Advertisement

Super Classical Quantum Mechanics: The Interpretation of Non-Relativistic Quantum Mechanics

  • Willis E. LambJr.
Conference paper
  • 534 Downloads

Abstract

Newtonian Classical Mechanics (NCM) suffers from several kinds of chaotic indeterminacy. These shortcomings can be repaired in a simple and obvious manner. The NCM theory is thereby transformed into a new (probabilistic) theory which is fully equivalent to the Non-relativistic Quantum Mechanics of Heisenberg, Schröinger, and Dirac with the Max Born probabilistic interpretation of the state function built in from the start. I call this new theory Super Classical Quantum Mechanics, (SCQM). With the help of Paul Ehrenfest’s 1927 theorem, the classical limit of the new theory, SCQM, gives exactly the results expected of an improved Newtonian theory of Classical Mechanics. This approach offers enormous advantages, not only for a physically reasonable interpretation of Quantum Mechanics, but also for its contribution to the Quantum Theory of Measurement, and for the avoidance of all of the so-alled paradoxes of traditional non? relativistic Quantum Mechanics.

Keywords

Quantum Mechanics Quantum Theory Free Particle Schrodinger Equation Physic Today 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. E. Lamb, Jr. “On the Electromagnetic Properties of Nuclear Systems”, Part 2 of Ph. D. Thesis, U. C., Berkeley, Phys. Review, 53, 651–656, (1938).zbMATHCrossRefGoogle Scholar
  2. 2.
    W. E. Lamb, Jr. “Suppose Newton had invented Wave Mechanics”, Am. J. Phys. 62, 201–206 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    W. E. Lamb, Jr. “The Borderland between Quantum and Classical Mechanics”, Physica Scripta T70, 7–13 (1997).CrossRefGoogle Scholar
  4. 4.
    W. E. Lamb, Jr., “An Operational Interpretation of Non-relativistic Quantum Mechanics”, Physics Today, 22, 23–28, (1969).CrossRefGoogle Scholar
  5. 5.
    J. von Neumann, “Mathematical Foundations of Quantum Mechanics”, English Translated by R. T. Beyer, (Princeton University Press, Princeton, N. Y.)Google Scholar
  6. 6.
    W. E. Lamb, Jr., “Von Neumann’s Reduction of the Wave Function”, in The Centrality of Science and Absolute Values, Proceedings of the Fourth International Conference on the Unity of the Sciences, pp. 297–303 ( ICF Press, N.Y., N.Y. 1975 ).Google Scholar
  7. 7.
    W. E. Lamb, Jr., “Remarks on the Interpretation of Quantum Mechanics,” in Science of Matter, ed. S. Fujita, pp. 1–8, ( Gordon and Breach, New York, 1979 ).Google Scholar
  8. 8.
    W. E. Lamb, Jr., “A Letter to Kip Thorne”, in CCNY Physics Symposium, in Celebration of Melvin Lax’s Sixtieth Birthday, ed. H. Falk, pp. 40–43, ( City University of New York, 1983 ).Google Scholar
  9. 9.
    E. Arthurs and J. Kelly, “On the Simultaneous Measurement of a Pair of Conjugate Observables”, Bell System Technical Journal 44, 725–729 (1965).CrossRefGoogle Scholar
  10. 10.
    W. E. Lamb, Jr., “Quantum Theory of Measurement”, Annals, New York Academy of Sciences, 480, pp. 407–416 (1986).ADSCrossRefGoogle Scholar
  11. 11.
    W. E. Lamb, Jr., “Theory of Quantum Mechanical Measurements” in Proceedings of the 2nd International Symposium on the Foundations of Quantum Mechanics: In the light of new technology, ed. M. Namiki, pp. 185–192 ( Japan Physical Society, 1987 ).Google Scholar
  12. 12.
    W. E. Lamb, Jr., “Sequential Measurements in Quantum Mechanics”. Lecture at Como NATO Advanced Research Workshop in Quantum Optics, September, 1986. In Quantum Measurement and Chaos, ed. E. R. Pike and S. Sarkar, pp. 183–193 ( Plenum Press, New York and London, 1987 ).Google Scholar
  13. 13.
    W. E. Lamb, Jr., “Classical Measurements on a Quantum Mechanical System” in Proceedings of the International Symposium on Spacetime Symmetries, eds. Y. S. Kim and W. M. Zachary, pp. 197–201, reprinted from Nuclear Physics B (Proc. Suppl.) 6, 1989 ( North-Holland, Amsterdam, 1989 ).Google Scholar
  14. 14.
    W. E. Lamb, Jr., “Quantum Theory of Measurement”, Lecture at Turin NATO Advanced Research Workshop on Noise and Chaos in Nonlinear Dynamical Systems, March, 1989, eds. F. Moss, L. Lugiato, W. Schleich, pp. 1–14, (Cambridge University Press, 1990 ).Google Scholar
  15. 15.
    J. A. Wheeler and W. H. Zurek, eds. “Quantum Theory and Measurement”, (Princeton University Press, 1983 ).Google Scholar
  16. 16.
    S. Goldstein, in Physics Today, vol. 22, March and April Issues, 1996.Google Scholar
