Abstract
The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed.
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References
A. Peres and N. Rosen,Phys. Rev. 118, 335 (1960).
N. Bohr and L. Rosenfeld,Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd. 12, No. 8 (1933).
N. Bohr and L. Rosenfeld,Phys. Rev. 78, 794 (1950).
B. S. DeWitt, inGravitation: An Introduction to Current Research, L. Witten, ed. (Wiley, New York, 1962).
C. A. Mead,Phys. Rev. 135B, 849 (1964).
E. Prugovečki,Stochastic Quantum Mechanics and Quantum Spacetime (Reidel, Dordrecht, 1984).
G. H. Hegerfeldt,Phys. Rev. D10, 3320 (1974).
E. P. Wigner, inQuantum Theory and Measurement, A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton, N.J., 1983).
M. Born,Rev. Mod. Phys. 21, 463 (1949).
M. Born,Kgl. Danske Videnskab. Selskab. Mat. Fys. Medd. 30, No. 2 (1955).
M. Born,Physics in My Generation (Pergamon Press, London, 1956).
D. I. Blokhintsev,Sov. J. Part. Nucl. 5, 242 (1975).
E. Prugovečki,Phys. Rev. 18D, 3655 (1978).
J. Ehlers, inGeneral Relativity and Cosmology, B. K. Sachs, ed. (Academic Press, New York, 1971).
S. T. Ali,J. Math. Phys. 20, 1385 (1979).
S. T. Ali and E. Prugovečki, “Extended Harmonic Analysis of Phase Space Representations for the Galilei Group,” preprint.
S. T. Ali and E. Prugovečki, “Harmonic Analysis and Systems of Covariance for Phase Space Representations of the Poincaré Group,” preprint.
G. C. Hegerfeldt and S. N. M. Ruijsenaars,Phys. Rev. D22, 377 (1980).
A. Landé,Phys. Rev. 56, 482, 486 (1939).
M. Born,Proc. Roy. Soc. Edinburgh 59, 219 (1939).
M. Castrigiano,J. Math. Phys. 12, 2203 (1971).
N. M. J. Woodhouse,J. Math. Phys. 14, 495 (1973).
J. Ehlers, inRelativity, Astrophysics and Cosmology, W. Israel, ed. (Reidel, Dordrecht, 1973).
A. Einsteinet al., The Principle of Relativity (Dover, New York, 1960).
J. A. Wheeler,Geometrodynamics (Academic Press, New York, 1962).
C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973).
E. Prugovečki,Found. Phys. 11, 355, 501 (1981).
E. Prugovečki,Nuovo Cimento 61A, 85 (1981).
H. Salecker and E. P. Wigner,Phys. Rev. 109, 571 (1958).
E. Prugovečki,Nuovo Cimento 62B, 17 (1981).
D. Greenwood and E. Prugovečki,Found. Phys. 14, 883 (1984).
A. Einstein, B. Podolsky, and N. Rosen,Phys. Rev. 47, 777 (1935).
F. E. Schroeck, Jr.,Found. Phys. (1984) (in press).
W. Guz,Found. Phys. 14, 821 (1984).
J. Glimm and A. Jaffe,Quantum Physics (Springer, New York, 1981).
S. S. Schweber,An Introduction to Relativistic Quantum Field Theory (Row-Peterson, Evanston, Ill., 1961).
C. S. Morawetz and W. A. Strauss,Commun. Pure Appl. Math. 25, 1 (1972).
L. de Broglie,C.R. Acad. Sci. Paris 200, 361 (1935).
N. Rosen,Phys. Rev. 72, 208 (1947).
N. Rosen,Ann. Phys. (N.Y.) 19, 165 (1962).
S. T. Ali,Rivista Nuovo Cimento (1984–85) (in press).
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Supported in part by NSERC Grant A5208.
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Prugovečki, E. The stochastic quantum mechanics approach to the unification of relativity and quantum theory. Found Phys 14, 1147–1162 (1984). https://doi.org/10.1007/BF01889316
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DOI: https://doi.org/10.1007/BF01889316