Frontiers of Physics

, 12:128503 | Cite as

Spin in the extended electron model

Research article

Abstract

It has been found that a model of extended electrons is more suited to describe theoretical simulations and experimental results obtained via scanning tunnelling microscopes, but while the dynamic properties are easily incorporated, magnetic properties, and in particular electron spin properties pose a problem due to their conceived isotropy in the absence of measurement. The spin of an electron reacts with a magnetic field and thus has the properties of a vector. However, electron spin is also isotropic, suggesting that it does not have the properties of a vector. This central conflict in the description of an electron’s spin, we believe, is the root of many of the paradoxical properties measured and postulated for quantum spin particles. Exploiting a model in which the electron spin is described consistently in real three-dimensional space–an extended electron model–we demonstrate that spin may be described by a vector and still maintain its isotropy. In this framework, we re-evaluate the Stern–Gerlach experiments, the Einstein–Podolsky–Rosen experiments, and the effect of consecutive measurements and find in all cases a fairly intuitive explanation.

Keywords

spin extended electron model geometric algebra Stern–Gerlach experiment Einstein–Podolsky–Rosen magnetism 

Notes

Acknowledgments

The authors acknowledge EPSRC funding for the UKCP consortium, grant No. EP/K013610/1.

References

  1. 1.
    J. D. Jackson, Classical Electrodynamics, Wiley, 1999MATHGoogle Scholar
  2. 2.
    R. Eisberg, R. Resnick, and J. Brown, Quantum physics of atoms, molecules, solids, nuclei, and particles, Phys. Today 39(3), 110 (1986)CrossRefGoogle Scholar
  3. 3.
    A. A. Rangwala and A. S. Mahajan, Electricity and Magnetism, McGraw Hill Education, 2004Google Scholar
  4. 4.
    W. Gerlach and O. Stern, Der experimentelle nachweis der richtungsquantelung im magnetfeld, Zeitschrift für Physik A Hadrons and Nuclei, 9(1), 349 (1922)ADSGoogle Scholar
  5. 5.
    C. E. Burkhardt and J. J. Leventhal, Foundations of Quantum Physics, Springer Science & Business Media, 2008CrossRefMATHGoogle Scholar
  6. 6.
    K.-H. Rieder, G. Meyer, S.-W. Hla, F. Moresco, K. F. Braun, K. Morgenstern, J. Repp, S. Foelsch, and L. Bartels, The scanning tunnelling microscope as an operative tool: Doing physics and chemistry with single atoms and molecules, Philos. Trans. A Math. Phys. Eng. Sci. 362(1819), 1207 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    W. A. Hofer, Heisenberg, uncertainty, and the scanning tunneling microscope, Front. Phys. 7(2), 218 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    W. A. Hofer, Unconventional approach to orbital-free density functional theory derived from a model of extended electrons, Found. Phys. 41(4), 754 (2011)ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    W. A. Hofer, Elements of physics for the 21st century, J. Phys.: Conf. Ser. 504, 012014 (2014)Google Scholar
  10. 10.
    D. Hestenes and G. Sobczyk, Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics, Vol. 5, Springer Science & Business Media, 2012MATHGoogle Scholar
  11. 11.
    S. Gull, A. Lasenby, and C. Doran, Imaginary numbers are not real: The geometric algebra of spacetime, Found. Phys. 23(9), 1175 (1993)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    G. Benenti, G. Strini, and G. Casati, Principles of Quantum Computation and Information, World Scientific, 2004CrossRefMATHGoogle Scholar
  13. 13.
    G. C. Ghirardi, A. Rimini, and T. Weber, Unified dynamics for microscopic and macroscopic systems, Phys. Rev. D 34(2), 470 (1986)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    R. Penrose, On gravity’s role in quantum state reduction, Gen. Relativ. Gravit. 28(5), 581 (1996)ADSMathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    W. Heisenberg, Language and Reality in Modern Physics, 1958Google Scholar
  16. 16.
    G. C. Knee, K. Kakuyanagi, M.-C. Yeh, Y. Matsuzaki, H. Toida, H. Yamaguchi, S. Saito, A. J. Leggett, and W. J. Munro, A strict experimental test of macroscopic realism in a superconducting flux qubit, arXiv: 1601.03728 (2016)Google Scholar
  17. 17.
    L. de Broglie, Research on the theory of quanta, Ann. Phys. 10, 22 (1925)CrossRefGoogle Scholar
  18. 18.
    E. Schrödinger, An undulatory theory of the mechanics of atoms and molecules, Phys. Rev. 28(6), 1049 (1926)ADSCrossRefMATHGoogle Scholar
  19. 19.
    D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables (I), Phys. Rev. 85(2), 166 (1952)ADSMathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables (II), Phys. Rev. 85(2), 180 (1952)ADSMathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    J. S. Bell, On the problem of hidden variables in quantum mechanics, Rev. Mod. Phys. 38(3), 447 (1966)ADSMathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    H. Everett, “Relative state” formulation of quantum mechanics, Rev. Mod. Phys. 29(3), 454 (1957)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    G. Hooft, The free-will postulate in quantum mechanics, arXiv: quant-ph/0701097 (2007)Google Scholar
  24. 24.
    G. Hooft, Entangled quantum states in a local deterministic theory, arXiv: 0908.3408 (2009)Google Scholar
  25. 25.
    O. C. de Beauregard, Time symmetry and interpretation of quantum mechanics, Found. Phys. 6(5), 539 (1976)ADSCrossRefGoogle Scholar
  26. 26.
    P. Dowe, A defense of backwards in time causation models in quantum mechanics, Synthese 112(2), 233 (1997)MathSciNetCrossRefGoogle Scholar
  27. 27.
    E. Santos, The failure to perform a loophole-free test of Bell’s inequality supports local realism, Found. Phys. 34(11), 1643 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys. 86(2), 419 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    W. A. Hofer, Solving the Einstein–Podolsky–Rosen puzzle: The origin of non-locality in Aspect-type experiments, Front. Phys. 7(5), 504 (2012)CrossRefGoogle Scholar
  30. 30.
    C. Doran, A. Lasenby, and S. Gull, States and operators in the spacetime algebra, Found. Phys. 23(9), 1239 (1993)ADSMathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    A. Einstein, B. Podolsky, and N. Rosen, Can quantummechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)ADSCrossRefMATHGoogle Scholar
  32. 32.
    A. Einstein, Physics and reality, Journal of the Franklin Institute, 221(3), 349 (1936)ADSCrossRefGoogle Scholar
  33. 33.
    B. Thaller, Advanced Visual Quantum Mechanics, Springer Science & Business Media, 2005MATHGoogle Scholar
  34. 34.
    B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, R. Ursin, and A. Zeilinger, Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering, New J. Phys. 14(5), 053030 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden variable theories, Phys. Rev. Lett. 23(15), 880 (1969)ADSCrossRefGoogle Scholar
  36. 36.
    L. de Broglie, Wave mechanics and the atomic structure of matter and of radiation, J. Phys. Radium 8, 225 (1927)CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of ChemistryNewcastle UniversityNewcastleUK

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