Abstract
QM could be considered a cluster of riddles and the world that it describes as a kind of impenetrable sphinx. As a matter of fact, the best minds of several generations have tried to cope with these mysteries, and consistent advancements have been made step by step although to date no congruent general interpretation that would capture the agreement of the physicists’ community has been provided. Here, I schematically summarise some of the main problems partitioning the whole in four broad subjects: significance of the quantum formalism, measurement, non–locality and causality. The possible solutions to these problems will be treated in the next chapters.
Randomness is where reason stops, it’s a statement that things are accidental, meaningless, unpredictable, and happen for no reason.
Gregory J. Chaitin, The Unknowable
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Notes
- 1.
Ludwig (1978, pp. 8–9). Physical reality also presents a fundamental domain (Grundbereich) that is relatively independent of the application prescriptions as well as of the mathematics.
- 2.
This has been clearly the standpoint of the young Heisenberg: see Heisenberg (1927).
- 3.
It may be discussed in which sense causal aspects need to be involved here (Margenau 1950, Sect. 8.1).
- 4.
- 5.
- 6.
I summarise here the arguments presented, e.g. in Auletta and Wang (2014, Sects. 3.5–3.7 and 7.8).
- 7.
- 8.
As recalled in Auletta and Wang (2014, Sect. 7.4).
- 9.
- 10.
- 11.
On this see Bokulich (2008, p. 55).
- 12.
Landau and Lifshitz (1976, Sect. 46).
- 13.
- 14.
A beam merger is like a beam splitter but works the other way around.
- 15.
- 16.
The MZ interferometer version of the interaction-free measurement was proposed for the fist time in Elitzur and Vaidman (1993) .
- 17.
I have followed here Auletta et al. (2009a, Sect. 1.4).
- 18.
What is to a certain extent also supported in Margenau (1950, Sects. 8.5 and 15.4).
- 19.
For this argument see Bohr (1949a, pp. 219–220).
- 20.
In D’ariano et al. (2017, Sect. 5.1) this is expressed by saying that measurement outcomes become irrelevant in a classical framework.
- 21.
Ludwig (1983, I, pp. 55–56).
- 22.
Ludwig used the term registration apparatus for denoting the detector (Ludwig 1983, I, p. 8).
- 23.
These arguments are also summarised in Auletta and Wang (2014, Sect. 9.1).
- 24.
- 25.
- 26.
Heisenberg (1927).
- 27.
I address the reader to von Neumann (1932, Chap. 6). This textbook was for a longer time the sole formal and conceptual treatment of quantum measurement. Apart from QM, the contributions of von Neumann are fundamental in many fields, ranging from cellar automata going through game theory up to the foundations of modern computation.
- 28.
I follow here the exposition in Auletta et al. (2009a, Sect. 9.1).
- 29.
This is the essence of abduction and induction, a problem on which I shall come back later.
- 30.
As pointed out in Tarozzi (1996).
- 31.
Descartes (1641a).
- 32.
As we shall discover, as far as Descartes’ standpoint would be limited to the statement that the operations of the mind respond to different processes than the operations of the body, I would agree. But this does not imply the existence of two separated substance (in the metaphysical language of that time).
- 33.
This problem worried very much J. Bell: see Bell (1981).
- 34.
- 35.
- 36.
In fact, one distinguishes between the subjectivist idealism of Ancient philosophy whose reference scholar is the Greek philosopher Plato (V–IV century BC) and the objectivist idealism of modern times whose most important representatives are the German Philosopher Friedrich W. J. Schelling (1775–1854) and the German theologian and philosopher George W. F. Hegel (1770–1831).
- 37.
- 38.
- 39.
Auletta (2000, p. 362).
- 40.
Likely the most influential one in the history of physics.
- 41.
- 42.
Auletta (2000, p. 534).
- 43.
Popper (1934).
- 44.
- 45.
Chaitin et al. (2011, pp. 75–79).
- 46.
- 47.
Margenau insists that metaphysical conceptual elements are even necessary (Margenau 1950, pp. 12–13).
- 48.
The model was first proposed in Bohm (1951, pp. 614–623).
- 49.
- 50.
Schrödinger (1936).
- 51.
Schrödinger (1935).
- 52.
See also Auletta (2000, pp. 536–537).
- 53.
See e.g. Einstein (1948).
- 54.
For a historical reconstruction of the problems around the EPR paper see Jammer (1974, Chap. 6).
- 55.
As pointed out in Maudlin (1994, p. 23).
- 56.
Earman (1986).
- 57.
- 58.
French (1968, Chap. 1). Note that French already remarked that CM did not set specific limitations on the speed of bodies.
- 59.
Galilei (1632, 2nd day).
- 60.
As pointed out in Rindler (2001, p. 6).
- 61.
Rindler (2001, p. 56). However, it may be noted that in the original EPR experiment the two entangled systems are considered as connected by a rigid bar.
- 62.
I follow here the derivation in French (1968, Chap. 3).
- 63.
Lorentz (1904).
- 64.
French (1968, Chap. 4).
- 65.
Rindler (2001, p. 12).
- 66.
Rindler (2001, pp. 39–40).
- 67.
Rindler (2001, p. 15).
- 68.
I follow here the derivation in French (1968, Chap. 1).
- 69.
Rindler (2001, p. 8).
- 70.
Rindler (2001, p. 113).
