Possible experimental test of local commutativity

Paul Benioff; Hans Ekstein

doi:10.1103/PhysRevD.15.3563

Access by Xinjiang University

Possible experimental test of local commutativity

Paul Benioff

Hans Ekstein

Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439

Centre de Physique Theorique, C.N.R.S. Marseille, France and Argonne National Laboratory, Argonne, Illinois 60439

PDF

Phys. Rev. D 15, 3563 – Published 15 June, 1977

DOI: https://doi.org/10.1103/PhysRevD.15.3563

Abstract

A direct experimental test for local commutativity (i.e., $[A, B] = 0$ if $A$ and $B$ are associated with mutually spacelike regions) is proposed. It consists of a comparison of the distribution of outcomes of $A$ measurements in the two cases where $A$ alone is measured (no measurement apparatus for $B$ present) and where both are measured on the same sample, in short, a test of the compatibility of the two observation procedures for $A$ and $B$ . The implication compatibility → commutativity (substantially proved by von Neumann, but questioned by Park and Margenau) is proved in a stronger form, with close attention paid to the distinction between different procedures corresponding to a given self-adjoint operator.

References (18)

G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley-Interscience, New York, 1972), Chap. 4
R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That (Benjamin, New York, 1964)
V. Blokhintsev, Space and Time in the Microworld (Reidel, Dordrecht, 1973), Chap. VII
A. Aspect, Phys. Rev. D 14, 1944 (1976) G. Farea, D. Gutkowski, S. Notarrigo, and A. R. Pennisi, Lett. Nuovo Cimento 9, 607 (1974) S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972)
R. Haag and D. Kastler, J. Math. Phys. 5, 848 (1964)
S. Schlieder, Commun. Math. Phys. 13, 216 (1969)
H. Ekstein, Phys. Rev. 184, 1315 (1969)
Y. Avishai and H. Ekstein, Found. Phys. 2, 257 (1972)
B. De Facio, Found. Phys. 6, 185 (1976) ibid.5, 229 (1975) B. De Facio and D. Taylor, Phys. Rev. D 8, 2729 (1973)
J. von Neumann, R. T. BeyerMathematical Foundations of Quantum Mechanics, translated by (Princeton Univ. Press, Princeton, New Jersey, 1955), Chap. III, Sec. 3
J. Park and H. Margenau, Int. J. Theor. Phys. 1, 211 (1968)
P. Benioff, Phys. Rev. D 7, 3603 (1973) P. Benioff and H. Ekstein, Nuovo Cimento B (to be published)
P. Benioff, Found. Phys. 5, 251 (1975)
Omitted endnote
H. Ekstein, J. Math. Phys. 16, 2313 (1975)
[1], Chap. 1, Sec. 2a
J. C. T. Pool, Commun. Math. Phys. 9, 118 (1968)
J. von Neumann, Ann. Math. (N.Y.) 32, 191 (1931)

[c1] G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley-Interscience, New York, 1972), Chap. 4

[c2] R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That (Benjamin, New York, 1964)

[c3] V. Blokhintsev, Space and Time in the Microworld (Reidel, Dordrecht, 1973), Chap. VII

[c4] A. Aspect, Phys. Rev. D 14, 1944 (1976) G. Farea, D. Gutkowski, S. Notarrigo, and A. R. Pennisi, Lett. Nuovo Cimento 9, 607 (1974) S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972)

[c5] R. Haag and D. Kastler, J. Math. Phys. 5, 848 (1964)

[c6] S. Schlieder, Commun. Math. Phys. 13, 216 (1969)

[c7] H. Ekstein, Phys. Rev. 184, 1315 (1969)

[c8] Y. Avishai and H. Ekstein, Found. Phys. 2, 257 (1972)

[c9] B. De Facio, Found. Phys. 6, 185 (1976) ibid.5, 229 (1975) B. De Facio and D. Taylor, Phys. Rev. D 8, 2729 (1973)

[c10] J. von Neumann, R. T. BeyerMathematical Foundations of Quantum Mechanics, translated by (Princeton Univ. Press, Princeton, New Jersey, 1955), Chap. III, Sec. 3

[c11] J. Park and H. Margenau, Int. J. Theor. Phys. 1, 211 (1968)

[c12] P. Benioff, Phys. Rev. D 7, 3603 (1973) P. Benioff and H. Ekstein, Nuovo Cimento B (to be published)

[c13] P. Benioff, Found. Phys. 5, 251 (1975)

[c14] Omitted endnote

[c15] H. Ekstein, J. Math. Phys. 16, 2313 (1975)

[c16] [1], Chap. 1, Sec. 2a

[c17] J. C. T. Pool, Commun. Math. Phys. 9, 118 (1968)

[c18] J. von Neumann, Ann. Math. (N.Y.) 32, 191 (1931)

Physical Review D

Export citation

Export citation

Possible experimental test of local commutativity

Abstract

References (18)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation