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Paradox in Wave-Particle Duality

We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment.

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References

  1. 1.

    Bohr N., (1928). “The quantum postulate and the recent development of atomic theory”. Nature 121, 580

    MATH  ADS  Google Scholar 

  2. 2.

    Bohr N., Albert Einstein: Philosopher-Scientist, Schilpp P.A. ed. (Open Court, La Salle, IL, 1949), pp. 200–241

  3. 3.

    N. Bohr, “Maxwell and modern theoretical physics,” Nature 128, 691 (1931); reprinted in Niels Bohr Collected Works, Vol. 6: Foundations of Quantum Physics I (1926–1932), ed. J. Kalckar (North-Holland, Amsterdam, 1985), pp. 359–360

  4. 4.

    Feynman R.P., (1963) The Feynman Lectures on Physics, Vol 3. Addison-Wesley, Reading MA, pp. 1–9

    Google Scholar 

  5. 5.

    Wooters W., Zurek W., (1979). “Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr’s principle”. Phys. Rev. D 19, 473

    Article  ADS  Google Scholar 

  6. 6.

    Greenberger D., Yasin A., (1988). “Simultaneous wave and particle knowledge in a neutron interferometer”. Phys. Lett. A 128, 391

    Article  ADS  Google Scholar 

  7. 7.

    Mandel L., (1991). “Coherence and indistinguishability”. Opt. Lett. 16: 1882

    ADS  Article  Google Scholar 

  8. 8.

    Jaeger G., Shimony A., Vaidman L., (1995). “Two interferometric complementarities”. Phys. Rev. A 51, 54

    Article  ADS  Google Scholar 

  9. 9.

    Englert B.-G., (1996). “Fringe visibility and which-way information: An inequality”. Phys. Rev. Lett. 77: 2154

    Article  ADS  Google Scholar 

  10. 10.

    Rauch H., Summhammer J., (1984). “Static versus time-dependent absorption in neutron interferometry”. Phys. Lett. A 104, 44

    Article  ADS  Google Scholar 

  11. 11.

    Mittelstaedt P., Prieur A., Schieder R., (1987). “Unsharp particle–wave duality in a photon split-beam experiment”. Found. Phys. 17, 891

    Article  ADS  Google Scholar 

  12. 12.

    Summhammer J., Rauch H., Tuppinger D., (1987). “Stochastic and deterministic absorption in neutron-interference experiment”. Phys. Rev. A 36: 4447

    Article  ADS  Google Scholar 

  13. 13.

    Wiseman H.M., Harrison F.E., Collett M.J., Tan S.M., Walls D.F., Killip R.B. (1997). “Nonlocal momentum transfer in welcher-weg measurements”. Phys. Rev. A 56, 55

    Article  ADS  Google Scholar 

  14. 14.

    Dürr S., Nonn T., Rempe G., (1998). “Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer”. Nature 395, 33

    Article  ADS  Google Scholar 

  15. 15.

    Scully M.O., Englert B.-G., Walther H., (1991). “Quantum optical tests of complementarity”. Nature 351, 111

    Article  ADS  Google Scholar 

  16. 16.

    De Martini F., De Dominicis L., Cioccolanti V., Milani G., (1992). “Stochastic interferometer”. Phys. Rev. A 45: 5144

    Article  ADS  Google Scholar 

  17. 17.

    Dürr S., Rempe G., (2000). “Can wave–particle duality be based on the uncertainty relation?”. Am. J. Phys. 68: 1021

    Article  ADS  Google Scholar 

  18. 18.

    Afshar S.S. “Sharp complementary wave and particle behaviours in the same welcher weg experiment,” Proc. SPIE 5866, 229–244 (2005); http://www.irims.org/quant-ph/030503; http://arxiv.org/abs/quant-ph/0701027

  19. 19.

    Afshar S.S. “Violation of Bohr’s complementarity: one slit or both?,” AIP Conf. Proc. 810, 294–299 (2006); http://www.irims.org/quant-ph/040901; http://arxiv.org/abs/quantph/0701028

  20. 20.

    Afshar S.S. “Experimental violation of complementarity: reply to critics,” submitted to Frontier Perspectives; http://www.itims.org/quant-ph/070101

  21. 21.

    Sanders B.C., Milburn G.J. (1989). “Complementarity in a quantum nondemolition measurement”. Phys. Rev. A 39, 694

    Article  ADS  Google Scholar 

  22. 22.

    Pryde G.J., O’Brien J.L., White A.G., Bartlett S.D., Ralph T.C. (2004). “Measuring a photonic qubit without destroying it”. Phys. Rev. Lett. 92: 190402

    Article  ADS  Google Scholar 

  23. 23.

    Wheeler J.A., Mathematical Foundations of Quantum Theory, A.R. Marlow, ed. (Academic, New York, 1978).

  24. 24.

    Bartell L.S., (1980). “Complementarity in the double-slit experiment: on simple realizable systems for observing intermediate particle-wave behavior”. Phys. Rev. D 21: 1698

    Article  ADS  MathSciNet  Google Scholar 

  25. 25.

    Hecht E., Zajac A., (1974). Optics. Addison-Wesley, Reading, MA

    Google Scholar 

  26. 26.

    Wheeler J.A., “Beyond the black hole,” Some Strangeness in Proportion, H. Woolf, ed. (Addison-Wesley, Reading, MA, 1980), pp. 341–375

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Correspondence to Shahriar S. Afshar.

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A Preliminary version of this paper was presented by S.S.A. at a Seminar titled “Waving Copenhagen Good-bye: Were the Founders of Quantum Mechanics Wrong?,” Department of Physics, Harvard University, Cambridge, MA 02138, 23 March, 2004.

Private communication by Einstein to his friend Michele Besso, 1951.

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Afshar, S.S., Flores, E., McDonald, K.F. et al. Paradox in Wave-Particle Duality. Found Phys 37, 295–305 (2007). https://doi.org/10.1007/s10701-006-9102-8

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Keywords

  • principle of complementarity
  • wave-particle duality
  • non- perturbative measurements
  • double-slit experiment
  • Afshar experiment

PACS numbers:

  • 03.65.Ta
  • 42.50.Xa
  • 14.70.Bh