References

[1] Mortimer J. Adler. Natural Theology, Chance, and God, pages 288–301. Encyclopedia Brittanica, Chicago, 1992.

[2] S. S. Afshar, E. Flores, K. F. McDonald, and E. Knoesel. Paradox in wave-particle duality. Foundations of Physics, 37:295–305, 2007.

[3] Y. Aharonov and D. Bohm. Significance of electromagnetic potentials in quantum theory. Phys. Rev., 115(3):485, 1959.

[4] A. H. Ali. The ensemble quantum state of a single particle. Int. J. Theor. Phys., 48:194–212, 2009.

[5] O. Alter and Y. Yamamoto. Quantum Measurement of a Single System. Wiley, New York, 2001.

[6] Philip W. Anderson. More is different. Science, 177(4047):393–396, August 1972.

[7] E. Arthurs and J. L. Kelly. On the simultaneous measurement of a pair of conjugate observables. Bell. Syst. Techn. J., 44:725–729, 1965.

[8] L. E. Ballentine. The statistical interpretation of quantum mechanics. Reviews of Modern Physics, 42:358–381, 1970.

[9] L. E. Ballentine. Comments on Stapp’s ’Copenhagen interpretation’ and the significance of Bell’s theorem. American Journal of Physics, 42:81–83, 1973.

[10] L. E. Ballentine. Probability theory in quantum mechanics. American Journal of Physics, 54:883–889, 1986.

[11] L. E. Ballentine. What do we learn about quantum mechanics from the theory of measurement? International Journal of Theoretical Physics, 27:211–218, 1988.

[12] L. E. Ballentine. Quantum Mechanics. Prentice Hall, Englewood Cliffs, NJ, 1989.

[13] L. E. Ballentine. Limitations of the projection postulate. Foundations of Physics, 20:1329–1343, 1990.

[14] L. E. Ballentine. Quantum measurement of a single system. American Journal of Physics, 71:639–640, 2003. book review.

[15] L. E. Ballentine and Jon P. Jarrett. Bell’s theorem: Does quantum mechanics contradict relativity? American Journal of Physics, 55:696–701, 1987.

[16] F. J. Belinfante. A survey of hidden-variables theories. Pergamon Press, Oxford, 1973.

[17] F. J. Belinfante. Measurements and Time Reversal in Objective Quantum Theory. Pergamon Press, Oxford, 1975.

[18] John S. Bell. On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38:447–452, 1966. Reprinted in [?, pp. 1-13].

[19] John S. Bell. Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge, 1987.

[20] John Stuart Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1:195–200, 1964.

[21] Mara Beller. The conceptual and the anecdotal history of quantum mechanics. Foundations of Physics, 26:545–557, 1996.

[22] E. G. Beltrametti and G. Cassinelli. The Logic of Quantum Mechanics. Addison-Wesley, Reading, MA, 1981.

[23] D. I. Blokhintsev. Quantum Mechanics. Reidel, Dordrecht, 1964.

[24] D. I. Blokhintsev. The Philosophy of Quantum Mechanics. Reidel, Dordrecht, 1968.

[25] Niels Bohr. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 48:696–702, 1935.

[26] S. D. Bosanac. Dynamics of particles and the electromagnetic field. World Scientific, Singapore, 2005.

[27] G. E. Bowman. Essential Quantum Mechanics. Oxford University Press, Oxford, 2008.

[28] Luis J. Boya. Rejection of the light quantum: The dark side of Niels Bohr. Int. J. of Theor. Phys., 42:2563–2573, 2003.

[29] M. Bozic and Z. Maric. Quantum interference, quantum theory of measurement, and (in)completeness quantum mechanics. Foundations of Physics, 28:415–427, 1998.

[30] Mario Bunge. Strife about complementarity i. The British Journal for the Philosophy of Science, 6:1–12, 1955.

[31] Mario Bunge. Strife about complementarity ii. The British Journal for the Philosophy of Science, 6:141–155, 1955.

[32] Mario Bunge. Survey of the interpretations of quantum mechanics. American Journal of Physics, 24:272–287, 1956.

[33] P. Busch, T. Heinonen, and P. Lahti. Heisenberg’s uncertainty principle. Physics Reports, 452:155–176, 2007.

[34] P. Busch and P. J. Lahti. On various joint measurements of position and momentum observables in quantum theory. Phys. Rev. D, 29:1634–1646, 1984.

[35] P. Busch and A. Shimony. Insolubility of the quantum measurement problem for unsharp observables. Stud. Hist. Phil. Mod. Phys., 27B:397–404, 1996.

