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The Quantum Mechanics Conundrum

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Abstract

In the previous chapter, we have deepened some formal issues developed in Chap. 3. Now, we shall deepen the related conceptual issues. I have stressed that notions like causal constraints and potentiality need to be effective in solving our problems in interpreting QM. In general, I have piecewise proposed a schematic interpretational framework that needs now to be constructively developed, improved and tested. In the first section, a preliminary examination of the concepts of quantum events and quantum features is developed, two notions that are problematic to deal with in a classical framework.

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Notes

  1. 1.

    Misner et al. (1970, p. 71).

  2. 2.

    Geroch (1978, p. 37).

  3. 3.

    On the Copernican revolution I recommend the classical (Kuhn 1957).

  4. 4.

    See Leibniz (1710, Discours Preliminaire, Sect. 65).

  5. 5.

    Misner et al. (1970, p. 6); Geroch (1978, Chap. 1) .

  6. 6.

    https://en.wikipedia.org/wiki/Event_(probability_theory). An extensive treatment of this subject can be found in Leon–Garcia (2008).

  7. 7.

    Rindler (2001, p. 42).

  8. 8.

    D’Ariano and Tosini (2013) .

  9. 9.

    Einstein (1934, pp. 168–69).

  10. 10.

    Reference papers are Hegerfeldt (1974, 1985).

  11. 11.

    As elegantly proved in Malament (1995).

  12. 12.

    Howard (1992).

  13. 13.

    ‘T Hooft (2016, pp. 30–31).

  14. 14.

    Wheeler (1983).

  15. 15.

    Carnap (1928); Margenau (1950, Sect. 4.5).  One has spoken of the “man–made” character of physical (scientific) theories (Rindler 2001, p. 190).

  16. 16.

    On these subject I suggest the following textbooks (Atkins and De Paula 2006; Atkins and Friedman 2005).  I shall come back on these problems.

  17. 17.

    Joos and Zeh (1985).

  18. 18.

    The first serious discussions of randomness are in Poincaré (1907), Borel (1920) .

  19. 19.

    Elitzur (1992).

  20. 20.

    On this distinction see Poincaré (1899).

  21. 21.

    A problem already analysed in such terms in ancient philosophy: (Aristotle 2019, 9, 19a).

  22. 22.

    Letter of June 2, 1674 to Jarig Jelles (Spinoza 1972, IV, p. 240).

  23. 23.

    Deutsch (2011, Chap. 12).

  24. 24.

    “Once the decision is made, it becomes ‘real’ and there is nothing random about it anymore” (Laughlin 2005, p. 44). See also Laughlin (2005, p. 130).

  25. 25.

    A quick introduction to the subject is in Auletta and Wang (2014, Sect. 7.9).

  26. 26.

    Kuhlmann (2013).

  27. 27.

    On this subject and its quantum-mechanical subtleties, see Auletta et al. (2009, Sect. 13.8). I shall come back on these problems.

  28. 28.

    Schrödinger (1935a).

  29. 29.

    Schrödinger (1935b).

  30. 30.

    For a review, see Auletta and Tarozzi (2004b).  See also Auletta (2014a).

  31. 31.

    On the problem of reductionist methodology see Auletta (2012).

  32. 32.

    As pointed out in Auletta and Torcal (2011).

  33. 33.

    See also Margenau (1950, Sect. 15.1).

  34. 34.

    Poincaré (1897).

  35. 35.

    As stressed in Peirce (1885).  See also Auletta (2011, Sects. 1.2.4, 2.2.3).

  36. 36.

    On this problem see also Schlosshauer (2007, Sect. 2.5.3).

  37. 37.

    D’ariano and Yuen (1996).

  38. 38.

    On the more general statistical interpretation of QM see Ballentine (1970).  For historical reconstruction see Jammer (1974, Chap. 10)  and for further references see also Auletta (2000, Sect. 6.5.2).

  39. 39.

    As reported in Heisenberg (1969, Chap. 5):  “vom prinzipiellen Standpunkt aus ist es ganz falsch, eine Theorie nur auf beobachtbare Größen gründen zu wollen. Denn es ist ja in Wirklichkeit genau umgekehrt. Erst die Theorie entscheidet darüber, was man beobachten kann. Sehen Sie, die Beobachtung ist ja im allgemeinen ein sehr komplizierter Prozeß. Der Vorgang, der beobachtet werden soll, ruft irgendwelche Geschehnisse in unserem Meßapparat hervor. Als Folge davon laufen dann in diesem Apparat weitere Vorgänge ab, die schließlich auf Umwegen den sinnlichen Eindruck und die Fixierung des Ergebnisses in unserem Bewußtsein bewirken. Auf diesem ganzen langen Weg vom Vorgang bis zur Fixierung in unserem Bewußtsein müssen wir wissen, wie die Natur funktioniert, müssen wir die Naturgesetze wenigstens praktisch kennen, wenn wir behaupten wollen, daß wir etwas beobachtet haben. Nur die Theorie, das heißt die Kenntnis der Naturgesetze, erlaubt uns also, aus dem sinnlichen Eindruck auf den zugrunde liegenden Vorgang zu schließen. Wenn man behauptet, daß man etwas beobachten kann, so müßte man also eigentlich genauer so sagen: Obwohl wir uns anschicken, neue Naturgesetze zu formulieren, die nicht mit den bisherigen übereinstimmen, vermuten wir doch, daß die bisherigen Naturgesetze auf dem Weg vom zu beobachtenden Vorgang bis zu unserem Bewußtsein so genau funktionieren, daß wir uns auf sie verlassen und daher von Beobachtungen reden dürfen.”

