Matter-Wave Mechanics

  • Jan C. A. Boeyens

Abstract

The concept of matter waves as a product of four-dimensionally curved space-time is examined. A vital step in the analysis is taking cognisance of the controversial concept of an all-pervading aether. The discrepancy between relativity and quantum theory is traced to the three-dimensional linear equations of wave mechanics, in contrast to Minkowski space-time. The notion of space-like interaction is re-examined and shown to arise from a superficial interpretation of space-time curvature. The more appropriate projective topology is shown to be suitable, in principle, to define four-dimensional matter waves. The transformation from the more general underlying space-time to the familiar three-dimensional affine space is shown to be mediated by the golden ratio, which is further characterized in terms of Fibonacci numbers, Farey sequences and other concepts of number theory. It is demonstrated conclusively that the observed periodic table of the elements and the wave-mechanical approximation are correctly simulated by number theory, with a clear distinction of the respective four- and three-dimensional bases of the two models.

Keywords

Light Cone Double Cover Hamilton Path Wave Mechanic Isotropic Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Dirac, P.A.M.: Is there an æther? Nature 168, 906–907 (1951) CrossRefGoogle Scholar
  2. 2.
    Whitrow, G.J.: Encyclopedia Brittanica 14, 604–606 (1977) Google Scholar
  3. 3.
    Podolny, R.: Something Called Nothing, translated from the Russian by N. Weinstein. Mir, Moscow (1986) Google Scholar
  4. 4.
    Maxwell, J.C.: On physical lines of force. Philos. Mag. 21, 281 (1861) Google Scholar
  5. 5.
    Einstein, A., Infeld, L.: The Evolution of Physics, reprint of the 1966 edition by Simon and Schuster, NY Google Scholar
  6. 6.
    Schrödinger, E.: The proper vibrations of the expanding universe. Physica 6, 899–912 (1939) CrossRefGoogle Scholar
  7. 7.
    Rüger, A.: Atomism from cosmology: Erwin Schrödinger’s work on wave mechanics and space-time structure. Stud. Hist. Philos. Sci. 18, 377–401 (1988) CrossRefGoogle Scholar
  8. 8.
    Hubble, E., Tolman, R.C.: Two methods of investigating the nature of the nebular red-shift. Astrophys. J. 82, 302–337 (1935) CrossRefGoogle Scholar
  9. 9.
    Bohm, D.: The Special Theory of Relativity. Routledge, London (1996) Google Scholar
  10. 10.
    Einstein, A.: On the Influence of Gravitation on the Propagation of Light, translation of 1911 German original, in [11] Google Scholar
  11. 11.
    Perrett, W., Jeffery, G.B. (translators): The Principle of Relativity, Dover, New York (1952) Google Scholar
  12. 12.
    Jennison, R.C., Drinkwater, A.J.: An approach to the understanding of inertia from the physics of the experimental method. J. Phys. A 10, 167–179 (1977) CrossRefGoogle Scholar
  13. 13.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935) CrossRefGoogle Scholar
  14. 14.
    Schrödinger, E.: Über die kräftefreie Bewegung in der relativistischer Quantenmechanik. Sitzungsber. Preus. Akad. Wiss., 418–428 (1930) Google Scholar
  15. 15.
    Jennings, G.A.: Modern Geometry with Applications. Springer, New York (1994) CrossRefGoogle Scholar
  16. 16.
    Elbaz, C.: Quelques propriétés cinématiques des ondes, stationaires. C. R. Acad. Sci. Paris 297, 455–458 (1983) Google Scholar
