The Main Interpretations

Auletta, Gennaro

doi:10.1007/978-3-030-16649-6_3

The Main Interpretations

Gennaro Auletta^2,3

Chapter
First Online: 18 August 2019

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Abstract

I have grouped the main problems in interpreting QM in the previous chapter. In the present chapter, we shall deal again with these four groups of problems (formalism, measurement, non-locality and causality) but by introducing the reader to the main solutions that have given to them and critically evaluating them. In fact, only a careful examination of what has been said on the subject could help us to find an original way to see the problems. It helps us to restrict the range of the viable pieces of interpretation by excluding those hypotheses that, for one reason or the other, cannot work and thus to attribute the right values to those hypotheses that resist critical analysis. I stress that no interpretation or hypothesis can be dismissed in few words for at least two good reasons: (i) QM looks like a complex array of puzzles, what requires extreme care in making any assertion, and (ii) all of these interpretations have been provided by excellent scholars who have tried to deeply penetrate that riddle.

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Notes

1.
For a quick summary see Auletta (2004b).
2.
London and Bauer (1939) .
3.
For this example see Auletta et al. (2009, Sect. 9.1).
4.
See Lüders (1951) .
5.
Wigner (1961). See also Stapp (1982, 1993).
6.
Apart from the Wigner’s theorem (Sect. 1.2.5), I recall here the quasi-probability Wigner function (of both position and momentum), important especially in quantum optics. I also recall his crucial contributions to group theory and its applications to QM.
7.
Wheeler (1983, p. 184). It has been pointed out that from 1930s on Bohr considered the term phenomenon as referred to a dynamical process and not to a state (Stachel 2017) .
8.
Although we can find some sparse statements of Bohr that go in this direction (Bohr 1948; Home and Whitaker 2007, p. 61).
9.
For a similar statement see Eddington (1939, p. 50) .
10.
For perception this was shown already by the Gestalt school. For a short summary see Auletta (2011a, Sect. 4.4.4).
11.
Zeilinger (2005) .
12.
Kant (1787). A point on which also Einstein agreed (Einstein 1934, p. 166) .
13.
Berkeley (1710) .
14.
It is not by chance that the idealist philosopher G. W. F. Hegel vindicated the supremacy of the ‘dialectical method’, that is, of the procedures over the facts.
15.
See Geroch (1978, p. 35) .
16.
The epoché is a notion introduced in philosophy by the father of phenomenology (Edmund Husserl 1859–1938; Husserl 1931) .
17.
Wigner (1960).
18.
Carnap (1928), Margenau (1950, Sect. 4.5) .
19.
Munowitz (2005, p. 43).
20.
Deutsch (1997, p. 57), Auletta (2011a, Chaps. 2 and 4). It seems to me that Einstein goes in the same direction when he says that there are conceptual constructions but they need to be validated in their reference to the “real” (Einstein 1949b) .
21.
Peirce (1898, p. 170). A synthetic examination of this issue can be found in Auletta (2011c Sect. 2.1.4). See also Popper (1982, Preface).
22.
As pointed out in Peirce (1877). This was very well understood by the Scottish philosopher Thomas Reid (1710–1796) (Reid 1764) .
23.
As also remarked in Heisenberg (1952, p. 22, 30) .
24.
Heisenberg (1927). On the problem see also Auletta (2000, Sect. 6.2).
25.
Renninger (1960). In his reply, annexed to Renninger’s paper, Heisenberg essentially reiterates his instrumentalist standpoint.
26.
See Auletta (2000, Sect. 14.2.1).
27.
As pointed out in Ballentine (1970). On the history of the problem see Jammer (1974). See also Adler (2004) and Auletta (2000, Sects. 6.5, 23.1) for a summary of these interpretations.
28.
Peres and Zurek (1982).
29.
Everett (1957) .
30.
Schrödinger (1935a) .
31.
