Measurement of Gravity and Gauge Fields using Quantum Mechanical Probes

  • J. Anandan
Chapter
Part of the NATO ASI Series book series (NATO ASI)

Abstract

It is well known that, historically, many important advances in physics were due to the application of the operational procedure. By this we mean the method which regards as physically important only those quantities that can, at least in principle, be experimentally observed. For example, the consideration of the experimental procedures in Newtonian physics for determining the inertial mass and the passive gravitational mass, which happen to be the same, led Einstein to adopt the now familiar curved space-time description of physics that made the latter mass unnecessary. Also, the physical importance attached by Bohr and Heisenberg to the observed spectral lines of atoms led them to disregard the unobserved (now classical) trajectories of the electron in an atom and instead focus on states of definite energies which are physically meaningful since the energy differences are observable.

Keywords

Gauge Field Josephson Junction Parallel Transport Inertial Mass Coherent Beam 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J. Anandan, Il Nuovo Cimento, 53A, 221 (1979).MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Anandan in Quantum Theory and Gravitation, edited by A.R. Marlow (Academic Press 1980).Google Scholar
  3. 3.
    J. Anandan and B. Lesche, Lett. al Nuovo Cimento, 37, 391 (1983).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    J. Audretsch and C. Lämmerzahl, J. Phys. A, 16, 2457 (1983). This paper does not consider the Lorentz transformations due to the mirrors on the beams which are treated in reference 3. The authors are wrong also in asserting in the “Note added in proof” that the “phase difference” in ref. 1 can be determined only in the low energy limit. Since ψ̄ ψ is proportional to the trace of the energy-momentum tensor for the Dirac field, this can be determined at ail energies. Also, the mirrors in the interference around an infinitesimal “parallelogram” that fails to close, considered in the appendix of ref. 1 were assumed to be parallel with respect to the full connection and hence the “closing gap” does give a phase shift, even though the neutron paths are influenced by the Christoffel connection only, unlike for the conditions assumed in ref. 3 or the present ref. Finally, a theory of the interferometer and inertial effects are contained in ref. 5, the results of which were assumed in ref.l.MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    J. Anandan, Phys. Rev. D, 15, 1448 (1977).ADSCrossRefGoogle Scholar
  6. 6.
    L. Stodolsky, Gen. Rel. and Gravitation, 11, 391 (1979).MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    J. Macek, Phys. Rev. Lett., 23, 1 (1969); H.J. Andrä, Phys. Rev. Lett., 325 (1970).ADSCrossRefGoogle Scholar
  8. 8.
    J. Anandan, Found, of Physics, 10, 601 (1980), see p. 621.MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    W. Ehrenberg and R.E. Siday, Proc. Phys. Soc. London, B62, 8 (1949),ADSCrossRefMATHGoogle Scholar
  10. 9a.
    Y. Aharonov and D. Bohm, Phys. Rev., 115, 485 (1959).MathSciNetADSCrossRefMATHGoogle Scholar
  11. 10.
    B.D. Josephson, Rev. Mod. Phys., 36, 216 (1964).ADSCrossRefGoogle Scholar
  12. 11.
    T.T. Wu and C.N. Yang, Phys. Rev. D, 12, 3843 (1975).MathSciNetADSCrossRefGoogle Scholar
  13. 12.
    See for example, J. Anandan, Journal of Physics A, 17, 1367 (1984).MathSciNetCrossRefGoogle Scholar
  14. 13.
    J.E. Zimmerman and J.E. Mercereau, Phys. Rev. Lett., 14, 887 (1965).MathSciNetADSCrossRefGoogle Scholar
  15. 14.
    J. Anandan, MPI-PAE/PTh 88/84.Google Scholar
  16. 15.
    J. Anandan in Conference on Differential Geometric Methods in Theoretical Physics, Trieste, July 1981, eds. G. Denardo and H.D. Doebner (World Scientific, 1983).Google Scholar
  17. 16.
    D. Greenberger, Ann. Phys., 47, 116 (1968).ADSCrossRefGoogle Scholar
  18. 17.
    This relation, which was considered revolutionary when it was first postulated by de Broglie could have been obtained fairly naturally by studying the gravitational fields of massive and massless particles. From the Einstein-Planck law (math) it follows that the gravitational field of a massless particle is proportional to the rate of change of its phase. This suggests that the phase acts as a source of gravity. Since a massive particle also gravitates, this suggests the association of a phase with it satisfying (math) in the rest frame, where m is its inertial mass, on using the equivalence of inertial and active gravitational masses.Google Scholar
  19. 18.
    J. Anandan, Int. Journal of Theor. Physics, 19, 537 (1980).MathSciNetADSCrossRefGoogle Scholar
  20. 19.
    R. de Bruyn Ouboter in Superconducting Machines and Devices, eds. S. Foner and B.B. Schwartz (Nato series B, vol.1, New York 1974).Google Scholar
  21. 20.
    J. Eells in Symp. Inter, de Topologia Alg., Mexico 1956 (Unesco 1958).Google Scholar
  22. 21.
    A surface spanned by (math) may be defined as follows. Take any y∈ i and let {Ks∈ P:s∈[0,1]}be a one-parameter family of curves which are piecewise differentiable and continuous in s, such that K t(0) =0, K t(1) = Y (t) and K 0(t) = 0 = K 1(t) for every t ∈ [0,1] then (math) Image Ks ⊂ M will be called a surface spanned by ℓ. Google Scholar
  23. 22.
    S. Kobayashi, Comptes Rendus, 238, 318, 443 (1954).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • J. Anandan
    • 1
    • 2
  1. 1.Max-Planck Institute for Physics and AstrophysicsWerner-Heisenberg-Institute for PhysicsMunich 40Germany
  2. 2.C.N.R.S./U.A. n° 769Institut Henri PoincaréParis Cedex 05France

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