Abstract
We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of them in the non-relativistic limit.
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References
Weyl, H.: Sitz. Preuss. Akad. Wiss. 26, 465 (1918)
London, F.: Z. Phys. 42, 375 (1927)
Riemann: In: Smith, D.E. (ed.) A Source Book in Mathematics, vol. 2. Dover, New York (1959)
Israelit, M.: Found. Phys. 28, 205 (1998)
Israelit, M.: Found. Phys. 29, 1303 (1999)
Israelit, M.: Found. Phys. 32, 295 (2002)
Israelit, M.: Found. Phys. 32, 945 (2002)
Canuto, V., Adams, P.J., Hsieh, S.H., Tsiang, E.: Phys. Rev. D 16, 1643 (1977)
Rosen, N.: Found. Phys. 13, 363 (1983)
Koch, B.: arxiv:0810.2786 [hep-th] (2008)
Koch, B.: arxiv:0901.4106 [gr-qc] (2009)
Santamato, E.: Phys. Rev. D 29, 216–222 (1984)
Holland, P., Kyprianidis, A., Vigier, J.P.: Phys. Lett. A 107, 376 (1985)
Gueret, Ph., Holland, P., Kyprianidis, A., Vigier, J.P.: Phys. Lett. A 107, 379 (1985)
Dirac, P.M.: Proc. R. Soc. Lond. A 333, 403 (1973)
Anderson, J.L.: Principles of Relativity Physics. Academic Press, London (1967)
Novello, M., Oliveira, L.A.R., Salim, J.M., Elbaz, E.: Int. J. Mod. Phys. D 1(4), 641–677 (1992)
Perlick, V.: Class. Quantum Gravity 8, 1369 (1991)
Bohm, D.: Phys. Rev. 85, 166 (1952)
Bohm, D.: Phys. Rev. 85, 180 (1952)
Bohm, D., Hiley, B.J.: The Undivided Universe. Routledge, London (1993)
Holland, P.R.: The Quantum Theory of Motion. Cambridge University Press, Cambridge (1993)
de Broglie, L.: Non-Linear Wave Mechanics: A Causal Interpretation. Elsevier, Amsterdam (1960)
Halbwachs, F.: Théorie Relativiste des Fluides a Spin. Gauthier-Villars, Paris (1960)
Holland, P.R.: Found. Phys. 17, 345–363 (1987)
Cufaro-Petroni, N., Dewdney, C., Holland, P., Kyprianidis, T., Vigier, J.P.: Phys. Lett. A 106, 368–370 (1984)
Kyprianidis, A.: Phys. Lett. A 111, 111–116 (1985)
Santamato, E.: J. Math. Phys. 25, 2477–2480 (1984)
Novello, M., Salim, J.M., Falciano, F.T.: arxiv:0901.3741 [gr-qc] (2009)
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Elsevier, Oxford (1975)
Synge, J.L.: Relativity: The Special Theory. North-Holland, Amsterdam (1958)
Tolman, R.C.: Relativity Thermodynamics and Cosmology. Oxford University Press, Oxford (1962)
Feshbach, H., Villars, F.: Rev. Mod. Phys. 30, 24 (1958)
Rosen, N.: Found. Phys. 12, 213 (1982)
Wheeler, J.T.: Phys. Rev. D 41, 431 (1990)
Shojai, F., Shojai, A.: Gravit. Cosmol. 9, 163 (2003)
Shojai, F., Shojai, A.: arxiv:gr-qc/0404102 (2004)
Carroll, R.: arxiv:0705.3921 [gr-qc] (2008)
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Falciano, F.T., Novello, M. & Salim, J.M. Geometrizing Relativistic Quantum Mechanics. Found Phys 40, 1885–1901 (2010). https://doi.org/10.1007/s10701-010-9496-1
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DOI: https://doi.org/10.1007/s10701-010-9496-1