ISRN Mathematical Physics

Volume 2012, Article ID 327278, 37 pages

http://dx.doi.org/10.5402/2012/327278

Research Article

## Quantum Histories and Quantum Complementarity

Department of Psychiatry and Neurobiology, Graduate School of Medical Science, Kanazawa University, 13-1 Takaramachi, Kanazawa, Ishikawa 920-8641, Japan

Received 6 August 2011; Accepted 27 September 2011

Academic Editor: F. Sugino

Copyright © 2012 Danko Georgiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- M. O. Scully, B. G. Englert, and H. Walther, “Quantum optical tests of complementarity,”
*Nature*, vol. 351, no. 6322, pp. 111–116, 1991. View at Google Scholar - H. Wiseman and F. Harrison, “Uncertainty over complementarity?”
*Nature*, vol. 377, no. 6550, p. 584, 1995. View at Google Scholar - B. G. Englert, “Fringe visibility and which-way information: An inequality,”
*Physical Review Letters*, vol. 77, no. 11, pp. 2154–2157, 1996. View at Google Scholar - D. M. Greenberger and A. Yasin, “Simultaneous wave and particle knowledge in a neutron interferometer,”
*Physics Letters A*, vol. 128, no. 8, pp. 391–394, 1988. View at Google Scholar - M. Chown, “Quantum rebel,”
*New Scientist*, vol. 183, no. 2457, pp. 30–35, 2004. View at Google Scholar - J. G. Cramer, “Bohr is still wrong,”
*New Scientist*, vol. 183, no. 2461, p. 26, 2004. View at Google Scholar - U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,”
*Science*, vol. 329, no. 5990, pp. 418–421, 2010. View at Publisher · View at Google Scholar · View at PubMed - S. S. Afshar, “Violation of the principle of complementarity, and its implications,” in
*Proceedings of the Nature of Light: What Is a Photon Conference*, vol. 5866 of*Proceedings of SPIE*, pp. 229–244, San Diego, Calif, USA, August 2005. View at Publisher · View at Google Scholar - S. S. Afshar, “Violation of Bohr's complementarity: one slit or both?” in
*Proceedings of the Quantum Theory: Reconsideration of Foundations Conference*, vol. 810 of*AIP Conference Proceedings*, pp. 294–299, June 2005. View at Publisher · View at Google Scholar - S. S. Afshar, E. Flores, K. F. Mcdonald, and E. Knoesel, “Paradox in wave-particle duality,”
*Foundations of Physics*, vol. 37, no. 2, pp. 295–305, 2007. View at Publisher · View at Google Scholar · View at MathSciNet - V. Jacques, N. D. Lai, A. Dréau et al., “Illustration of quantum complementarity using single photons interfering on a grating,”
*New Journal of Physics*, vol. 10, Article ID 123009, 2008. View at Publisher · View at Google Scholar - O. Steuernagel, “Afshar's experiment does not show a violation of complementarity,”
*Foundations of Physics*, vol. 37, no. 9, pp. 1370–1385, 2007. View at Publisher · View at Google Scholar · View at MathSciNet - W. G. Unruh, “Shahriar Afshar—Quantum Rebel?” 2004, http://axion.physics.ubc.ca/rebel.html.
- L. Motl, “Violation of complementarity?” 2004, http://motls.blogspot.com/2004/11/violation-of-complementarity.html.
- E. V. Flores, “Reply to comments of Steuernagel on the Afshar's experiment,”
*Foundations of Physics*, vol. 38, no. 8, pp. 778–781, 2008. View at Publisher · View at Google Scholar - E. V. Flores, “Ether, the theory of relativity and quantum physics,” in
*Space, Time, and Spacetime*, V. Petkov, Ed., vol. 167 of*Fundamental Theories of Physics*, pp. 147–155, Springer, 2010. View at Google Scholar - E. V. Flores and J. M. de Tata, “Complementarity paradox solved: surprising consequences,”
*Foundations of Physics*, vol. 40, no. 11, pp. 1731–1743, 2010. View at Publisher · View at Google Scholar - R. E. Kastner, “Why the Afshar experiment does not refute complementarity,”
*Studies in History and Philosophy of Science Part B*, vol. 36, no. 4, pp. 649–658, 2005. View at Publisher · View at Google Scholar - R. E. Kastner, “On visibility in the Afshar two-slit experiment,”
*Foundations of Physics*, vol. 39, no. 10, pp. 1139–1144, 2009. View at Google Scholar - A. Drezet, “Wave particle duality and the Afshar experiment,”
*Progress in Physics*, vol. 1, pp. 57–64, 2011. View at Google Scholar - N. J. Gunther and G. B. Beretta, “Towards practical design rules for quantum communications and quantum imaging devices,” in
