The Double Rotation as Invariant of Motion in Quantum Mechanics

Zeps, Dainis (2010) The Double Rotation as Invariant of Motion in Quantum Mechanics. Prespacetime Journal, 1 (1). pp. 4-11. ISSN 2153-8301

[thumbnail of Double.Rotation.Quantum.Mechanics.pdf]
PDF - Published Version
[thumbnail of Double.Rotation.Quantum.Mechanics.docx] Microsoft Word - Accepted Version

Official URL:


Quantum mechanics may loose its weirdness if systematically geometric algebra methods would be used more and more. Crucial aspect is to find laws of quantum mechanics be present in macroworld in form of description of motions rather than objects. To help to reach this goal we suggest to use double rotation as one of base invariants in quantum mechanics.

Item Type:Article
Uncontrolled Keywords:quantum mechanics, geometrical algebra, rotation, double rotation, reflection
Subjects:Q Science > QC Physics > QC01 Quantum mechanics
Divisions:University of Latvia > CI Institute of Mathematics and Computer Science
1. Bohm, David. Wholeness and the Implicate Order. London : Routledge, 2002.

2. Zeps, Dainis. Quantum Distinction: Quantum Distinctiones! Leonardo Journal of Sciences : (LJS), 2009 (8), p. 252-261. Issue 14 (January-June).

3. —. Mathematics as Reference System of Life. Riga : Internet publication, 2009.

4. —. On Reference System of Life. Riga : Quantum Distinctions, 2009.

5. Huang, Kerson. Fundamental Forces of Nature. The Story of Gauge Fields. Singapore : World Scientific, 2007.

6. —. Quarks, Leptons and Gauge Fields. Singapore : Worlds Scientific Publishing Co Pte. Ltd, 1982.

7. Marathe, K.B. and Martucci, G. The Mathematical Foundations of Gauge Theories. Amsterdam : North Holland, 1992.

8. Hestenes, David and Sobczyk, Garret. Clifford algebra to geometric calculus: a unified language for mathematics and physics. Dortrecht, Holland : Reidel Publishing Company, 1987. 165 pp.

9. Baylis, William E. Applications of Clifford Algebras in Physics. s.l. : University of Windsor, 2003. 54 pp.

10. Vince, John. Geometric Algebra for Computer Graphics. London : Springer Verlag, 2008.

11. Doran, C and Lasenby, A. Geometric algebra for physicists. s.l. : CUP, 2003. 589 pp.

12. Zeps, D. Cognitum hypothesis and cognitum consciousness. How time and space conception of idealistic philosophy is supported by contemporary physics. 2005.

13. —. Classical and Quantum Self-reference Systems in Physics and Mathematics. Prague : KAM-DIMATIA Series, 2007. 807, 24pp..

14. Hu, Huping Hu and Wu, Maoxin. Spin as Primordial Self-Referential Process Driving Quantum Mechanics, Spacetime Dynamics and Consciousness. New York : Biophysics Consulting Group, 2003.

15. Penrose, Roger. The Road to Reality. A Complete Guide to the Laws of the Universe. New Yourk : Vintage Books, 2007.

16. Penrose, Rogen and Rindler, Wolfgang. Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (Cambridge Monographs on Mathematical Physics). London : Cambridge University Press, 1987.

17. Hestenes, David. CLIFFORD ALGEBRA AND THE INTERPRETATION OF QUANTUM MECHANICS. Reidel : in Clifford Algebras and their Applications in Mathematical Physics, 1986. 321-346.

18. Smolin, Lee. Three Roads to Quantum Gravity. New Yourk : Basic Books, 2001.

19. —. The Trouble with Physics. The Rise of String Theory, the Fall of a Science and What Comes Next. s.l. : A Mariner Book, 2006.

20. Hardy, Lucien. Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. s.l. : Phys. Rev. Lett. , 1992. 68, 2981 - 2984.

21. Lundeen, J.S. and Steinberg, A.M. Experimental joint weak measurement on a photon pair as a probe of Hardy’s Paradox. University of Toronto : Toronto, 2008. arXiv:0810.4229v1.

22. Yokota, Kazuhiro, et al. Direct observation of Hardy’s paradox by joint weak measurement with an entangled photon pair. : New Journal of Physics, 2009. 11, 033011 (9pp).

23. Whorf, Benjamin Lee. Language, Mind and Reality. 1952. pp. Vol. IX, No 3, 167-188.

24. Zeps, Dainis. Cogito ergo sum. 2008.

25. Hall, Brian C. Lie Groups, Lie Algebras, and Representations. An Elementary Introduction. New Yourk : Springer, 2003.

26. Rashewsky, Peter. Rieman Geometry and Tensor Analysis. In Russian. 1967.

27. Steiner, Rudolf. Die vierte Dimension. Mathematik und Wirklichkeit. R. Steiner Verl., 1995, 310 pp. . Dornach : R. Steiner Verlag, 1995.

28. Wigner, E. The unreasonable effectiveness of Mathematics in the natural science. 1960. pp. 1-14.

29. Woit, Peter. Not Even Wrong. The Failure of String Theory and the Continuing Challange to Unify the Laws of Physics. London : Jonathan Cape, 2007.

30. Girard, Patrick R. Quaternions, Clifford Algebras and Relativistic Physics. Basel : Birkhauser, 2007.

31. HESTENES, DAVID and ZIEGLER, RENATUS. Projective Geometry with Clifford Algebra. 1991 : Acta Applicandae Mathematicae. Vol. 23, 25–63..

32. Hestenes, David. Point Groups and Space Groups in Geometric Algebra. Tempe, Arizona, USA : Department of Physics and Astronomy, Arizona State University,. Computational Geometry - 4-1.

33. Bohm, David. Quantum Mechanics.

34. Hiley, B. J. Non-commutative Geometry, the Bohm Interpretation and the Mind-Matter Relationship. 2000.

35. Lando, Sergei K and K, Zvonkin Alexander. Graphs on Surphaces and Their Applications. s.l. : Springer, 2003.

36. Ouspensky, Peter. Tertium Organum. Key to Solving Mysteries of the World. In Russian. 1911.

37. Isham, Chris J. Modern Differential Geometry for Physicists. New Jersey : World Scientific, 2003.

38. Nakahara, M. Geometry, Topology and Physics. New York : Taylor & Francis, 2003.

39. Landau, L.D and Lifshitz, E.M. Mechanics, in Russian. M : Gosizd. fiz.mat.lit., 1958.

40. Vladimirov, J. S. Geometrofizika. In Russian. M. : s.n., 2005.

41. Zeps, Dainis. Four levels of complexity in mathematics and physics. Riga : Quantum Distinctions, 2009.

42. —. Mathematical mind and cognitive machine (In Latvian). 2008. p. 11.

43. —. Rudolf Steiner on mathematics and reality. In Latvian. 2008. p. 7 pp.

44. —. The trouble with physics. How physics missed main part of the observer and what comes next. Riga : s.n., 2008. p. 9.

45. —. Trouble with physical interpretations or time as aspect of reference system of life. 2008.

46. Tegmark, Max. Mathematical Universe. 2007. arXiv:0704.0646v2.

47. Berezin, F. A. The Method of Second Quantization. Moscow : Nauka, 1965. In Russian, 235 pp.

48. Dorst, Leo, Fontijne, Daniel and Mann, Stephen. Geometric Algebra for Computer Science. An Object-Oriented Approach to Geometry. 2007.

ID Code:25
Deposited By: Dainis Zeps
Deposited On:16 Oct 2009 19:29
Last Modified:06 Feb 2021 14:40

Repository Staff Only: item control page