Abstract
A new probability interpretation of interference phenomena in the double-slit experiment is proposed. It differs from the standard interpretation (based on elementary events happening in complementary, mutually exclusive setups—arrivals of waves to the screen when one of the slits is closed) which encounters the “paradox” that the law of total probability is violated. This new interpretation is free of such difficulties and paradoxes since it is based on compatible elementary events (events happening in the same setup in which happenall events considered—arrivals of quantons to the screen when both slits are open). Quantum objects—quantons—possess simultaneously particle and wave properties. Compatible statistical interpretation synthesizes in a consistent way the superposition principle for waves and the law of total probability applied to compatible events. Such synthesis is a theoretical expression of de Broglie's observation, now fully confirmed by experiments, that the interference fringes obtained on a photographic plate result from an infinite number of tiny local spots which display arrival of quantons, while the set of fringes is a statistical effect of the wave aspect.
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References
E. Schrödinger, “The meaning of wave mechanics,” inLouis de Broglie, Physicien et Penseur (Michel, Paris, 1953).
L. de Broglie,Etude critique des bases de l'interpretation actuelle de la mecanique ondulatoire (Gauthier-Villars, Paris, 1963).
A. Einstein, “Electrons et photons,”Rapports et discussions du cinquieme Conseil de physique—Bruxelles du 24 au 29 octobre sous les auspices de l'Institut International de physique Solvay (Gauthier-Villars, Paris, 1928), p. 253.
N. Bohr, “Discussion with Einstein on epistemological problems in atomic physics,” inAlbert Einstein: Philosopher-Scientist, P. A. Schilpp, ed. (Open Court, La Salle, Illinois, 1949), p. 200.
R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (Addison-Wesley, Reading, Massachusetts, 1963).
E. T. Jaynes, inFoundations of Radiation Theory and Quantum Electrodynamics, A. O. Barut, ed. (Paris, Michel, 1953), p. 16.
P. Granier, G. Roger, and A. Aspect,Ann. N.Y. Acad. Sci. 480, 99 (1986);Europhys. Lett. 1 173 (1986).
A. Zeilinger, R. Gaheler, C. G. Shull, and W. Treimer, inProceedings, Conference on Neutron Scattering (Argonne, 1981), J. Faber Jr., ed. (American Institute of Physics, New York, 1982), p. 93.
G. Mollenstedt and C. Jonsson,Z. Phys. 155 472 (1959).
C. Jonsson, Thesis, Tübingen, 1960;Z. Phys. 161 454 (1961).
C. Jonsson,Am. J. Phys. 42 4 (1974).
A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki,Am. J. Phys. 57, 117 (1989).
G. Mollenstedt,Physica B 151, 201 (1988).
O. Carnal and J. Mlynek,Phys. Rev. Lett. 66, 2689 (1991).
D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard,Phys. Rev. Lett. 66, 2693 (1991).
J. M. Lévy-Leblond and F. Balibar,Quantique (Rudiments) (Interéditions-CNRS, Paris, 1984);Physica B 151, 314 (1988).
C. Cohen-Tannoudji, B. Diu, and F. Laloë,Mecanique quantique I (Hermann, Paris, 1977), Chap. I.
A. O. Barut,Phys. Lett. 143, 349 (1990).
A. O. Barut, ICTP preprint, IC/90/99.
N. Bohr,Naturwissenschaften 16, 245 (1928).
J. A. Wheeler, inMathematical Foundations of Quantum Theory, A. R. Marlow, ed. (Academic Press, New York, 1978).
A. Zeilinger,Physica B 137, 235 (1986).
W. K. Wooters and W. H. Zurek,Phys. Rev. D 19, 473 (1979).
M. O. Scully, B. G. Englert, and H. Walther,Nature (London) 351, 6322 (1991).
L. de Broglie,La physique quantique, restera-t-elle indeterministe? (Gauthier-Villars, Paris, 1953).
The Wave-Particle Dualism, S. Diner, D. Fargue, G. Lochak, and F. Selleri, (Reidel, Dordrecht, 1984).