*Proceedings of Quantum Communications and Quantum Imaging III*, vol. 5893 of*Proceedings of SPIE*, pp. 1–22, August 2005. View at Publisher · View at Google Scholar - T. Qureshi, “Complementarity and the Afshar experiment,” . In press, http://arxiv.org/abs/quant-ph/0701109.
- D. Reitzner, “Comment on Afshar's expriments,” . In press, http://arxiv.org/abs/quant-ph/0701152.
- D. Georgiev, “Single photon experiments and quantum complementarity,”
*Progress in Physics*, vol. 2, pp. 97–103, 2007. View at Google Scholar - D. Georgiev, “Exact mapping of quantum waves between Unruh's and Afshar's setup,”
*Progress in Physics*, vol. 3, pp. 28–33, 2007. View at Google Scholar - D. Georgiev, “Quantum operator approach to Unruh's and Afshar's setups,”
*ICFAI University Journal of Physics*, vol. 1, pp. 7–33, 2008. View at Google Scholar - R. P. Feynman, “Space-time approach to non-relativistic quantum mechanics,”
*Reviews of Modern Physics*, vol. 20, no. 2, pp. 367–387, 1948. View at Publisher · View at Google Scholar - R. P. Feynman,
*QED: The Strange Theory of Light and Matter*, Princeton University Press, 1983. - R. B. Griffiths, “Consistent interpretation of quantum mechanics using quantum trajectories,”
*Physical Review Letters*, vol. 70, no. 15, pp. 2201–2204, 1993. View at Publisher · View at Google Scholar · View at MathSciNet - R. B. Griffiths, “Consistent histories and quantum reasoning,”
*Physical Review A*, vol. 54, no. 4, pp. 2759–2774, 1996. View at Google Scholar - R. B. Griffiths, “Consistent resolution of some relativistic quantum paradoxes,”
*Physical Review A*, vol. 66, no. 6, pp. 621011–621021, 2002. View at Google Scholar - R. B. Griffiths,
*Consistent Quantum Theory*, Cambridge University Press, 2003. - J. B. Hartle, “The spacetime approach to quantum mechanics,”
*Vistas in Astronomy*, vol. 37, pp. 569–583, 1993. View at Google Scholar - J. B. Hartle, “What connects different interpretations of quantum mechanics?” in
*Quo Vadis Quantum Mechanics?*A. C. Elitzur, S. Dolev, and N. Kolenda, Eds., pp. 73–82, Springer, 2005. View at Google Scholar - C. J. Isham, “Quantum logic and the histories approach to quantum theory,”
*Journal of Mathematical Physics*, vol. 35, no. 5, pp. 2157–2185, 1994. View at Google Scholar - R. Omnès,
*Understanding Quantum Mechanics*, Princeton University Press, 1999. - S. Gudder, “Hilbert space representations of decoherence functionals and quantum measures,” . In press, http://arxiv.org/abs/1011.1694.
- C. J. Isham, N. Linden, K. Savvidou, and S. Schreckenberg, “Continuous time and consistent histories,”
*Journal of Mathematical Physics*, vol. 39, no. 4, pp. 1818–1834, 1998. View at Google Scholar - R. De la Madrid, “Rigged Hilbert space approach to the Schrödinger equation,”
*Journal of Physics A*, vol. 35, no. 2, pp. 319–342, 2002. View at Publisher · View at Google Scholar · View at MathSciNet - J. Townsend,
*A Modern Approach to Quantum Mechanics*, University Science Books, 2000. - E. Hecht,
*Optics*, Addison Wesley, 4th edition, 2003. - W. G. Unruh, “Comment on “Single photon experiments and quantum complementarity”
by D. Georgiev,”
*Progress in Physics*, vol. 3, p. 27, 2007. View at Google Scholar - J. W. Goodman,
*Introduction to Fourier Optics*, McGraw-Hill, 1996. - D. Dürr and S. Teufel,
*Bohmian Mechanics: The Physics and Mathematics of Quantum Theory*, Springer, 2009. - S. Goldstein, “Bohmian mechanics,” in
*Stanford Encyclopedia of Philosophy*, 2006. View at Google Scholar - A. Zeilinger, “Experiment and the foundations of quantum physics,”
*Reviews of Modern Physics*, vol. 71, no. 2, pp. S288–S297, 1999. View at Google Scholar - R. P. Crease,
*The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg*, W. W. Norton & Company, 2009. - N. D. Mermin, “Is the moon there when nobody looks? Reality and the quantum theory,”
*Physics Today*, vol. 38, no. 4, pp. 38–47, 1985. View at Google Scholar - K. von Meyenn,
*W. Pauli, “[2015] Pauli an Bohr” in Scientific Correspondence with Bohr, Einstein, Heisenberg, a.o. Vol. 4, Part 3: 1955-1956*, Springer, 2001. - E. Schrödinger, “An undulatory theory of the mechanics of atoms and molecules,”
*Physical Review*, vol. 28, no. 6, pp. 1049–1070, 1926. View at Publisher · View at Google Scholar - J. Polkinghorne,
*Quantum Theory: A Very Short Introduction*, Oxford University Press, 2002. - J. Al-Khalili, “The Illusion of Reality,” Atom, BBC, BBC Two, 2008.