Spinoza (1677). The reader interested in this kind of subtleties may consult (Auletta 1994, Chap. 2).
32.
Deutsch (2011, Chap. 12) .
33.
Dewitt (1970, 1971) . See also Everett (1973) .
34.
Zurek (1981). See also Auletta and Wang (2014, Sect. 9.4).
35.
Basic references are Wang et al. (1991), Scully et al. (1991) .
36.
For the relevance of the context see also Epperson and Zafiris (2013, p. 92) .
37.
Zurek (2010, p. 410).
38.
As affirmed in Wallace (2012, Sect. 1.9) .
39.
A certain reject of the measurement problem by the scientific community is well expressed by the title “Against‘Measurement”’ of reference (Bell 1990).
40.
The problem was discussed in Graham (1973) where the solution offered appears to be ad hoc. See also Maudlin (1994, p. 5). For a collection of different points of view on such an issue see Saunders et al. (2010, Parts 3–4) .
41.
As in Wallace (2012, Chap. 4) .
42.
On this stuff see also Norsen (2017, Sect. 10.2) .
43.
Leibniz (1686, 1710). For an examination of the problem see also Auletta (1994, Chap. 4).
44.
Lewis (1986) .
45.
Leibniz an Arnauld, 14th July 1686, in Leibniz (2019, II, pp. 53–54) : “Si dans la vie de quelque personne et même dans tout cet univers quelque chose alloit autrement qu’elle ne va, rien nous empêcheroit de dire que se seroit une autre personne ou un autre universe possible”.
46.
Deutsch (1997, p. 93) .
47.
As pointed out in Auletta (2009). Once, addressing the audience of a symposium, D. Deutsch has said: “I’ll start with a simple fact: in this room, in some nearby universes, Hugh Everett is here with us, celebrating. Perhaps he’s there, in that seat where Simon is. And therefore, in those universes, Simon is somewhere else” (Deutsch 2010, p. 542) .
48.
Deutsch (1997, p. 126) .
49.
Wallace (2010, p. 54) .
50.
The problem was first raised in Barrow and Tipler (1986). For a different point of view on the subject see Rees (1999). See also Tegmark et al. (2006). The existence of natural constants does not seem to be in contrast with the relational standpoint that I support. With the words of Robert Laughlin, “all the fundamental constants require an environmental context to make sense” (Laughlin 2005, p. 19).
51.
Tegmark (2003) .
52.
Zurek (2004, 2007, 2009). See also Smolin (1997).
53.
There is a whole debate on this subject: see Lockwood (1996), Deutsch (1996), Chalmers (1996). See also Auletta (2004b). This was actually an important idea in oriental philosophy: see Schrodinger (1958, Chap. 4) and also Shimony (1981) .
54.
The first seeds of this new approach can be found in Zeh (1970). For a wide but rather technical account see Auletta et al. (2009, Sect. 9.4).
55.
This was the subject of what is become now a classical study (Zurek 1982). For a good and extensive introduction to decoherence see Schlosshauer (2007) .
56.
A point of view strongly supported in Joos and Zeh (1985). See also Giulini et al. (1996), Schlosshauer (2007, Chap. 3) .
57.
Quoted in Mehra and Rechenberg (1982, VI, p. 754).
58.
Joos and Zeh (1985), Schlosshauer (2007, p. 135) .
59.
See Hartle and Hawking (1983), Griffiths (1984), Halliwell (1993). See also Wallace (2012, Sect. 3.9) .
60.
Halliwell (2010).
61.
Zurek (1989a, b), Barnett and Phoenix (1989), Cerf and Adami (1997) . See also Auletta et al. (2009, Sect. 17.2), Auletta and Wang (2014, Sect. 11.7).
62.
Zurek (2007, 2013).
63.
Zurek (2010).
64.
Elby and Bub (1994). See also Auletta et al. (2009, Sect. 9.4.1).
65.
Bell (1990).
66.
