Compatibility of Quantum Mechanics and Relativity

  • Evert Jan Post
Chapter
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 181)

Abstract

The objective of this chapter is to gather evidence that the long-abided reconciliation of quantum laws and relativity is met by the period integral recipes of quantization. This compatibility, then, automatically extends to any quantum cohomology based on those period integral laws. Some of the obstacles that stood in the way of such a reconciliation are here identified. It is primarily the unsubstantiated expectation that Schroedinger’s equation and its Dirac relativistic version had to be viewed as intermediate steps on the road to an encompassing quantum theory meeting the requirements of the general theory of relativity. By restoring the ensemble as their object of description, the wave equations of quantum mechanics become released from the unreasonable imposition of having to satisfy the principle of general covariance. The treatment of single systems is, by contrast, based on the restoration of generally invariant integral laws of physics. They can be adapted to serve as period integrals in the sense of a de Rham-type cohomology for assessing topology. Since Diffeo-4 invariance is a prerequisite for assuming the role of spacetime topological probe, compatibility of these integrals with the principle of general covariance is now no longer a problem. The presented investigation compares mathematical-physical techniques. Since notations in this overworked area of physics easily call up unwanted associations, language, rather than formalism, is given priority to delineate fundamentals.

Keywords

Quantum Mechanic Dirac Equation Maxwell Equation Lorentz Group Invariance Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Science+Business Media Dordrecht 1995

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  • Evert Jan Post

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