Abstract
Zeilinger's observation that phenomena of the Aharonov-Bohm type lead to non-dispersive, i.e., energy-independent, phase shifts in interferometers is generalized in a new proof which shows that the precise condition for nondispersivity is a force-free interaction. The converse theorem is disproved by a conceptual counter-example. Applications to several nondispersive interference phenomena are reviewed briefly. Those fall into two classes which are objectively distinct from each other in that in the first class phase shifts depend only on the topology of the interfering beam paths, while in the second class force-free physical interactions take place at identifiable points along the path. Apparent disagreements in the literature about the topological nature of the phenomena in the second class stem from differing definitions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. Zeilinger, in Fundamental Aspects of Quantum Theory, V. Gorini and A. Frigerio, eds. (NATO ASI Series B, Vol. 144), (Plenum, New York, 1986), p. 311.
M. Peshkin and A. Tonomura, The Aharonov - Bohm Effect (Lecture Notes in Physics 340), (Springer, New York, 1989), p. 28.
Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
R. G. Chambers, Phys. Rev. Lett. 5, 3 (1960).
G. Mollenstedt and W. Bayh, Phys. Blatte 18, 299 (1962). W. Bayh, Z. Phys. 169, 492 (1962).
G. Mollenstedt, Naturwissenschaften 4, 81 (1962).
M. Peshkin and A. Tonomura, The Aharonov- Bohm Effect (Lecture Notes in Physics 340) (Springer, New York, 1989), Part 2, Sect. 5.
Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984).
J. Anandan, Phys. Rev. Lett. 48, 1660 (1982). J. Anandan, in Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics, Tokyo, S. Kobayashi, H. Ezawa, Y. Murayama, and S. Nomura, eds. (Physical Society of Japan, Tokyo, 1989), p. 98.
A. Cimmino, G. Opat, A. G. Klein, H. Kaiser, S. A. Werner, M. Arif, and R. Clothier, Phys. Rev. Lett. 63, 380 (1989).
H. Kaiser, S. A. Werner, R. Clothier, M. Arif, A. G. Klein, G. I. Opat, and A. Cimmino, Atomic Physics 12, J. Zorn and R. Lewis, eds. (AIP, New York, 1991).
K. S angster, E. A. Hinds, S. M. Barnett, and E. Riis, Phys. Rev. Lett. 71, 3641 (1993).
K. Sangster, E. A. Hinds, S. M. Barnett, E. Riis, and A. Sinclair, Phys. Rev. A 46, 1776 (1995).
B. E. Allman, A. Cimmino, A. G. Klein, G. I. Opat, H. Kaiser, and S. A. Werner, Phys.Rev. Lett. 68, 2409 (1992); Phys. Rev. A 48, 1799 (1993).
G. Badurek, H. Weinfurter, R. Gahler, A. Kollmar, S. Wehinger, and A. Zeilinger, Phys.Rev. Lett. 71, 307 (1993).
W.-T. Lee, O. Motrunich, B. E. Allman, and S. A. Werner, Phys. Rev. Lett. 80, 3165 (1998).
M. Peshkin and H. J. Lipkin, Phys. Rev. Lett. 74, 2847 (1995).
A. S. Goldhaber, Phys. Rev. Lett. 62, 482 (1989).
M. V. Berry, Proc. Roy. Soc. A 392, 45 (1984).
See, e.g., P. Pfeifer, Phys. Rev. Lett. 72, 305 (1994); Refs. 1, 8, 11 12, 15, and 17.
Rights and permissions
About this article
Cite this article
Peshkin, M. Force-Free Interactions and Nondispersive Phase Shifts in Interferometry. Foundations of Physics 29, 481–489 (1999). https://doi.org/10.1023/A:1018831318661
Issue Date:
DOI: https://doi.org/10.1023/A:1018831318661