  17. 17.
    Feinberg, G.: Possibility of faster-than-light particles. Phys. Rev. 159, 1089–1105 (1967) CrossRefGoogle Scholar
  18. 18.
    Veblen, O., Hoffmann, B.: Projective relativity. Phys. Rev. 36, 810–822 (1930) CrossRefGoogle Scholar
  19. 19.
    Boeyens, J.C.A.: Chemical Cosmology. www.springer.com (2010) CrossRefGoogle Scholar
  20. 20.
    Boeyens, J.C.A.: Cosmology and science. In: Travena, A., Soren, B. (eds.) Recent Advances in Cosmology. Nova Publ. (Nova Science Publishers) New York (2013) Google Scholar
  21. 21.
    Boeyens, J.C.A.: The geometry of quantum events. Specul. Sci. Technol. 15, 192–210 (1992) Google Scholar
  22. 22.
    Sommerfeld, A.: Simplified deduction of the field and the forces of an electron moving in any given way. Proc. Kon. Acad. Wet. Amst. 8, 346–367 (1904) Google Scholar
  23. 23.
    Corben, H.C.: Relativistic selftrapping of hadrons. Lett. Nuovo Cimento 20, 645–648 (1977) CrossRefGoogle Scholar
  24. 24.
    Horodecki, R.: Is a massive particle a compound bradyon-pseudotachyon system? Phys. Lett. A 133, 179–182 (1988) CrossRefGoogle Scholar
  25. 25.
    Genz, H.: Die Entdeckung des Nichts. Hanser Verlag, Munich (1994) Google Scholar
  26. 26.
    Flegg, H.G.: From Geometry to Topology. Dover, Mineola (1974) Google Scholar
  27. 27.
    Schrödinger, E.: Über eine bemerkenswerte Eigenschaft der Quantenbahnen eines einzelnen Elektrons. Z. Phys. 12, 13–23 (1922) Google Scholar
  28. 28.
    Schrödinger, E.: The energy-momentum theorem for material waves, in [29, pp. 131–136] Google Scholar
  29. 29.
    Schrödinger, E.: Collected Papers on Wave Mechanics, 2nd edn. Chelsea, New York (1978) Google Scholar
  30. 30.
    London, F.: Quantenmechanische Deutung der Theorie von Weyl. Z. Phys. 42, 275–389 (1927) Google Scholar
  31. 31.
    George, R.E., Robledo, L.M., Maroney, O.J.E., Blok, M.S., Bernien, H., Markham, M.L., Twitchen, D.J., Morton, J.J.L., Briggs, G.A.D., Hanson, R.: Opening up three quantum boxes causes classically undetectable wavefunction collapse. Published online before print February 14, 2013, doi: 10.1073/pnas.1208374110 PNAS February 14, 2013 201208374
  32. 32.
    Dirac, P.A.M.: The electron wave equation in de-Sitter space. Ann. Math. 36, 657–669 (1935) CrossRefGoogle Scholar
  33. 33.
    Taub, A.H.: Quantum equations in cosmological spaces. Phys. Rev. 51, 512–525 (1937) CrossRefGoogle Scholar
  34. 34.
    Kappraff, J.: Beyond Measure. World Scientific, Singapore (2002) Google Scholar
  35. 35.
    Boeyens, J.C.A.: Chemistry from First Principles. www.springer.com (2008) CrossRefGoogle Scholar
  36. 36.
    Boeyens, J.C.A., Levendis, D.C.: All is number. Struct. Bond. 148, 161–179 (2013) CrossRefGoogle Scholar
  37. 37.
    Boeyens, J.C.A.: Periodicity of the stable isotopes. J. Radioanal. Nucl. Chem. 257, 33–43 (2003) CrossRefGoogle Scholar
  38. 38.
    Boeyens, J.C.A., Levendis, D.C.: Number Theory and the Periodicity of Matter. www.springer.com (2008) CrossRefGoogle Scholar
  39. 39.
    Boltyanski, V.G.: Mathematical Methods of Optimal Control, translated from the Russian by K.N. Trirogoff and I. Tarnove. Holt, Rinehart & Winston, New York (1971) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Jan C. A. Boeyens
    • 1
  1. 1.Centre for Advancement of ScholarshipUniversity of PretoriaPretoriaSouth Africa

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