Special Issue: Advances in Foundations of Quantum Mechanics and Quantum Information with atoms and photons, QUANTUM 2012No Access

SOLVING THE NONLOCALITY RIDDLE BY CONFORMAL QUANTUM GEOMETRODYNAMICS

ENRICO SANTAMATO

Dipartimento di Fisica, Università Federico II, Napoli 80126, CINSM - Consorzio Nazionale Interuniversitario per la Struttura della Materia, Italy

Search for more papers by this author

and

FRANCESCO DE MARTINI

Accademia dei Lincei, via della Lungara 10, I-00165 Roma, Italy

Dipartimento di Fisica, Università La Sapienza, I-00185 Roma, Italy

Search for more papers by this author

https://doi.org/10.1142/S0219749912410134Cited by:4 (Source: Crossref)

Abstract

Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.

Keywords:

References

A. Einstein , B. Podolsky and N. Rosen , Phys. Rev. 47 , 777 ( 1935 ) . Crossref, Google Scholar
R. Haag , Local Quantum Physics, Fields, Modern Quantum Mechanics Algebras ( Springer-Verlag , Berlin , 1994 ) . Google Scholar
S. Doplicher , J. Math. Phys. 51 , 015218 ( 2010 ) . Crossref, Web of Science, Google Scholar
J. S. Bell , Speakable and Unspeakable in Quantum Mechanics ( Cambridge University Press , Cambridge , 1987 ) . Google Scholar
M. Redhead , Incompleteness, Nonlocality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics ( Clarendon Press , Oxford , 1987 ) . Google Scholar
M. F. Pusey , J. Barrett and T. Rudolph , Nat. Phys. 8 , 475 ( 2012 ) . Crossref, Web of Science, Google Scholar
F. Bushemi , Phys. Rev. Lett. 108 , 200401 ( 2012 ) . Crossref, Web of Science, Google Scholar
R. Colbeck and R. Renner , Phys. Rev. Lett. 108 , 150402 ( 2012 ) . Crossref, Web of Science, Google Scholar
E. Santamato , Phys. Rev. D 29 , 216 ( 1984 ) . Crossref, Web of Science, Google Scholar
E. Santamato , Phys. Rev. D 32 , 2615 ( 1985 ) . Crossref, Web of Science, Google Scholar
F. De Martini and E. Santamato, Derivation of Diracs equation from conformal differential geometry, in Quantum Foundations, ed. A. Khrennikov, AIP (Melville, 2012). (2011) , arXiv: quant-ph/1107.3168v1 . Google Scholar
A. R. Edmonds , Angular Momentum in Quantum Mechanics ( Princeton University Press , Princeton , 1985 ) . Google Scholar
H. Weyl, Space, Time, Matter, 4th edn. (Dover Publications, Inc., New York, 1952). Google Scholar
W. Pauli , Theory of Relativity ( Dover , New York , 1981 ) . Google Scholar
P. G. Bergmann , Introduction to the Theory of Relativity ( Dover , New York , 1976 ) . Google Scholar
J. A. Wheeler , Geometrodynamics ( Academic Press , New York , 1962 ) . Google Scholar
J. von Neumann , Mathematical Foundations of Quantum Mechanics ( Benjamin , New York , 1963 ) . Google Scholar
M. O. Scully and M. S. Zubairy , Quantum Optics ( Cambridge University Press , Cambridge UK , 1997 ) . Crossref, Google Scholar
E. Schrödinger , Proc. Cambridge Phil. Soc. 31 , 555 ( 1935 ) . Crossref, Google Scholar