Abstract
The non-local aspects of interaction between quantum systems are investigated. These aspects are particularly conspicuous in quantum phenomena without a classical analog, such as the quantum effects of electromagnetic potentials. The study of the potential effect leads to the introduction of a new type of dynamical variable, the modular variable, which brings out the physical features of quantum mechanical non-locality.
Similar content being viewed by others
References
Aharonov, Y. and Bohm, D. (1959).Physical Review,115, 485.
Boersch, H., Hamisch, H., Grohmann, D. and Wohllenben, D. (1960).Zeitschrift für Physik,159, 397.
Boersch, H., Hamisch, H., Grohmann, D. and Wohllenben, D. (1961a).Zeitschrift für Physik,164, 55.
Boersch, H., Hamisch, H., Grohmann, D. and Wohllenben, D. (1961b).Zeitschrift für Physik,165, 69.
Boersch, H., Hamisch, H., Grohmann, D. and Wohllenben, D. (1962a).Zeitschrift für Physik,167, 72.
Boersch, H., Hamish, H., Grohmann, D. and Wohllenben, D. (1962b).Zeitschrift für Physik,169, 263.
Bohr, N. (1949). Discussion with Einstein on Epistemological Problems in Atomic Physics. In:Albert Einstein-Philosopher-Scientist, p. 199, ed. Schupp, P. A. The Library of Living Philosophers, Inc., New York.
Chambers, R. G. (1960).Physical Review Letters,5, 3.
Fowler, H. A., Marton, L., Simpson, Y. A. and Suddeth, J. A. (1961).Journal of Applied Physics,32, 1153.
Furry, W. H. and Ramsey, N. F. (1960).Physical Review,118, 623.
Jaklevic, R. C., Lambe, J., Silver, A. H. and Mercereau, J. E. (1964a).Physical Review Letters,12, 159.
Jaklevic, R. C., Lambe, J., Silver, A. H. and Mercereau, J. E. (1964b).Physical Review Letters,12, 274.
Marton, L., Arol Simpson, J. and Suddeth, J. A. (1954).Review of Scientific Instruments,25, 1099.
Möllenstedt, G. and Bayh, W. (1962a).Die Naturwissenschaften,49, 81.
Möllenstedt, G. and Bayh, W. (1962b).Physikalische Blätter,18, 299.
Werner, F. G. and Brill, D. R. (1960).Physical Review Letters,4, 344.
Author information
Authors and Affiliations
Additional information
The material contained in this article is based on work done in the period 1965–67. This work was supported in part by O.A.R. Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A., under Contracts No. AF 19(629)-5143 and AF 19(628)-5833.
Rights and permissions
About this article
Cite this article
Aharonov, Y., Pendleton, H. & Petersen, A. Modular variables in quantum theory. Int J Theor Phys 2, 213–230 (1969). https://doi.org/10.1007/BF00670008
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00670008