For a deeper understanding of this issue I recommend (Zwolak and Zurek 2013). I shall come back on these problems.
67.
As shown in Zurek (1982, 1991).
68.
Wallace (2010) .
69.
See Paz et al. (1993, 489–94) .
70.
For the use of the notion of global see also Schlosshauer (2007, Sect. 2.3) .
71.
Brune et al. (1996), Monroe et al. (1996).
72.
At one moment Bohr says that “our interpretation of the experimental material rests essentially upon the classical concepts” (Bohr 1928) .
73.
Pioneering studies are Wootters and Zurek (1979), Mittelstaedt et al. (1987). See also De Muynck (2002).
74.
Peirce (1891).
75.
Mehra and Rechenberg (1982, VI, p. 709). In fact, Heisenberg explicitly criticised this point: see also Heisenberg (1969, Chap. 6); Mehra and Rechenberg (1982, VI, p. 738 and ff.).
76.
In general, Einstein was quite sympathetic with the views of Schrödinger (Home and Whitaker 2007, pp. 33–34, 86), at least until 1935.
77.
For deepening the subject see Lindblad (1973, 1983) .
78.
Tegmark et al. (2006) .
79.
Serjeant (2010, Chap. 6) .
80.
For a short summary on classical information theory see Khinchin (1957). On quantum entropy see the rather technical book (Ohya and Petz 1993).
81.
Shannon (1948).
82.
For this thermodynamical quantities the reader may consult a textbook like (Huang 1963) .
83.
Attempts at falsifying Shannon’s measure of information in its application to QM have proved to be not very successful so far. For a relative recent approach in this sense see Brukner and Zeilinger (1999, 2001, 2005) and relative literature: (Mana 2004; Shafiee et al. 2006).
84.
Wehrl (1978). This is an extensive paper on the subject.
85.
Lieb (1975).
86.
For some additional considerations see Auletta (2011a, Chap. 2).
87.
For a measure of entanglement see Vedral et al. (1997).
88.
Barnett and Phoenix (1989). See also Auletta et al. (2009, Sect. 17.2).
89.
See Barnett and Phoenix (1991) for details on these proofs.
90.
Deutsch (1983). See also Nielsen and Chuang (2000, p. 503). For an overview of other proposals see Auletta (2000, Sect. 42.2).
91.
I synthesise here the results of Partovi (1989). See also Auletta et al. (2009, Sect. 17.3).
92.
Araki and Lieb (1970). See also Wehrl (1978) .
93.
Although there is often a difference between Boltzmann and Shannon entropy related to the degrees of freedom (which in general are higher in the former case), when we deal with elementary particles they converge (Bekenstein 2003).
94.
As recalled in Auletta (2011c, Sect. 3.2.1).
95.
Quoted in Shimony (1965, p. 317). Shimony defines Schrödinger as a realist.
96.
Wheeler (1990) .
97.
They are formulated in Bell (1990).
98.
A personal communication reported in Auletta (2011a, p. 38).
99.
Planck (1922) .
100.
Auletta (2011a, Sect. 2.1).
101.
Timpson (2013, Sects. 2.2.5, 4.4).
102.
As pointed out in Schumacher (1990), Rozema et al. (2014). See also Auletta (2006b, 2011a, Sect. 2.2.2).
103.
See also Deutsch (1997, p. 97) .
104.
Holevo (1998). See also Nielsen and Chuang (2000, Sect. 12.1.1).
105.
A good and basic textbook is Ling and Xing (2004) .
106.
On quantum computation a good textbook is Nielsen and Chuang (2000). For a short summary of the subject see Auletta et al. (2009, Sect. 17.7), Auletta and Wang (2014, Sect. 11.4). I shall come back on these problems.
107.
D’Ariano et al. (2017, Sect. 12.3) .
108.
On this distinction see Auletta (2011c, Sect. 3.2.5).
109.
Conway and Kochen (2006, 2009) .
110.
Zurek (2013).
111.