  17. 17.
    Schrödinger Cat Paradox: Translated to English in Ref. 15, pp. 152–167.Google Scholar
  18. 18.
    W. E. Lamb, Jr., “Schrödinger’s Cat” in “Paul Adrian Maurice Dirac”, eds. B. N. Kursuoglu and E. P. Wigner (Cambridge University Press, 1987 ).Google Scholar
  19. 19.
    Physics TodayGoogle Scholar
  20. 20.
    Physics WorldGoogle Scholar
  21. 21.
    Delayed ChoiceGoogle Scholar
  22. 22.
    Comments by W. E. Lamb“, in Workshop on Quantum Cryptography and Quantum Computing, Proceedings, February 15, 1995, edited by H. Everitt, U. S. Army Research Office, pp. 24–25.Google Scholar
  23. 23.
    Max Born, “On the Interpretation of Quantum Mechanics”, in Les Prix Nobel en 1954, Stockholm.Google Scholar
  24. 24.
    W. E. Lamb, Jr. and H. Fearn, “Classical Theory of Measurement: A Big Step Toward the Quantum Theory of Measurement”, in “Amazing Light”: A Volume Dedicated to Charles Hard Townes on his 80th Birthday, (Edited by R. V. Chiao) Springer-Verlag, New York, N.Y.).Google Scholar
  25. 25.
    See biography of Luisa Agnesi, and article on special functions in Encyclopedia Britanica.Google Scholar
  26. 26.
    J. G. Crowther, “Maxwell’s Inaugural Lecture”, New Scientist and Science Journal, (4 March, 1971 ), pp. 478–481.Google Scholar
  27. 27.
    H. Poincare “New Methods of Celestial Mechanics”, in 3 vols., ed. by D. L. Goroff, ( A. I. P., 1993 ).Google Scholar
  28. 28.
    W. E. Lamb, Jr., “Quantum Chaos and the Theory of Measurement”, NATO Advanced Research Workshop on “Quantum Chaos”, Como, June, 1983. In “Chaotic Behavior in Quantum Systems. Theory and Applications”, ed. G. Casati, pp. 253–261. ( Plenum Press, New York, 1985 ).Google Scholar
  29. 29.
    J. Lighthill, “The Recently Recognized Failure of Predictability in Newtonian Dynamics”, Proc. Roy. Soc. A407, 35–50 (1936).ADSGoogle Scholar
  30. 30.
    G. Duffing, “Forced Vibrations at Various Frequencies and their Technical Significance”, Sammlung 41–42 ( F. Vieweg, Braunschweig, 1918 ).Google Scholar
  31. 31.
    E. Fermi, J. R. Pasta, and S. Ulam, “Studies of Noninear Problems”, in Los Alamos Report LA-1940, 1955.Google Scholar
  32. 32.
    M. Toda, J. Phys. Soc. Japan 21, 431 (1967).CrossRefGoogle Scholar
  33. 33.
    M. Born, Waynflete Lecture, Magdelen College, Oxford, 1949.Google Scholar
  34. 34.
    P. Ehrenfest, “Notes on the Approximate Validity of Quantum Mechanics”, Z. Physik, 455–457 (1927).Google Scholar
  35. 35.
    L I Schiff, “Quantum Mechanics”, 3rd ed., pp. 28–30, 178–182, (Mc-Graw-Hill, 1955 ).Google Scholar
  36. 36.
    E. Schrödinger, “Collected Papers on Wave Mechanics”, ( Blackie, London, 1928 ).zbMATHGoogle Scholar
  37. 37.
    E. H. Kennard, “The Quantum Mechanics of Simple Types of Motion”, Z. Phys. 44, 326–352 (1927).ADSzbMATHCrossRefGoogle Scholar
  38. 38.
    R. J. Glauber, “Coherent and Incoherent States of the Radiation Field”, Phys. Rev. 2766–2788 (1964).Google Scholar
  39. 39.
    M. Sargent, M. O. Scully and W. E. Lamb, Jr., “Laser Physics”, in Appendix H, “The Coherent State”, (Wiley, 1977 ). Largely based on Kennard’s approach. Many results are simpler to get using the complex Gaussian method of this paper.Google Scholar
  40. 40.
    W. E. Lamb, Jr. “Anti-Photon”, Applied Physics B, Lasers and Optics, 60, 77–84 (1995).CrossRefGoogle Scholar
  41. 41.
    J. Bolte and S. Keppeler, “Semiclassical Time Evolution and Trace Formula for Relativistic Spin-2 1 Particles” Phys. Rev. Letters, 81, 1987–1990 (1998).MathSciNetADSzbMATHCrossRefGoogle Scholar
  42. 42.
    M. V. Berry. From a Lecture in May, 1999, at the University of Arizona.Google Scholar
  43. 43.
    T. A. Welton, “Some Observable Effects of the Quantum Mechanical Fluctuation of the Electromagnetic Field”, Phys. Rev. 74, 1157–1167 (1948).ADSzbMATHCrossRefGoogle Scholar
  44. 44.
    S. Bourzeix, et al, “High Resolution Spectroscopy of the Hydrogen Atom: Determination of the 1S Lamb Shift.”, Phys. Rev. Letters, 76, 384–387 (1996).Google Scholar
  45. 45.
    See Einstein’s Remarks on Radioactive Decay in “Albert Einstein: Philosopher-Scientist”, pp. 665–688, edited by P. A. Schilpp. (Open Court Publishing, La Salle, IL, 1970).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Willis E. LambJr.
    • 1
  1. 1.Optical Sciences Center and Department of PhysicsUniversity of ArizonaTucsonUSA

Personalised recommendations