Abstract
Is Einstein's metric theory of gravitation to be quantized to yield a complete and logically consistent picture of the geometry of the real world in the presence of quantized material sources? To answer this question, we give arguments that there is a consistent way to extend general relativity to small distances by incorporating further geometric quantities at the level of the connection into the theory and introducing corresponding field equations for their determination, allowing thereby the metric and the Levi-Civita connection to remain classical quantities. The dualism between matter and geometry is extended to quantized fields with the help of a Hibert bundle ℋ raised over a Riemann-Cartan spacetime. Quantized subnuclear matter fields (generalized quantum mechanical wave functions) are sections on ℋ which determine generalized bilinear currents acting as sourc currents for the bundle geometry at small distances. The established dualism between matter and the underlying bundle geometry contains general relativity as a classical part.
Similar content being viewed by others
References
J. A. Wheeler,Einstein's Vision (Springer, Berlin, 1968).
N. Hartmann,Der Aufbau der realen Welt (Walter de Gruyter, Berlin, 1940).
E. Prugovečki,Quantum Geometry (Kluwer, Dordrecht, 1992).
W. Drechsler,Fortschr. Phys. 23, 607 (1975).
A. O. Barut and A. Böhm,Phys. Rev. 139, 1107 (1965).
A. Böhm,Phys. Rev. 145, 1212 (1966).
W. Drechsler,Fortschr. Phys. 38, 63 (1990).
W. Drechsler and E. Prugovečki,Found. Phys. 21, 513 (1991).
W. Drechsler,Found. Phys. 22, 1041 (1992).
W. Drechsler,Class. Quantum Grav. 6, 623 (1989).
W. Drechsler,Ann. Inst. Henri Poincaré 37, 155 (1982).
Author information
Authors and Affiliations
Additional information
Dedicated to Asim Barut on his 65th birthday.
Rights and permissions
About this article
Cite this article
Drechsler, W. Classical versus quantum gravity. Found Phys 23, 261–276 (1993). https://doi.org/10.1007/BF01883629
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01883629