This is extensively discussed in Auletta (2011a, Chaps. 7–11). See literature quoted there.
112.
The reader may have a look at Auletta (2011a, Sect. 2.2).
113.
As pointed out in Auletta (2006b).
114.
Rovelli (1996, 2005) .
115.
Bennett (1973).
116.
Shannon (1948).
117.
Schrödinger (1992) .
118.
Brillouin (1962).
119.
Lieb (1975).
120.
On this issue see Ott (1993), Schuster (1988) .
121.
On this point see Cohen-Tannoudji (1991, pp. 52–53, 68–69) .
122.
Shannon (1948). See also Nielsen and Chuang (2000, Sect. 12.2.1).
123.
On this see Battail (2014, p. 56) .
124.
Laplace (1796, pp. 541–44) .
125.
The reference papers in this subject are Plesch and Buz̆ek (2010) for the theoretical study and (Rozema et al. 2014) for the performed experiment.
126.
This is likely due especially to Podolsky (Home and Whitaker 2007, p. 109), although I think that Einstein considerably contributed.
127.
The reader may also have a look at Auletta et al. (2009, Sect. 16.1), Auletta and Wang (2014, Sect. 10.1).
128.
On these problems see Jammer (1974, Chap. 6). See also Harrigan and Spekkens (2010), although I disagree with the authors (and with A. Fine, who first introduced this idea in Fine (1981)) that the EPR paper does not correspond to Einstein’s view (the fact that Podolsky may have been the material extensor of the article tells us nothing about the issue at the stake), and consider their judgement about the presumed “opaque” logical structure of the argument a true misunderstanding of what the paper says. The argument is clearly complex but not obscure: it could have been reduced to implication (3.99) and an experimental evidence, but to assume the hypothetical validity of the uncertainty relations was mandatory.
129.
As pointed out in Howard (1992) .
130.
Einstein et al. (1935) .
131.
See also Margenau (1950, pp. 299–300) .
132.
Bohr (1935a, b). See also Auletta and Wang (2014, Sect. 10.2).
133.
Bohr (1928) .
134.
On this point see Braginsky and Khalili (1992, pp. 40–49). For a short summary see also Auletta et al. (2009, Sect. 9.11.1).
135.
Bohr (1935a) .
136.
This way of thinking pertains the family of forms of non-monotonic reasoning that are typical for empirical problems especially when induction is involved: see Pearl (1988, p. 59) .
137.
Quoted in Home and Whitaker (2007, p. 64).
138.
For a look at the different forms that the Copenhagen Interpretation has received see Auletta (2000, Chaps. 6–8). See also Shimony (1981) on Bohr’s epistemology.
139.
See, e.g. Deutsch (2011, Chap. 12) .
140.
Already in 1918 Einstein tells us that “no logical path leads from perceptions to the principles of the theory” (Einstein 1918, p. 109). See also Einstein (1930, p. 114). This conviction accompanies the great physicist through his whole life since still in 1952 he tells us that “there is, of course, no logical way to the establishment of a theory”, quoted in Rindler (2001, p. 33). From this correct premise, Einstein infers that “all concepts, even those that are closest to experience, are from the point of view of logic freely chosen conventions” (“Alle Begriffe, auch die erlebnis–nächsten, sind vom logischen Gesichtspunkte aus freie Setzungen”) (Einstein 1949a, pp. 12 and 13) .
141.
As stressed by authoritative epistemologists (Hempel 1953, Nagel 1961). In Margenau (1950, Sect. 8.2) one speaks of “latency”. See also D’Espagnat (1995, pp. 221–22), Bird (2007) .
142.
Whitaker (2004), Maudlin (1994) .
143.
It is not by chance that in Bohr (1949, p. 230) Bohr speaks of “the necessity of considering the whole experimental arrangement”.
144.
Bohr (1935b) .
145.
Although doubts can be cast on whether Bohr had ever consequently supported an interactionist point of view (Stachel 2017) .
