General covariance and quantum theory
 Bahram Mashhoon
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The extension of the principle of relativity to general coordinate systems is based on the hypothesis that an accelerated observer is locally equivalent to a hypothetical inertial observer with the same velocity as the noninertial observer. This hypothesis of locality is expected to be valid for classical particle phenomena as well as for classical wave phenomena but only in the shortwavelength approximation. The generally covariant theory is therefore expected to be in conflict with the quantum theory which is based on waveparticle duality. This is explicitly demonstrated for the frequency of electromagnetic radiation measured by a uniformly rotating observer. The standard Doppler formula is shown to be valid only in the geometric optics approximation. A new definition for the frequency is proposed, and the resulting formula for the frequency measured by the rotating observer is shown to be consistent with expectations based on the classical theory of electrons. A tentative quantum theory is developed on the basis of the generalization of the Bohr frequency condition to include accelerated observers. The description of the causal sequence of events is assumed to be independent of the motion of the observer. Furthermore, the quantum hypothesis is supposed to be valid for all observers. The implications of this theory are critically examined. The new formula for frequency, which is still based on the hypothesis of locality, leads to the observation of negative energy quanta by the rotating observer and is therefore in conflict with the quantum theory.
 Wigner, E. (1956) Jubilee of Relativity Theory (Bern, 1955),Helv. Phys. Acta, Suppl. IV. Birkhäuser Verlag, Basel
 Kretschmann, E. (1917) Ann. Phys. 53: pp. 575
 Einstein, A. (1905) Ann. Phys. 17: pp. 891
 Lorentz, H. A. (1915) The Theory of Electrons. Dover, New York
 Whittaker, E. T. (1951) A History of the Theories of Aether and Electricity. Nelson, London
 Landau, L. D., Lifshitz, E. M. (1960) Mechanics. Pergamon Press, Oxford
 Rabi, I. I., Ramsey, N. F., Schwinger, J. (1954) Rev. Mod. Phys. 26: pp. 167 CrossRef
 Weisberg, J. M., Taylor, J. H. (1984) Phys. Rev. Lett. 52: pp. 1348 CrossRef
 Mashhoon, B. (1974) Nature 250: pp. 316
 Mashhoon, B. (1975) Phys. Rev. D 11: pp. 2679 CrossRef
 Title
 General covariance and quantum theory
 Journal

Foundations of Physics
Volume 16, Issue 7 , pp 619635
 Cover Date
 19860701
 DOI
 10.1007/BF01889625
 Print ISSN
 00159018
 Online ISSN
 15729516
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Industry Sectors
 Authors

 Bahram Mashhoon ^{(1)} ^{(2)}
 Author Affiliations

 1. Institut für Theoretische Physik, Universität zu Köln, D5000, Cologne 41, Federal Republic of Germany
 2. Department of Physics and Astronomy, University of MissouriColumbia, 65211, Columbia, Missouri