- 71.
- 72.
Penrose (2004, Chap. 15).
- 73.
- 74.
Misner et al. (1970, p. 10).
- 75.
Misner et al. (1970, p. 241).
- 76.
Although one could hypothesise the existence of superluminal particles (the so-called tachyons) without physical inconsistencies, it is also admitted that this move would be of no use for solving the EPR problem (Maudlin 1994, pp. 72–80).
- 77.
But the convention \((-+++)\) is also used.
- 78.
Schwartz (2014, Chap. 10).
- 79.
- 80.
Peirce (1958, 1.326).
- 81.
Nevertheless, starting from the fact that dyadic relations represent a kind of resistance to certain classes of action, he interpreted the latter as dynamical while understood triadic relations as displaying accordance with a law, what can be considered even as a reversal of the above distinction (Peirce 1958, 5.472). This was pointed out in Auletta (2011a, Sect. 3.2.3). See also Auletta (2016).
- 82.
The reader might take into account the rather technical exposition in Ruelle (1990).
- 83.
Poincaré (1907).
- 84.
As first pointed out in Howard (1985).
- 85.
- 86.
Clauser et al. (1969).
- 87.
Einstein (1948).
- 88.
Descartes (1641a, pp. 25–26), and relative objections of Gassendi with responses.
- 89.
- 90.
- 91.
- 92.
- 93.
Leibniz (1702).
- 94.
- 95.
A problem pointed out in Peirce (1886). Peirce calls this the iconic side of signs and representations.
- 96.
On this difficult subject see the well-documented book (Earman 1989). Although I do not always agree with some of the conclusions it is a fundamental reference work.
- 97.
- 98.
- 99.
- 100.
Einstein (1948).
- 101.
An interpretation that it is likely to have been formulated by one of the fathers of the theory of symmetries, the German mathematician and physicist Hermann Weyl (1885–1955) for the first time (Weyl 1949). Interesting are the conversation between Popper and Einstein in which the former defined this vision as Parmenidean (Popper 1974, pp. 148–150). For a brief and untechnical examination of the problem see Auletta (2011a, Sect. 3.3.4).
- 102.
- 103.
Leibniz (1715–1716, p. 25) : “Continuatis autem in tempore, extensione, qualitatibus, motives, omnique naturae transitu reperitur, qui numquam fit per saltum”.
- 104.
- 105.
- 106.
- 107.
Leibniz (1712–1714, Sect. 32) : “Nous considerons qu’aucun fait ne sauroit se trover vray ou existant, aucune Enontiation veritable, sans qu’il y ait une raison suffisante, pourquoy il en soit ainsi et non pas autrement, quoyque ces raisons le plus souvent ne puissent point nous tre connues”. See also Leibniz (1677). About the potential conflict between the classical principle of sufficient reason and QM see Auletta (2006).
- 108.
Bohr (1928).
- 109.
Kistler (2006, p. 9).
- 110.
On this the work of the French physics and mathematician Laplace is paradigmatic Laplace (1825).
- 111.
Quoted in D’ariano et al. (2017, Sect. 5.1). I fully agree with what the authors say here about the confusion causality–determinism.
- 112.
D’ariano et al. (2017, Sect. 5.1).
- 113.
In Mehra and Rechenberg (1982–2001, VI, p. 678) , a definition of a physics dictionary has been reported: “The physicist considers causality as identical with determinism, that is, with the unique fixing of the future events by the present ones according to the laws of nature”.
- 114.
Poincaré (1911, p. 49).
- 115.
Born (1949b, Chaps. 2–4).
- 116.
Although a deterministic mechanics is still possible that does not satisfy continuity: see Auletta (2004).
- 117.
Hume (1777, pp. 32–47).
- 118.
Russell (1912–1913).
- 119.
Norton (2003).
- 120.
Bohr (1928).
- 121.
- 122.
- 123.
- 124.
- 125.
Armstrong (1983, Chaps. 2–3). This philosopher has contributed very much to our understanding of the laws of Nature.
- 126.
Armstrong (1983, p. 31).
- 127.
- 128.
See also Kistler (2006, p. 67).
- 129.
- 130.
See van Fraassen (1989), especially p. 275.
- 131.
It seems that E. Anscombe has been the first scholar to have proposed a particularist view of causality (Anscombe 1971).
- 132.
This why Margenau tells us that causality is nothing else than a law ruling the transformation of a physical state into another minus the temporal dimension (Margenau 1950, Chap. 19).
- 133.
Auletta (2005).
- 134.
Poincaré (1907).
- 135.
Poincaré (1907).
- 136.
Tryon (1973) .
- 137.
See Shimony (1965) for interesting comments on Whitehead relative to this issue.
- 138.
Laplace (1796, pp. 541–544).
- 139.
Bohr (1949a, p. 230).
- 140.
See Auletta (2000, p. 131).
- 141.
- 142.
Such a description can be found in Auletta (2000, p. 448).
- 143.
See Auletta (2000, pp. 449–451).
- 144.
- 145.
- 146.
A similar point has been discussed in Kistler (2006, pp. 34–35).
- 147.
- 148.
Greenberger and Svozil (2005).
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Auletta, G. (2019). The Main Problems. In: The Quantum Mechanics Conundrum. Springer, Cham. https://doi.org/10.1007/978-3-030-16649-6_2
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