146.
Schrödinger (1935a, b). See also Auletta and Wang (2014, Sect. 10.2).
147.
Schrödinger (1936) .
148.
Schrödinger (1936). For a summary see also Auletta (2000, Sect. 34.1).
149.
Mehra and Rechenberg (1982, VI, p. 744).
150.
As proposed in Auletta (2007).
151.
For historical survey see Jammer (1974, Chap. 7). According to Jammer, hidden variables are one of the most recent attempts at explaining visible things with invisible ones. Einstein himself may have initially contributed (Home and Whitaker 2007, p. 89), although is engagement appears modest and he was never particularly supportive of this research project (Jammer 1974, pp. 254–55) .
152.
Auletta (2000, p. 543).
153.
Auletta (2000, p. 544).
154.
Bohm (1952) .
155.
de Broglie (1956). On this issue see also Auletta (2000, Sect. 28.1), Auletta et al. (2009, Sect. 16.3).
156.
See Auletta (2000, Sects. 28.2–28.3).
157.
As proposed in Bialynicki and Mycielski (1976). Experimental tests disproved this hypothesis (Shull et al. 1980).
158.
The original idea was formulated in Selleri (1969). There is wide literature on that issue (Garuccio et al. 1982; Croca 1987; Hardy 1992; Zou et al. 1992; Auletta and Tarozzi 2004). See also Fano (2014) .
159.
See Jammer (1974, Sect. 7.5) .
160.
On this subject I recommend the extensive book (Holland 1993). For understanding Bohm’s quantum potential theory I recommend (Bricmont 2016) .
161.
On this subject see Auletta et al. (2009, Sect. 10.5.3).
162.
Bohm (1980), Bohm and Hiley (1993), Holland (1993), Hiley (1999) . See also Auletta (2000, Sect. 32.6). Bohm proposed that the multidimensionality of information should correspond to a certain extension of the Hilbert space’s structure.
163.
This seems related to the fact, pointed out by the German physicist Walther Bothe (1891–1957), that, even when wave functions of the two EPR particles are factorised (that is, are in a product state of the kind (1.388)), the HVs of the two systems can be still mutually dependent (Home and Whitaker 2007, p. 89).
164.
On this see Auletta (2000, p. 561).
165.
Englert et al. (1994).
166.
One has spoken of exorcised Bohmian theory (Conway and Kochen 2006, p. 1454) .
167.
Hiley (1999).
168.
Originally proposed in Aharonov and Bohm (1959). There is a now a wide literature in this subject and a helpful textbook is Peshkin and Tonomura (1989).
169.
Berry (1984, 1987). For a summary see also Auletta et al. (2009, Sect. 13.8).
170.
Von Neumann (1932, pp. 163–71) .
171.
Bell (1966).
172.
Bell (1966, 1971).
173.
Gleason (1957). See also Landsman (2017, Sects. 2.7–2.8 and 4.4), Auletta (2000, Sect. 11.5).
174.
Bell (1966).
175.
Auletta (2000, Sect. 32.3), Auletta et al. (2009, Sect. 16.4.1).
176.
Kochen and Specker (1965). See also Pitowsky (1989), Auletta and Wang (2014, Sect. 10.7), Landsman (2017, Sect. 6.1) .
177.
De Morgan (1847) .
178.
See also Bub (1989) .
179.
Whitehead (1925).
180.
Bell (1964).
181.
Auletta (2000, pp. 549–50).
182.
Conway and Kochen (2006) .
183.
I have, also in collaboration with other scholars, dealt several times with these problems (Auletta 2000, pp. 589–91; Auletta et al. 2009, Sect. 16.4.2; Auletta and Wang 2014, Sect. 10.4).
184.
Clauser et al. (1969). The authors used for the first time a stochastic HV theory and not a deterministic one as in the case of Bell’s previous paper. The formulation that I have reported here is slightly different relative to that of their original paper and is due to a later paper of Bell (1971).
