Bohmian analysis of momentum transfer in welcher Weg measurements

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 3, 1998, Pages 1740-1756

  Wiseman, H M ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

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EID: 0005391305     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.1740     Document Type: Article

References (40)

1. N. Bohr, in Albert Einstein: Philosopher-Scientist, edited by P. A. Schlipp (Library of Living Philosophers, Evaston, 1949), pp. 200–241;reprinted in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, NJ, 1983), pp. 8–49.
2. M. O. Scully, B.-G. Englert, and H. Walther, Nature (London) 351, 111 (1991).NATUAS
3. E. P. Storey, S. M. Tan, M. J. Collett, and D. F. Walls, Nature (London) 367, 626 (1994).NATUAS
4. B.-G. Englert, H. Fearn, M. O. Scully, and H. Walther, in Quantum Interferometry, edited by F. Martini, G. Denardo, and A. Zeilinger (World Scientific, Singapore, 1994), pp. 103–119;E. P. Storey, S. M. Tan, M. J. Collett, and D. F. Walls., pp. 120–129.
5. B.-G. Englert, M. O. Scully, and H. Walther, Nature (London) 375, 367 (1995); NATUAS
6. Nature (London)E. P. Storey, S. M. Tan, M. J. Collett, and D. F. Walls, 375, 368 (1995).
7. H. M. Wiseman et al, Phys. Rev. A 56, 55 (1997).PLRAAN
8. D. Bohm, Phys. Rev. 85, 166 (1952); PHRVAO
9. Phys. Rev.D. Bohm85, 180 (1952).See also the following reference for a good overview of the field.
10. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, England, 1993).
11. L. de Broglie, Tentative d’interpretation causale et non-linéaire de la méchanique ondulatoire (Gauthier-Villars, Paris, 1956).
12. W. R. McKinnon and C. R. Leavens, Phys. Rev. A 51, 2748 (1995).PLRAAN
13. U. Schwengelbeck and F. H. M. Faisal, Phys. Lett. A 199, 281 (1995); PYLAAG
14. Phys. Lett. AF. H. M. Faisal and U. Schwengelbeck, 207, 31 (1995).
15. R. H. Parminter and R. W. Valentine, Phys. Lett. A 201, 1 (1995); PYLAAG
16. Phys. Lett. AR. H. ParminterR. W. Valentine213, 319 (1995).
17. C. Dewdney and Z. Malik, Phys. Rev. A 48, 3513 (1993).PLRAAN
18. L. P. Hughston, R. Jozsa, and W. K. Wootters, Phys. Lett. A 183, 14 (1993).PYLAAG
19. H. M. Wiseman and F. E. Harrison, Nature (London) 377, 584 (1995).NATUAS
20. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1965), Vol. III.
21. E. P. Wigner, Phys. Rev. 40, 749 (1932).PHRVAO
22. J. S. Bell, of Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England, 1987), p. 128.
23. Bohmian Mechanics and Quantum Theory: An Appraisal, edited by J. T. Cushing, A. Fine, and S. Goldstein (Kluwer, Dordrecht, 1996).
24. P. R. Holland, Phys. Rep. 224, 95 (1993).PRPLCM
25. H. Frisk, Phys. Lett. A 227, 139 (1997).PYLAAG
26. A. Valentini, Phys. Lett. A 156, 5 (1991); PYLAAG
27. Phys. Lett. AA. Valentini158, 1 (1991).
28. A. Valentini, pp. 45–66 of Ref. 19, also remarks upon other explanations of the origin of quantum probabilities.
29. C. Philippidis, C. Dewdney, and B. J. Hiley, Nuovo Cimento B B52, 15 (1979).NIFBAP
30. In replacing the particle’s wave function (Formula presented) by an effective reduced wave function (Formula presented) it is actually a crucial assumption that the results of the measurement be distinguished by the position of at least one particle in the apparatus before the wave packet passing through the upper slit begins to interfere with that passing through the lower slit. If this is not the case then the Bohmian trajectories can take on bizzare (even “surrealistic” 26) features. In particular, as shown in Refs. 2627, the particle’s Bohmian trajectory can pass through the upper slit even though the detector registers the particle’s passing through the lower slit. It should be noted, however, that this assumption regarding the time at which the measurement is complete does not mean that the minimum momentum transfer derived in Sec. VII is invalidated through lack of generality. The Bohmian trajectories suffering minimum momentum transfer will still be those for which the particle’s effective wave function is an equally weighted superposition. Thus we might as well assume that this quantum eraser arrangement 31 is effected immediately after the interaction of the particle with the probe by a suitable coupling to the position of at least one particle in the apparatus.
31. B-G. Englert, M. O. Scully, G. Süssmann, and H. Walther, Z. Naturforsch. Teil A 47A, 1175 (1992).ZTAKDZ
32. Y. Aharanov and L. Vaidman, Bohemian Mechanics and Quantum Theory: An Appraisal (Ref. 19), pp. 141–154.
33. J. S. Bell, Rev. Mod. Phys. 38, 447 (1966).RMPHAT
34. J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).PYCSAP
35. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England, 1987), p. 115.
36. M. O. Scully and K. Drühl, Phys. Rev. A 25, 2208 (1982).PLRAAN
37. S. M. Tan and D. F. Walls, Phys. Rev. A 47, 4663 (1993).PLRAAN
38. A. Stern, Y. Aharanov, and Y. Imry, Phys. Rev. A 41, 3436 (1990).PLRAAN
39. S. T. Rachev, Probability Metrics and the Stability of Stochastic Models (Wiley, New York, 1991).
40. G. Monge, Mémoire sur la Theorie des Déblais et des Remblais (Histoires de l’Acadamie des Sciences de Paris, Paris, 1781), p. 666.