  40. 40.

    Heisenberg (1958, p. 90).

  41. 41.

    ‘T Hooft (2016, p. 33).

  42. 42.

    Born (1949, p. 33).

  43. 43.

    On this subject the interested reader may have a look at Auletta (2011, Sect. 20.6), where also further literature is quoted. I recall here that Peirce clearly considered these two different kinds of association (Peirce 1898, pp. 234–36).

  44. 44.

    Lewontin (2000).

  45. 45.

    See e.g. Dirac (1945).  On this problem see also Bokulich (2008, Sect. 3.2).  The author stresses that Dirac had supported an inverse correspondence principle, according to which QM can lead analogically into new developments in CM.

  46. 46.

    Brown and Porter (2006).  This enlightening paper is also a good conceptual introduction to category theory, of which a lot will be said below. I had only used the term abductive instead of inductive (see the end of Sect. 3.3.3). Among the first scientists to have acknowledged the role of analogy in science, and especially in mathematics, is H. Poincaré (1897). See also Poincaré (1902, pp. 158–59); Poincaré (1905, p. 38).

  47. 47.

    As pointed out in Auletta and Tarozzi (2004b). 

  48. 48.

    See also Auletta and Wang (2014, Sects. 4.8, 5.4–5.6).

  49. 49.

    Auletta and Tarozzi (2004a).  In this paper, due to some misprint, some displaced imaginary units appear in some calculations.

  50. 50.

    Pusey et al. (2012).

  51. 51.

    This can be brought in harmony with the idea that the quantum state is prescriptive (Healey 2017, Sect. 4.5).

  52. 52.

    Aharonov and Bohm (1959).

  53. 53.

    Misner et al. (1970, Sect. 8.3).

  54. 54.

    The reference paper is Ollivier and Zurek (2001).  See also Auletta and Wang (2014, Sect. 11.7).

  55. 55.

    I synthesise in the following the main arguments of Zwolak and Zurek (2013).

  56. 56.

    Bohm (1980, pp. 147–71).

  57. 57.

    These arguments have been synthesised in Auletta and Torcal (2011).  See also Auletta and Wang (2014, Sect. 5.5).

  58. 58.

    Greenberger and Yasin (1988).

  59. 59.

    Greenberger and Yasin (1988).  A similar result can be found in Englert (1996).

  60. 60.

    As pointed out in Maudlin (1994, p. 22).

  61. 61.

    Ma et al. (2013).  I shall come back on this experiment.

  62. 62.

    Suarez (2001).  This possibility was anticipated in Auletta (2000, Sect. 46.4).   See also (Maudlin 1994, p. 23).

  63. 63.

    As pointed out in Bennett and Shor (1998).

  64. 64.

    As stated in Gottesman and Chuang (1999).

  65. 65.

    Stefanov et al. (2002).

  66. 66.

    Wheeler (1990).  See also Verlinde (2011)  for a model, on which I shall come back.

  67. 67.

    Grunbaum (1973, p. 729).

  68. 68.

    The transactional interpretation of QM reaches a similar conclusion about the nature of events (Kastner 2013).

  69. 69.

    Geroch (1978, p. 79).

  70. 70.

    See also Rovelli (2004, pp. 49–50);  Grunbaum (1973, pp. 322–24).

  71. 71.

    Bridgman (1927, p. 75).

  72. 72.

    I summarise here the arguments exposed in Auletta (2011, Sect. 3.3.4).

  73. 73.

    Consider in this context the difficulties with the notion of extended time (Bridgman 1927, pp. 76–77).

  74. 74.

    This argument was presented by the British-Australian philosopher J. Smart (1920–2012) (Smart 1954). See also Lockwood (2005, Chap. 11).

  75. 75.

    Wheeler (1983).

  76. 76.

    Schrodinger (1958, Chap. 3).

  77. 77.

    Bohm (1980, pp. 196–213).

  78. 78.

    Somewhere he also appears to follow the epistemic interpretation (Wheeler 1988).

  79. 79.

    This is the main goal of my book (Auletta 2011).

  80. 80.

    See the summary in Auletta and Wang (2014, Sect. 12.3).

  81. 81.

    Heisenberg (1958, pp. 46–47).

  82. 82.

    D’Ariano et al. (2017, Sects. 2.4 and 5.1).