185.
The reference paper is Braunstein et al. (1992).
186.
I invite the reader who likes to know more about these experiments to consult (Auletta 2000, Chap. 35) and literature quoted there. With the language of category theory, we have now an equaliser of quantum theory and experiment (Spivak 2013, Sect. 2.5.3).
187.
Aspect et al. (1982) .
188.
Santos (1991) .
189.
Among the first reported experiments I quote (Shih and Alley 1988; Ou and Mandel 1988) .
190.
Marshall et al. (1983), Garuccio and Selleri (1984), Marshall and Santos (1985), Ferrero et al. (1990) .
191.
Żukowski et al. (1993). See also Auletta et al. (2009, Sect. 16.6).
192.
Braunstein et al. (1992).
193.
Shimony (1983) .
194.
This is why to say that entanglement is an exclusive and discriminating connection among particles, as unfortunately is written in Maudlin (1994, p. 23), is a mistake.
195.
First proposed in Bennett and Wiesner (1992), Bennett et al. (1993). See also Auletta and Wang (2014, Sect. 11.5).
196.
Bouwmeester et al. (1997), Furusawa et al. (1998).
197.
Horodecki et al. (2005), Cavalcanti et al. (2011) .
198.
Cerf and Adami (1997) .
199.
Wiesner (1983).
200.
Bennett and Brassard (1984) .
201.
Battail (2014, p. 15) .
202.
See Abramsky and Coecke (2009) .
203.
As pointed out in Timpson (2013, Sects. 3.7 and 4.1).
204.
Eberhard (1978). See also Auletta (2000, Sect. 36.5), Auletta and Wang (2014, Sect. 10.6).
205.
The original paper is Popescu and Rohrlich (1994). A summary of this subject can be found in Auletta and Wang (2014, Sect. 12.2).
206.
Auletta (2011b).
207.
Pawłowski and Scarani (2016) .
208.
Tsirelson (1980).
209.
Masanes et al. (2006) .
210.
Formulated in Pawłowski et al. (2009). See also Pawłowski and Scarani (2016) .
211.
Another way to consider the problem is that hyper-correlations would violate the uncertainty relations (Oppenheim and Wehner 2010) .
212.
‘T Hooft (2016, p. 32) .
213.
Pawłowski and Scarani (2016) .
214.
As pointed out in Auletta (2011b).
215.
Wiesner (1983).
216.
See the summary in Nielsen and Chuang (2000, Sect. 12.5.1).
217.
As pointed out in Auletta (2011a, Chap. 2).
218.
The connection between network of entangled systems and non-locality has been explored in Cavalcanti et al. (2011).
219.
Greenberger et al. (1989, 1990). See also Auletta et al. (2009, Sect. 16.7.2).
220.
As shown in Krenn and Zeilinger (1996) .
221.
As proposed in Aravind (1997).
222.
The reference paper is Auletta et al. (2008).
223.
Aristotle Phys. (1950, I, 7–9) .
224.
I think that the notion of Quasi-gegenstand (almost object) introduced by Carnap aims at both types and type–tokens, since it concerns general objects but also some individual ones (Carnap 1928, Sect. 27). Armstrong has supported a theory of universals (Armstrong 1978). In Armstrong (1983, pp. 100–101) he introduces the notion of quasi-universal that perhaps expresses the same concept of type–token here. See also Margenau (1950, Sect. 15.4) .
225.
‘T Hooft (2016, pp. 8–9). Superposition states are called templates, which corresponds somehow to the notion of type.
226.
‘T Hooft (2016, p. 44) .
227.
The author seems aware of this problem (‘T Hooft 2016, pp. 51–54) .
228.
Collins (2010) .
229.
Auletta et al. (2008).
230.
Boltzmann (1896, 1898). On this subject see Auletta (2011a, Chap. 25).
231.
Born (1949, p. 44) .
232.
