (1968)].

21. O. Klein. Generalization of Einstein principle of equivalence so as to embrace the field equations of gravitation. Phys. Scr. 9, 69 (1974).

https://doi.org/10.1088/0031-8949/9/2/001

22. S.L. Adler. Einstein gravity as a symmetry-breaking effect in quantum field theory. Rev. Mod. Phys. 54, 3 (1982).

https://doi.org/10.1103/RevModPhys.54.729

23. P. Cameron. Impedance approach to the chiral anomaly (2014). rxiv.org/pdf/1402.0064vA.pdf.

24. P. Cameron. Generalized quantum impedances: A background independent model for the unstable particle spectrum (2012). http://dx.doi.org/10.13140/RG.2.2.25702.84800.

25. B.I. Lev. Geometrical presentation of elementary particle wave function. Low Temp. Phys. 48, 938 (2022).

https://doi.org/10.1063/10.0014593

26. G. Kasanova. Vector Algebra (Presses Universitaires de France, 1976).

27. M.J. Hadley. Spin-1/2 in classical general relativity. Class. Quantum Grav. 17, 4187 (2000).

https://doi.org/10.1088/0264-9381/17/20/303

28. A.G. Klein. Schr¨odinger inviolate: Neutron optical searches for violations of quantum mechanics. Physics B 151, 44, (1988).

https://doi.org/10.1016/0378-4363(88)90143-X

29. A.C. Bakai, Yu.G. Stepanovskij. Adiabatic Invariant (Naukova Dunka, 1981).

30. P. Nandi, F.G. Scholtz. The hidden Lorentz covariance of quantum mechanics. Annals Phys. 464, 169643 (2024).

https://doi.org/10.1016/j.aop.2024.169643

31. P. Kustaanheimo. Spinor regularization of the Kepler motion. Ann. Univ. Turku. Ser. A 73, 1 (1964).

32. P. Kustaanheimo, E. Stiefel. Perturbation theory of Kepler motion based on spinor regularization. J. Reine, Angew. Math. 218, 204 (1965).

https://doi.org/10.1515/crll.1965.218.204

33. B.E. Laurent. A variational principle and conservation theorems in connection with the generally relativistic Dirac equation. Phys. Scripta 16 (25), 263 (1960).

34. K. Bliokh. Geometric amplitude, adiabatic invariants, quantization, and strong stability of Hamiltonian systems. J. Math. Phys. 43 (1), 25 (2002).

https://doi.org/10.1063/1.1418718

35. R. Louise. Loi de titius-bode et formalisme ondulatoire. Moon Planets 26, 389 (1982).

https://doi.org/10.1007/BF00941641

36. M.D. de Oliveira, Alexandre G.M. Schmidt. Exact solutions of Dirac equation on a static curved space-time. Annals of Physics 401, 21 (2019).

https://doi.org/10.1016/j.aop.2018.11.025

37. J. Llibre, C. Pinol. A gravitational approach to the Titius-Bode law. J.: Astronomical Journal 93, 1272 (1987).

https://doi.org/10.1086/114410

38. C.X. Huang, G.A. Bakos. Testing the Titius-Bode law predictions for Kepler multiplanet systems. MNRAS 442, 674 (2014).

https://doi.org/10.1093/mnras/stu906

Published

2025-06-28

How to Cite

Lev, B. (2025). Clifford Algebra as a Way to Quantum Gravity. Ukrainian Journal of Physics, 70(6), 361. https://doi.org/10.15407/ujpe70.6.361

Issue

Section

General physics

Most read articles by the same author(s)

Similar Articles

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 > >> 

You may also start an advanced similarity search for this article.