Wave-particle duality in general relativity

Details Wave-particle duality in general relativity Wave-particle duality in general relativity

1997-01-15

arxiv.org/abs/gr-qc/9701034v1

Nuovo Cim. B111 (1996) 779-810

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, AMSTEX

Scientific paper

In this paper a one to one correspondence is established between space-time metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell's equation for a photon follows while in the case of a particle with mass, Dirac's equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized. PACS NUMBERS: 03.65, 04.60

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