Aristotle Phys. (1950, II, 3). For deepening these issues see Anagnostopoulos (2009) .
233.
It could be said that this insight was originally due to the Italian physicist Franco Selleri (1936–2013) when he affirmed that quantum waves can have physical effects although deprived of momentum and energy, i.e. of dynamical characters, what hints implicitly to a kind of causal constraint (Selleri 1969). Unfortunately, in the following Selleri was not always consequent with this position and searched for an empty wave as a kind of localised object (Sect. 3.3.4), loosing in this way the notion of causal constraint that was implicit in his former point of view.
234.
See Pasnau (2004), Torcal (2013) .
235.
As I have recalled in Auletta (2011a, Sect. 11.1.2; 2011c, Sect. 3.3.7).
236.
In fact, there is currently a flourishing of Aristotelian and neo-Aristotelian studies in philosophy.
237.
As pointed out in Auletta (2008, 2013), Stanzione (2013) .
238.
As remarked in Peirce (1902). Unfortunately, here and elsewhere Peirce speaks of final causes and not of formal ones.
239.
On network theory I recommend (Barabási 2002; Barrat et al. 2008) .
240.
On the subject see Edelman and Gally (2001). See also Auletta (2011a, Sect. 8.2.5) and literature quoted there.
241.
I have stressed this in Auletta (2011c, Sect. 3.2.5). See also Auletta and Torcal (2011) .
242.
On this see D’Ariano et al. (2017, Sect. 5.1) .
243.
Born (1949, Chap. 2) .
244.
Born (1949, Chaps. 3–4, 9) .
245.
Laplace (1825) .
246.
Baumgarten (1739), Kant (1763) . For an examination of the problem see also Auletta (2004a), Auletta (2006a).
247.
Aristotle (1950, 201a 10–19) .
248.
See Auletta (2011a, Sects. 8.2.1–8.2.4).
249.
Whitehead (1929, pp. 43–46 and 61). See also Epperson and Zafiris (2013, Chap. 4) .
250.
Bell (1976, 1981). See also Dieks (1994) .
251.
Shimony (1993): see the index of the volumes.
252.
Zurek (2013).
253.
As reported in Heisenberg (1969, Chap. 5) .
254.
Bridgman (1927, p. 5).
255.
Bridgman (1927, p. 25, 28).
256.
Bridgman (1927, p. 12).
257.
Bridgman (1927, pp. 22–23).
258.
Heisenberg (1927) .
259.
Bridgman (1949).
260.
Einstein (1949b, p. 679) .
261.
Heisenberg (1927) .
262.
Heisenberg (1958, Chap. 3). In my previous work I was too negative on this point although the distinction between possibility and potentiality was already pointed out (Auletta 2000, Sect. 29.2.2).
263.
See also Auletta and Tarozzi (2004, pp. 1680–81) .
264.
It seems that W. Pauli somehow supported a view in this sense (Home and Whitaker 2007, p. 63).
265.
Shimony, who is supportive of the notion of potentiality, reminds us that H. Margenau had already used (in 1949) the notion of “latency” (Margenau 1950, Sect. 8.2; Shimony 1981) .
266.
Heisenberg (1958, pp. 54–55; see also pp. 137–38) .
267.
See also Van Fraassen (1991).
268.
Heisenberg (1958, p. 142) .
269.
As pointed out in Born (1949, Chaps. 6–7) .
270.
Deutsch (2011, Chap. 12) .
271.
An operationalist standpoint in this sense has been supported for the first time in Poincaré (1905, Chap. 3). In particular, he tells us that “to localise an object means to represent the movements needed for reaching it” (Poincaré 1905, p. 67).
272.
As reported in Renninger (1960).

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Gennaro Auletta
Pontifical Gregorian University, Rome, Italy
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Auletta, G. (2019). The Main Interpretations. In: The Quantum Mechanics Conundrum. Springer, Cham. https://doi.org/10.1007/978-3-030-16649-6_3

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