D. Bohm,Phys. Rev. 84, 166 (1951);85, 166 (1952).
D. Bohm and J. P. Vigier,Phys. Rev. 96, 208 (1954).
C. Philipidis, C. Dewdney, and B. J. Hiley,Nuovo Cimento 52, 15 (1979).
J. P. Vigier,Astr. Nachr. 303, 61 (1982).
J. P. Vigier,Physica B 151, 386 (1988).
D. Bohm, B. J. Hiley, and P. N. Kaloyerou,Phys. Rep. 144(6), ??? (1987).
F. Selleri,Ann. Fond. L. de Broglie 7, 45 (1982).
F. Selleri,Quantum Paradoxes and Physical Reality, A. van der Merwe, ed. (Kluwer, Dordrecht, 1990).
F. Selleri and G. Tarozzi,Nuovo Cimento A 43, 31 (1978).
G. Tarozzi, inThe Wave-Particle Dualism, S. Dineret al., eds. (Reidel, Dordrecht, 1984).
M. Božić and Z. Marić,Phys. Lett. A 158, 33 (1991).
H. Rauch and J. P. Vigier,Phys. Lett. A 151, 269 (1990).
P. Ghose, D. Home, and G. S. Agarwal,Phys. Lett. A 153, 403 (1991).
P. Ghose and S. N. Roy,Phys. Lett. A 161, 5 (1991).
M. Božić, “Neutron optics,” inNew Frontiers of Quantum Electrodynamics and Quantum optics, A. O. Barut, ed. (Plenum, New York, 1990).
R. P. Feynman, inProceedings, Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, 1951).
B. O. Koopman, “Quantum theory and the foundations of probability,” inProceedings, Symposia in Applied Mathematics VII, L. A. MacColl, ed. (McGraw-Hill, New York, 1955).
L. E. Ballentine,Am. J. Phys. 54, 883 (1986).
J. P. Vigier, inProceedings, 3rd International Symposium, Foundations on Quantum Mechanics (Physical Society of Japan, Tokyo, 1983), p. 140.
G. Lochak, inThe Wave-Particle Dualism, S. Diner, D. Fargue, G. Lochak, and F. Selleri, eds. (Reidel, Dordrecht, 1984).
T. Hellmuth, H. Walther, A. Zajonc, and W. Schleich,Phys. Rev. A 35, 2532 (1987).
N. Cufaro-Petroni, C. Dewdney, P. Holland, and J. P. Vigier,Lett. Nuovo Cimento 42, 285 (1985).
N. Cufaro-Petroni and J. P. Vigier,Phys. Lett. A 160, 107 (1991).
E. Nelson,Quantum Fluctuations (Princeton University Press, Princeton, 1985).
F. Guerra,Phys. Rep. 77, 263 (1981).
L. de la Pena and A. M. Cetto,Found. Phys. 5, 355 (1975).
J. P. Vigier,Pramana, J. Phys. 25, 397 (1985).
N. Cufaro-Petroni and J. P. Vigier,Found. Phys. 22, 1 (1992).
J. B. Fanchi and W. J. Wilson,Found. Phys. 13, 571 (1983).
N. Cufaro-Petroni, C. Dewdney, P. Holland, A. Kyprianidis, and J. P. Vigier,Phys. Rev. D 32, 1375 (1985).
N. Cufaro-Petroni, Z. Marić, A. Kyprianidis, and J. P. Vigier,Phys. Lett. A 100, 229 (1984);101, 4 (1984).
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Božić, M., Marić, Z. & Vigier, J.P. De Broglian probabilities in the double-slit experiment. Found Phys 22, 1325–1344 (1992). https://doi.org/10.1007/BF01883664
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DOI: https://doi.org/10.1007/BF01883664