[36] M. Cini and M. Serva. Where is an object before you look at it ? Foundations of Physics Letters, 3:129–151, 1990.

[37] E. B. Davies and T. Lewis. An operational approach to quantum probability. Comm. Math. Phys., 17:239–260, 1970.

[38] A. C. de la Torre, A. Daleo, and I. Garcia-Mata. The photon-box Bohr-Einstein debate demythologized. Eur. J. Phys., 21:253–260, 2000.

[39] Willem M. de Muynck. Preparation and measurement: Two independent sources of uncertainty in quantum mechanics. Foundations of Physics, 30:205–225, 2000.

[40] Willem M. de Muynck. Foundations of Quantum Mechanics, an Empiricist Approach. Kluwer Academic Publishers, New York, 2004.

[41] P. A. M. Dirac. The principles of quantum mechanics. Oxford at the Clarendon Press, Oxford, fourth edition, 1958.

[42] P. A. M. Dirac. The principles of quantum mechanics. Oxford University Press, Oxford, 4. edition, 1958. p. 88.

[43] A. Einstein. Physics and reality. J. Franklin Inst., 221:349, 1936.

[44] A. Einstein. Reply to criticism. In Albert Einstein, Philosopher-Scientist. Tudor Publishing Company, New York, 1949.

[45] A. Einstein. Reply to Criticism, page 665. Harper and Row, New York, 1949.

[46] A. Einstein, B. Podolsky, and N. Rosen. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev., 47(10):777–780, May 1935.

[47] A. Elby, H. R. Brown, and S. Foster. What makes a theory physically ’complete’ ? Foundations of Physics, 23:971–985, 1993.

[48] J. Erhart, S. Sponar, G. Sulyok, B. Badurek, M. Ozawa, and Y. Hasegawa. Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin-measurement. Nature Physics, 8:185, 2012. also available at: arXiv:1201.1833v1 [quant-ph].

[49] Arthur Fine. Insolubility of the quantum measurement problem. Physical Review D, 2:2783–2787, 1970.

[50] Arthur Fine. On the completeness of quantum theory. Synthese, 29:257–280, 1974.

[51] Arthur Fine. The Shaky Game. The University of Chicago Press, Chicago and London, 1986.

[52] E. V. Flores and J. M. De Tata. Complementarity paradox solved: Surprising consequences. Foundations of Physics, 40:1731–1743, 2010.

[53] J. Frenkel. Einführung in die Wellenmechanik. Springer, Berlin, 1929.

[54] Christopher A. Fuchs. Distinguishability and accessible information in quantum theory. arXiv:quant-ph/9601020v1, thesis, 1995.

[55] K. Fujikawa. A universally valid Heisenberg uncertainty relation. Phys. Rev., A 85:062117, 2012.

[56] Claudio Garola and Sandro Sozzo. A semantic approach to the completeness problem in quantum mechanics. Foundations of Physics, 34:1249–1266, 2004.

[57] Daniel T. Gillespie. Untenability of simple ensemble interpretations of quantum measurement probabilities. Am. J. Phys., 54:889–894, 1986.

[58] P. Grangier, G. Roger, and A. Aspect. A new light on single photon interferences. Ann. N.Y. Acad. Sci., 480:98, 1986.

[59] H. J. Groenewold. On the principles of elementary quantum mechanics. Physica, 12:405–460, 1946.

[60] W. Heisenberg. The Physical Principles of Quantum Theory. University of Chicago Press, Chicago, Ill., 1930.

[61] W. Heisenberg. Physics and Philosophy, the Revolution in Modern Science. Harper and Row, New York, 1966. p. 84.

[62] W. Heisenberg. Gesammelte Werke, volume C1. Piper, Mnchen, 1984. p.26.

[63] Carsten Held. Can quantum mechanics be shown to be incomplete in principle? In: 15th UK and European Meeting on the Foundations of Physics (Leeds, 29-31 March 2007).

[64] Carsten Held. Axiomatic quantum mechanics and completeness. Foundations of Physics, 38:707–732, 2008.

[65] Karl Hess, Hans De Raedt, and Kristel Michielsen. Hidden assumptions in the derivation of the Theorem of Bell. 2011. invited paper presented at FQMT11, available at http://www.arxiv.org/abs/arXiv:1108.3583.

[66] H. F. Hofmann. Measurement uncertainties in the quantum formalism: quasi-realities of individual systems. In Proceedings of QIT26, 2012, available at http://arXiv.org/abs/quant-ph/1205.0073.

[67] D. H. Holze and W. T. Scott. The consequences of measurement in quantum mechanics ii. a detailed position measurement thought experiment. Annals of Physics, 47:489–515, 1968.