  83. 83.

    Reference papers are Bennett and Wiesner (1992); Mattle et al. (1996) .  See also Nielsen and Chuang (2000, Sect. 2.3).

  84. 84.

    On this subject see Nielsen and Chuang (2000, Sect. 4.4).

  85. 85.

    See the original study (Wang et al. 1991).  For the remnant of this subsection see Auletta et al. (2009, Sect. 9.5).

  86. 86.

    Scully et al. (1991).

  87. 87.

    In a further experiment, the erasure is provided by one of two entangled photons (Kim et al. 2000).

  88. 88.

    Storey et al. (1994).

  89. 89.

    Englert et al. (1995).  

  90. 90.

    Armstrong (1983, Chap. 6).

  91. 91.

    On this subject see Auletta (2005).

  92. 92.

    Fundamental and now classical textbooks on the subject are Davies (1976); Kraus (1983) .  See also Busch et al. (1995); de Muynck (2002).  Fort a summary, see Auletta et al. (2009, Sect. 9.10); Auletta (2014b).

  93. 93.

    Kraus (1983, p. 10).

  94. 94.

    D’Ariano et al. (2017, Sect. 2.4).

  95. 95.

    D’Ariano et al. (2017, Sects. 2.8.5 and 3.6–3.7).

  96. 96.

    On this subject see Finkelstein (1996).

  97. 97.

    On this helpful formalism see Nielsen and Chuang (2000, pp. 356–73, 386–89);  Auletta et al. (2009, Sect. 14.3).

  98. 98.

    See Lindblad (1983). For derivation of this equation see Auletta et al. (2009, Sect. 14.2). On Master equation and decoherence see Schlosshauer (2007, Chap. 4).

  99. 99.

    Which is again a superoperator, a formal aspect that does not need to be considered here.

  100. 100.

    I follow here (Nielsen and Chuang 1997, Sect. 8.3.5; Auletta et al. 2009, Sect. 14.3).

  101. 101.

    I follow here   (Martens and de Muynck 1990; de Muynck et al. 1991). See also Auletta et al. (2009, Sect. 9.10.3).

  102. 102.

    See Busch et al. (1995, Sect. I.1.2).

  103. 103.

    D’Ariano et al. (2017, Sect. 2.12).

  104. 104.

    D’Ariano et al. (2017, Sect. 7.10).

  105. 105.

    It may be noted that in Ludwig (1983, I, p. 7) preparation–registration procedures are part of the fundamental (operational–ontological) domain of QM but not the assigned properties. For this reason, he stresses that such selection procedures or operations should not be mixed up with formal tools like density matrices or projectors (Ludwig 1983, I, Chap. 3).

  106. 106.

    Recent attempts at using the so-called weak measurement for showing a supposed dissociation between system and properties (Denkmayr et al. 2014) have subsequently been explained in terms of ordinary quantum interference effects (Corrêa et al. 2015).

  107. 107.

    See also Rovelli (2005).

  108. 108.

    Ludwig (1983, I, p. 42).

  109. 109.

    Ludwig (1983). See also Kraus (1983), Busch et al. (1995).

  110. 110.

    Ludwig (1983, I, pp. 31, 43–47).

  111. 111.

    It might be noted that already Kraus, although still maintaining the notion of equivalence class, prefers to speak of equivalence classes of instruments and not of operations (Kraus 1983, p. 6) .

  112. 112.

    See Davies (1976, pp. 17–18) . For what follows see also Auletta et al. (2009, Sect. 9.10).

  113. 113.

    See Kraus (1983) .

  114. 114.

    Properly speaking, also effect operators are superoperator, but for them I follow the general convention.

  115. 115.

    See Royer (1989).

  116. 116.

    See Kraus (1983, p. 42) .

  117. 117.

    D’Ariano et al. (2017, Sect. 7.9).

  118. 118.

    D’Ariano et al. (2017, Sect. 8.12).

  119. 119.

    Coecke and Lal (2012).

  120. 120.

    As pointed out in Auletta and Torcal (2011).

  121. 121.

    Rovelli (1996, 2005).  See also Epperson and Zafiris (2013).

  122. 122.

    For instance by Peirce (1903, 1.25).

  123. 123.

    For reasons that are partly different from my approach, the so-called transactional interpretation of QM has stressed the ‘reality’ of possibility (Kastner 2013, Chap. 4).

  124. 124.

    von Bertalanffy (1950).  See also Auletta (2011, Sect. 2.4.4). Science as knowledge of systems and in particular of relations is the object of Carnap (1928).

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  1. University of Cassino and Southern Lazio, Cassino, Frosinone, Italy

    Gennaro Auletta

  2. Pontifical Gregorian University, Rome, Italy

    Gennaro Auletta

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Auletta, G. (2019). Ontological Ascription and Operations. In: The Quantum Mechanics Conundrum. Springer, Cham. https://doi.org/10.1007/978-3-030-16649-6_5

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