Riemannian structure of space-time as a consequence of quantum mechanics
Different axiomatic approaches to general relativity which use light rays and classical test particles as primitive concepts remain incomplete because they end with a Weylian instead of a Riemannian structure of space-time. It is shown that the final step to a Riemann space can be obtained as a necessary consequence if quantum mechanics, as the theory of matter, is made part of the total scheme. Quantum mechanics must contain classical particle mechanics as a limiting case. The self-consistency requirement that in Weyl space this limiting case should agree with the axiomatically introduced classical-test-particle behavior implies the conclusion that the Weyl geometry of space-time must be restricted to the special case of a Riemann geometry. This is shown in detail for massive spin-(1/2) particles after a general discussion of the theory of unquantized tensor fields and two-spinor fields in Weyl space. The result is independent of the Weyl type chosen for the orthotetrad (Lorentz basis). The same conclusion is obtained from massive Klein-Gordon theory in Weyl space in demanding that the physically reasonable current should be divergence-free.
- Research Organization:
- Fakultat fuer Physik der Universitat Konstanz, Postfach 5560, D-7750 Konstanz, Federal Republic of Germany
- OSTI ID:
- 5834062
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 27:12; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
KLEIN-GORDON EQUATION
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
RIEMANN SPACE
SPACE
SPACE-TIME
SPINORS
UNIFIED-FIELD THEORIES
WAVE EQUATIONS
WEYL UNIFIED THEORY