Abstract
We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism∫ ds. In weak fieldsh μυ this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 ∫h μυ P υ dx μ whereP υ is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the “dragging of the ether frame” by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 ∫h μυ K υ dx μ, whereK υ is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.
Similar content being viewed by others
References
Overhauser, A. W., and Collela, R. (1974).Phys. Rev. Lett.,33, 1237; Collela, R., Overhauser, A. W., and Werner, S. A. (1975).Phys. Rev. Lett.,34, 1472; see also Greenberger, D. M., and Overhauser, A. W. (1979).Rev. Mod. Phys.,51, 43.
Landau, L., and Lifshitz, E. (1965)The Classical Theory of Fields (Addison-Wesley, Reading, Massachusetts).
Feynman, X. (1966).The Feynman Lectures on Physics (Addison-Wesley, Reading, Massachusetts), pp. 11–12, Vol. III.
Anandan, J. (1977).Phys. Rev. D,15, 1448.
Börner, G., and Schlieder, S. (1978). Max-Planck-Inst. Preprint, MPI-PAE/PTh 48/78.
Kafka, P. (1977). In:Proceedings of the International School of Cosmology and Gravitation, Erice, 1975, ed. Weber, J. (Plenum Press, New York); also (1975). “Some Remarks on Gravitational Wave Experiments,” Max-Planck-Inst. Preprint; and private communication.
Michelson, A. A. (1925)Astrophys. J.,61, 137; Michelson, A. A., Gale, H. G., and Pearson, F. (1925).Astrophys. J.,61, 140; Page, L. A. (1915).Phys. Rev. Lett.,35, 543; Werner, S. A., Staudemann, J.-L., and Collela, R. (1979).Phys. Rev. Lett.,42, 1103.
Winkler, W. private communication.
Davies, R. W. (1974). InProceedings of the International School of Physics, Enrico Fermi Course LVI (1974, Varenna), ed. Berlotti, B. (Academic Press, New York).
Collins, C. B., and Hawking, S. W. (1973).Mon. Not. R. Astron. Soc.,162, 367.
Estabrook, F. B., and Wahlquist, H. D. (1975).Gen. Rel. Grav.,6, 439.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stodolsky, L. Matter and light wave interferometry in gravitational fields. Gen Relat Gravit 11, 391–405 (1979). https://doi.org/10.1007/BF00759302
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00759302