[68] D. Home and S. Sengupta. Heisenberg’s gedanken experiment revisited. Am. J. Phys., 51(6):567–569, 1983.

[69] D. Home and M. A. B. Whitaker. Ensemble interpretations of quantum mechanics. a modern perspective. Physics Reports, 210(4):223–317, May 1992.

[70] G. Hunter. Realism in the realized Popper’s experiment. AIP Conf. Proc., 646:243–248, 2002.

[71] H. Ioannidou. Statistical interpretation of the Planck constant and the uncertainty relation. International Journal of Theoretical Physics, 22:1129–1139, 1983.

[72] V. Jacques, N. D. Lai, A. Dreau, D. Zheng, D. Chauvat, F. Treussart, P. Grangier, and J-F. Roch. Illustration of quantum complementarity using single photons interfering on a grating. New Journal of Physics, 10:123009, 2008.

[73] Max Jammer. The Philosophy of Quantum Mechanics. John Wiley & Sons, New York, 1974.

[74] J. M. Jauch. Foundations of Quantum Mechanics. Addison-Wesley, Reading, MA., 1968.

[75] E. T. Jaynes. Probability in quantum theory. In W. H. Zurek, editor, Complexity, Entropy, and the Physics of Information. Addison-Wesley, Reading MA, 1990.

[76] T. F. Jordan and E. C. G. Sudarshan. Simply no hidden variables. Am. J. Phys., 59:698, 1991.

[77] Olival Freire Jr. Marxism and quantum controversy: Responding to max jammer’s question. Paper to be presented at the conference Intelligentsia: Russian and Soviet Science on the World Stage, 1860-1960, University of Georgia, Athens GA, on 29-31 October 2004.

[78] E. C. Kemble. The general principles of quantum mechanics. part I. Rev. Mod. Phys., 1:157–215, 1929.

[79] E. C. Kemble. The Fundamental Principles of Quantum Mechanics. Dover, New York, 1958.

[80] E. H. Kennard. Zur Quantenmechanik einfacher Bewegungstypen. Z. Physik, 44:326–352, 1927.

[81] Y. H. Kim and Y. H. Shih. Experimental realization of popper’s experiment: violation of the uncertainty principle ? Foundations of Physics, 29:1849–1861, 1999.

[82] K. A. Kirkpatrick. ’quantal’ behavior in classical probability. Foundations of Physics Letters, 16:199–224, 2003.

[83] U. Klein. Schrödinger’s equation with gauge coupling derived from a continuity equation. Foundations of physics, 39:964, 2009.

[84] U. Klein. The statistical origins of quantum mechanics. Physics Research International, Article ID 808424, 2011. Open access paper available at http://downloads.hindawi.com/journals/phys/2010/808424.pdf.

[85] U. Klein. What is the limit $ℏ → 0$ of quantum theory? Am. J. Phys., 80:1009, 2012. ’online available at http://arxiv.org/abs/1201.0150.

[86] A. Komar. Indeterminate character of the reduction of the wave packet in quantum theory. Phys. Rev., 126:365–369, 1962.

[87] Henry Krips. Statistical interpretation of quantum theory. Am. J. Phys., 43:420–422, 1975.

[88] T. Krüger. An attempt to close the Einstein-Podolsky-Rosen debate. Can. J. Phys., 82:53–65, 2004.

[89] Alfred Landé. Foundations of Quantum Theory. Yale University Press, New Haven, 1955.

[90] Alfred Landé. Quantum fact and fiction III. American Journal of Physics, 37:541–548, 1969.

[91] Robert B. Laughlin. A Different Universe. Basic Books, Cambridge, 2005.

[92] P. G. Lewis, D. Jennings, J. Barrett, and T. Rudolph. Distinct quantum states can be compatible with a single state of reality. Phys. Rev. Lett., 109:150404, 2012.

[93] R. Loudon M. J. Collet. Popper versus Copenhagen. Nature, 328:675, 1987.

[94] E. Madelung. Quantentheorie in hydrodynamischer Form. Z. Phys., 40:322–326, 1926.

[95] H. Margenau. Quantum-mechanical description. Physical Review, 49:24–242, 1935.

[96] H. Margenau. Measurements and quantum states: Part I. Philosophy of Science, 30(1):1–16, 1963.

[97] H. Margenau. Measurements and quantum states: Part II. Philosophy of Science, 30(2):138–157, 1963.

[98] H. Margenau. Measurements in quantum mechanics. Annals of Physics, 23:469–485, 1963.

