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Interference, Reduced Action, and Trajectories

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Abstract

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the trajectories of the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function’s trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.

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References

  1. Floyd, E.R.: Phys. Rev. D 34, 3246 (1986)

    Article  ADS  Google Scholar 

  2. Floyd, E.R.: The philosophy of the trajectory representation of quantum mechanics. In: Amoroso, R.L., Hunter, G., Kafatos, M., Vigier, J.-P. (eds.) Gravitation and Cosmology: From the Hubble Radius to the Planck Scale. Proceedings of a Symposium in Honour of the 80th Birthday of Jean-Pierre Vigier, pp. 401–408. Kluwer Academic, Dordrecht (2002), extended version promulgated as quant-ph/0009070

    Google Scholar 

  3. Faraggi, A.E., Matone, M.: Phys. Rev. Lett. 78, 163 (1997), hep-th/9606063

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Faraggi, A.E., Matone, M.: Phys. Lett. B 437, 369 (1997), hep-th/9711028

    ADS  Google Scholar 

  5. Faraggi, A.E., Matone, M.: Phys. Lett. B 445, 77 (1999), hep-th/9809125

    ADS  MathSciNet  Google Scholar 

  6. Faraggi, A.E., Matone, M.: Phys. Lett. B 445, 357 (1999), hep-th/9809126

    Article  ADS  Google Scholar 

  7. Faraggi, A.E., Matone, M.: Phys. Lett. B 450, 34 (1999), hep-th/9705108

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Faraggi, A.E., Matone, M.: Phys. Lett. A 249, 180 (1998), hep-th/9801033

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. Faraggi, A.E., Matone, M.: Int. J. Mod. Phys. A 15, 1869 (2000) hep-th/98090127

    MATH  ADS  MathSciNet  Google Scholar 

  10. Bertoldi, G., Faraggi, A.E., Matone, M.: Class. Quantum Gravity 17, 3965 (2000), hep-th/9909201

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Carroll, R.: Can. J. Phys. 77, 319 (1999), quant-ph/9904081

    Article  ADS  Google Scholar 

  12. Carroll, R.: Quantum Theory, Deformation and Integrability, pp. 50–56. Elsevier, Amsterdam (2000)

    MATH  Google Scholar 

  13. Carroll, R.: Uncertainty, trajectories, and duality. quant-ph/0309023

  14. Floyd, E.R.: Phys. Rev. D 25, 1547 (1982)

    Article  ADS  Google Scholar 

  15. Floyd, E.R.: Phys. Rev. D 26, 1339 (1982)

    Article  ADS  Google Scholar 

  16. Floyd, E.R.: Found. Phys. Lett. 9, 489 (1996), quant-ph/9707051

    Article  MathSciNet  Google Scholar 

  17. Floyd, E.R.: Phys. Rev. D 29, 1842 (1984)

    Article  ADS  Google Scholar 

  18. Floyd, E.R.: Ann. Fond. L. de Broglie 20, 263 (1995)

    MathSciNet  Google Scholar 

  19. Reinisch, G.: Physica A 206, 229 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  20. Reinisch, G.: Phys. Rev. A 56, 3409 (1997)

    Article  ADS  Google Scholar 

  21. Matone, M.: Found. Phys. Lett. 15, 311 (2002), hep-th/0005274

    Article  MathSciNet  Google Scholar 

  22. Floyd, E.R.: Int. J. Theor. Phys. 27, 273 (1988)

    Article  MATH  Google Scholar 

  23. Floyd, E.R.: Phys. Lett. A 214, 259 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. Floyd, E.R.: Phys. Lett. A 206, 307 (2002), quant-ph/0206114

    Article  ADS  MathSciNet  Google Scholar 

  25. Floyd, E.R.: Int. J. Mod. Phys. A 14, 1111 (1999), quant-ph/9708026

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. Floyd, E.R.: Int. J. Mod. Phys. A 15, 1363 (2000), quant-ph/9907092

    MATH  ADS  MathSciNet  Google Scholar 

  27. John, M.V.: Found. Phys. Lett. 15, 329 (2002), quant-ph/0109093

    Article  MathSciNet  Google Scholar 

  28. Bouda, A.: Found. Phys. Lett. 14, 17 (2001), quant-ph/0004044

    Article  MathSciNet  Google Scholar 

  29. Bouda, A.: Int. J. Mod. Phys. A 18, 3347 (2003), quant-ph/0210193

    Article  MATH  ADS  MathSciNet  Google Scholar 

  30. Bouda, A., Djama, T.: Phys. Lett. A 285, 27 (2001), quant-ph/0103071

    Article  MATH  ADS  MathSciNet  Google Scholar 

  31. Bouda, A., Djama, T.: Phys. Lett. A 296, 307 (2002), quant-ph/0206149

    Article  MathSciNet  ADS  Google Scholar 

  32. Bouda, A., Djama, T.: Phys. Scr. 66, 97 (2002), quant-ph/0108022

    Article  MATH  ADS  Google Scholar 

  33. Floyd, E.R.: Phys. Essays 7, 135 (1994)

    Google Scholar 

  34. Holland, P.R.: The Quantum Theory of Motion, pp. 86–87, 141–146. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  35. Wyatt, R.E.: Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics, Chap. 14. Springer, New York (2005)

    MATH  Google Scholar 

  36. Floyd, E.R.: Welcher Weg? A trajectory representation of a quantum Young’s diffraction experiment. Found. Phys. (2007, in press). doi: 10.1007/s10701-007-9155-3

  37. Floyd, E.R.: Phys. Essays 5, 135 (1992)

    Article  MathSciNet  Google Scholar 

  38. Poirier, B.: J. Chem. Phys. 121, 4501 (2004)

    Article  ADS  Google Scholar 

  39. Floyd, E.R.: Found. Phys. Lett. 13, 235 (2000), quant-ph/9708007

    Article  MathSciNet  Google Scholar 

  40. Barton, G.: Ann. Phys. (N.Y.) 166, 322 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  41. Hartman, T.E.: J. Appl. Phys. 33, 3247 (1962)

    Article  Google Scholar 

  42. Fletcher, J.R.: J. Phys. C 18, L55 (1985)

    Article  ADS  Google Scholar 

  43. Landsberg, A.S., Knobloch, E.: Phys. Lett. A 159, 17 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  44. Knobloch, E., Landsberg, A.S., Moehlis, J.: Phys. Lett. A 255, 287 (1999)

    Article  ADS  Google Scholar 

  45. Martel, C., Knobloch, E., Vega, J.M.: Physica D: Nonlinear Phenomena 137, 94 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  46. Born, M., Wolf, E.: Principle of Optics, pp. 18–22. Pergamon, New York (1959)

    Google Scholar 

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Authors and Affiliations

  1. 10 Jamaica Village Road, CA, 92118-3208, Coronado, USA

    Edward R. Floyd

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  1. Edward R. Floyd
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Correspondence to Edward R. Floyd.

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Communicated by Alwyn van der Merwe.

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Floyd, E.R. Interference, Reduced Action, and Trajectories. Found Phys 37, 1386–1402 (2007). https://doi.org/10.1007/s10701-007-9154-4

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  • DOI: https://doi.org/10.1007/s10701-007-9154-4

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