[99] H. Margenau and J. L. Park. The physics and the semantics of quantum measurement. Foundations of Physics, 3(1):19–28, 1973.

[100] Tim Maudlin. Quantum Non-Locality and Relativity. Blackwell Publishers, Malden, USA, 2002.

[101] L. S. Mayants, W. Yourgrau, and A. J. van der Merwe. Some methodological problems in quantum physics. Annalen der Physik, 33(1):21–35, 1976.

[102] Rodrigo Medina. Orthodox quantum mechanics free from paradoxes. Annales de la Foundation Lous de Broglie, 24:129–157, 1999.

[103] M. B. Mensky. Heisenberg’s uncertainty relation may be violated in a single measurement. J. of Russian Laser Research, 27:332, 2006.

[104] N. D. Mermin. Hidden variables and the two theorems of John Bell. Reviews of Modern Physics, 65:803–815, 1993.

[105] A. M. L. Messiah. Quantum mechanics, volume I and II. Interscience, New York, 1958. Russian translation: Nauka, Moscow, 1978 (vol. I) and 1979 (vol. II).

[106] Margaret Morrison. Emergence, reduction, and theoretical principles: Rethinking fundamentalism. Philosophy of Science, 73:876–887, 2006.

[107] Roger G. Newman. Probability interpretation of quantum mechanics. Am. J. Phys., 48:1029–1034, 1980.

[108] G. Nimtz. Tunneling confronts special relativity. Foundations of Physics, DOI 10.1007/s10701-011-9539-2, 2011.

[109] M. Ozawa. Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurements. Phys. Rev. A, 67:042105, 2003.

[110] M. Ozawa. Uncertainty relations for joint measurements of noncommuting observables. Phys. Lett., A 320:367–374, 2004.

[111] Masanao Ozawa. Operations, disturbance, and simultaneous measurability. Phys. Rev. A, 63:032109, 2001.

[112] M. R. Pahlavani, editor. Measurements in Quantum Mechanics, chapter ’A statistical derivation of non-relativistic quantum theory’, by U. Klein, pages 141–174. InTech, Rijeka, 2012. online available at http://www.intechopen.com/download/pdf/29091.

[113] J. L. Park and H. Margenau. Simultaneous measurability in quantum theory. International Journal of Theoretical Physics, 1:211–283, 1968.

[114] James L. Park. Nature of quantum states. Am. J. Phys., 36:211–226, 1968.

[115] Philip Pearle. Alternative to the orthodox interpretation of quantum theory. Am. J. Phys., 127:742–753, 1967.

[116] Asher Peres. Quantum Theory : Concepts and Methods (Fundamental Theories of Physics, Vol 57). Kluwer Academic Publishers, 1995.

[117] A. B. Pippard. The interpretation of quantum mechanics. Eur. J. Phys., 7:43–48, 1986.

[118] K. Popper. Popper versus copenhagen. Nature, 328:675, 1987.

[119] Karl R. Popper. The Logic of Scientific Discovery. Basic Books, New York, 1959. German original: Die Logik der Forschung, 1934.

[120] Karl R. Popper. The Open Universe - an Argument for Indeterminism. Rowman and Littlefield, Totowa, 1982.

[121] Karl R. Popper. Quantum theory and the schism in physics. Rowman and Littlefield, Totowa, 1982.

[122] D. E. Pritchard, T. D. Hammond, J. Schmiedmayer, C. R. Eckstrom, and M. S. Chapman. Atom interferometry. In F. de Martini, G. Denardo, and A. Zeilinger, editors, Quantum Interferometry. World Scientific, Singapore, 1994.

[123] E. Prugovečki. On a theory of measurement of incompatible observables in quantum mechanics. Can. J. of Physics, 45:2173–2219, 1967.

[124] E. Prugovečki. A postulational framework for theories of simultaneous measurement of several observables. Foundations of Physics, 3:3–18, 1973.

[125] M. F. Pusey, J. Barrett, and T. Rudolph. On the reality of the quantum state. Nature Physics, 8:476, 2012.

[126] R. Quadt. The nonobjectivity of past events in quantum mechanics. Foundations of Physics, 19:1027–1035, 1989.

[127] T. Qureshi. Understanding popper’s experiment. Am. J. Phys., 73:541–544, 2005.

[128] Hans De Raedt and Kristel Michielsen. Event-by-event simulation of quantum phenomena. Ann. Phys.(Berlin), 524(8):392–410, 2012.

[129] H. Rauch. Scope of neutron interferometry. In U. Bonse and H. Rauch, editors, Neutron interferometry. Clarendon Press, Oxford, 1979.

[130] Michael Redhead. Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics. Clarendon Press, Oxford, 1990.

[131] G. Rigolin. Uncertainty relations for entangled states. arXiv:quant-ph/0008100v2.

[132] H. P. Robertson. The uncertainty principle. Phys. Rev., 34:163–164, 1929.

[133] N. Rosen. The relation between classical and quantum mechanics. Am. J. Phys., 32:597–600, 1964.

[134] A. A. Ross-Bonney. Does god play dice ? - a discussion of some interpretations of quantum mechanics. Nuovo Cimento, 30 B:55, 1975.

[135] L. A. Rozema, A. Darabi, D. H. Mahler, A. Hayat, Y. Soudagar, and A. M. Steinberg. Violation of heisenberg’s measurement-disturbance relationship by weak measurements. Phys. Rev. Lett., 109:100404, 2012. also available at: arXiv:1208.0034v2 [quant-ph].

[136] P. Sancho. Popper’s experiment revisited. Foundations of Physics, 32:789–805, 2002.

[137] M. Schlosshauer and A. Fine. Implications of the Pusey-Barrett-Rudolph quantum no-go theorem. Phys. Rev. Lett, 108:260404, 2012.

[138] Erwin Schrödinger. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften, 23:807–812, 823–828, 844–849, 1935. English translation in [152] and [160, pp. 152-167].

[139] J. R. Shewell. On the formation of quantum-mechanical operators. Am. J. Phys., 27:16–21, 1959.

[140] Abner Shimony. Approximate measurement in quantum mechanics. ii. Physical Review D, 9:2321–2323, 1974.

[141] H. Shirai. Reinterpretation of quantum mechanics based on the statistical interpretation. Foundations of Physics, 28:1633–1662, 1998.

[142] A. J. Short. Popper’s experiment and conditional uncertainty relations. Found. Phys. Lett., 14(3):275–284, 2001.

[143] Mark P. Silverman. Quantum Superposition. Springer, New York, 2008. p.10.

[144] J. C. Slater. J. Franklin Inst., 207:449, 1929.

[145] H. P. Stapp. Bell’s theorem and the world process. Il Nuovo Cimento, 29B:270–276, 1975.

[146] O. Steuernagel. Afshar’s experiment does not show a violation of complementarity. Foundations of Physics, 37:1370–1385, 2007.

[147] A. Sudberry. Popper’s variant of the EPR experiment does not test the copenhagen interpretation. Phil. Sci., 52:470–476, 1985.

[148] G. Temple. Quantum and wave mechanics. Rep. Progr. Phys., 1:1, 1934.

[149] F. J. Tipler. The Physics of Immortality. Doubleday, New York, 1994.

[150] A. Tonomura, J. Endo, T. Matsuda, and T. Kawasaki. Demonstration of single-electron buildup of an interference pattern. Am. J. Phys., 57(2):117–120, 1989.

[151] Y. Toyozawa. Theory of measurement. Progress of Theoretical Physics, 87:293–305, 1992.

[152] J. D. Trimmer. The present situation in quantum mechanics: a translation of Schrödinger’s “cat paradox”. Proc. Am. Phil. Soc., 124:323–338, 1980. Reprinted in [160, pp. 152-167].

[153] H. R. Tschudi. On the statistical interpretation of quantum mechanics. Helvetica Physica Acta, 60:363–383, 1987.

[154] J. B. Uffink and J. Hilgevoord. Uncertainty principle and uncertainty relations. Foundations of Physics, 15(9):925–944, 1985.

[155] C. S. Unnikrishnan. Popper’s experiment, signal locality, uncertainty principle and momentum conservation. Found. Phys. Lett., 13:197–200, 2000.

[156] R. von Mises. Probability Statistics and Truth. Dover, New York, 1957. German original: Wahrscheinlichkeit, Statistik und Wahrheit (2nd edition), Springer, Berlin, 1936.

[157] J. von Neumann. Mathematical foundations of quantum mechanics. Princeton Univ. Press, Princeton, New Jersey, 1955.

[158] Yu. I. Vorontsov. Uncertainty relation and the measurement error-perturbation relation. Physics - Uspekhi, 48(10):999–1013, 2005.

[159] R. F. Werner. The uncertainty relation for joint measurements of position and momentum. Quant. Inf. Comp., 4:546–562, 2004.

[160] John Archibald Wheeler and Wojciech Hubert Zurek. Quantum Theory and Measurement. Princeton University Press, Princeton, 1983.

[161] David Wick. The Infamous Boundary. Birkhäuser, Boston, 1995.

[162] R. H. Young. Quantum mechanics based on position. Foundations of Physics, 10:33–56, 1980.