Feyerabend on the Quantum Theory of Measurement: A Reassessment

ABSTRACT

In 1957, Feyerabend delivered a paper titled ‘On the Quantum-Theory of Measurement’ at the Colston Research Symposium in Bristol to sketch a completion of von Neumann's measurement scheme without collapse, using only unitary quantum dynamics and well-motivated statistical assumptions about macroscopic quantum systems. Feyerabend's paper has been recognised as an early contribution to quantum measurement, anticipating certain aspects of decoherence. Our paper reassesses the physical and philosophical content of Feyerabend's contribution, detailing the technical steps as well as its overall philosophical motivations and consequences. Summarising our results, Feyerabend interpreted collapse as a positivist assumption in quantum mechanics leading to a strict distinction between the uninterpreted formalism of unitary evolution in quantum mechanics and the classically interpreted observational language describing post-measurement outcomes. Thus Feyerabend took the no-collapse completion of the von Neumann measurement scheme to show the dispensability of the positivist assumption, leading the way to a realistic interpretation of quantum theory. We note, however, that there are substantial problems with his account of measurement that bring into question its viability as a legitimate foil to the orthodox view. We further argue that his dissatisfaction with the von Neumann measurement scheme is indicative of early views on theoretical pluralism.

Acknowledgments

The authors would like to thank Jan Faye, Geoffrey Hellman, Don Howard, Thomas Müller and Jos Uffink as well as audiences at the universities of Konstanz, Minnesota and Wuppertal for illuminating discussions and useful feedback. We also want to thank two anonymous referees for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Of the first phase, not much evidence is available; see Feyerabend (2016) and commentary in Kuby (2016).

2 See e.g. Feyerabend (2015a, 34, 2015b, 12).

3 See Kuby (2021) for a review and assessment of this phase in the context of Feyerabend's general conception of philosophy; cf. also van Strien (2019) for similar conclusions.

4 The paper was published in English as Feyerabend (1957a); a shorter version, excluding the philosophical discussion, was published in German as Feyerabend (1957b) in Zeitschrift für Physik.

5 It is important to remember that the concept denoted by the German expression ‘Wissenschaft’ and ‘wissenschaftliche Erkenntnis’ is not limited to the natural sciences, but includes humanities and formal sciences, too.

6 As Faye and Jaksland (2021, 264) note:

Around that time [1927], it was generally assumed that unobservable quantities should be eliminated from physics, a view advocated by Pauli, Born and Jordan, and that Einstein [in 1905], under the influence of Ernst Mach, had been successful in his attempt to meet this demand by first rejecting Newton's notion of absolute simultaneity and then Newton's absolute space and time.

7 See e.g. Kaiser (1992), Chevalley (1994), Cuffaro (2010) for Neo-Kantian interpretations of Bohr's philosophy.

8 That is to say, a system which is not part of an ensemble and whose preparation we have complete knowledge of and so can be treated as being in a pure state.

9 Connecting with Del Santo (2022), the Colston Symposium occurred during a period in which Feyerabend's role with Popper as the sympathetic pupil was beginning to show the first crack. This is made apparent in his contribution in which he defends a subjective account of probabilities directly opposing the propensities view of Popper, yet is still compelled to cite Popper's propensities account in his bibliography (ref. 18 of Feyerabend (1957a)), despite never citing it in the main text. And in a letter sent to Popper shorty before the Colston Research Symposium we read:

[Y]our revision of the usual interpret. of probability is neutral towards the above problem [i.e. has the electron definite momentum and definite position at the same time?] which I think is the central problem of any interpretation of QM, and which has led to the ‘quantum-mess’. Hence I must say that, although your paper is most important for probability as well as for the interpretation of the classical statistical disciplines, it does not contain any contribution towards the main problem of quantum-mechanics, mentioned above. Or if it does, this contribution clearly contradicts the Neumann proof which is not changed by introducing the propensity-interpretation instead of the usual interpretation in terms of relative frequencies (which von Neumann uses). (Feyerabend to Popper, 27 March 1957, p. 3, reproduced in Feyerabend 2020, 254)

See also Collodel (2016) for an extensive analysis of Feyerabend's relation to Popper and his school.

10 See Uffink (2007, Sec. 4) for an extended critical analysis of the H-theorem, Bolzmann's Stosszahlensatz, and the Second Law of thermodynamics from which irreversibility is typically explained.

11 We critically assess the legitimacy of this apparent analogy in section 3.2.

12 Note, this condition on macroscopicity has no bearing on the number of degrees of freedom in question: many-body systems such as superconducting quantum interference devices (SQUIDs) violate assumption (B) with respect to the observers who study them (cf. Ryu, Samson, and Boshier 2020) and are therefore not ‘macroscopic’ in the requisite sense, despite having many degrees of freedom.

13 See Paul Feyerabend, ‘On the quantum-theory of measurement’, undated typescript, HF 08-33-24, Herbert Feigl papers, University Archive, University of Minnesota (referenced in Feyerabend 2020, 254, fn 11).

14 See also van Kampen (1988), where the macroscopicity assumption is applied to quantum measurement.

15 We thank Jos Uffink for several clarifying remarks and suggestions with this reconstruction.

16 A more detailed account of a similar perspective is found in van Kampen (1954).

17 The given labels are our own terminology.

18 Recall that Feyerabend left the details here ambiguous as well, merely alluding to the possible existence of some Hamiltonian operator which would bring about an evolution of a particular form.

19 This point is relevant to the proposal we make in the following section that Feyerabend may have intended for his scheme to serve only as a sort of stop-gap theory.

20 We thank Geoffrey Hellman for raising this point.

21 We thank an anonymous referee for raising this point.

22 For philosophical discussion of this topic, see Barrett (1995) and Callender (2007).

23 Cf. Feyerabend (1960b). Feyerabend first met Bohm at the Colston Symposium in 1957, but only a few months later he would become his colleague at Bristol, where Maurice Pryce hired Bohm as a research fellow (who in turn brought with him his student Yakir Aharonov). In 1961, Bohm became full professor at King's College London.

24 While an extensive treatment of the history of decoherence theory is well-beyond our current aims, it is worth remarking that H. Dieter Zeh, one of the founders of decoherence theory, was at least tangentially aware of Feyerabend's proposal, citing his 1957 paper in Zeh (1989).

25 For a review, see Schlosshauer (2005) and the references therein.

26 Feyerabend is not alone in proposing a pragmatic account: For example, Wilfrid Sellars's pragmatic account shares many similarities and would eventually be adopted by Bas van Fraassen. Another pragmatic account can be found in Everett's account of observers in the relative state formalism defined in his long thesis defended in 1957 to promote a realistic interpretation of quantum theory:

…systems which represent observers…can be conceived as automatically functioning machines (servomechanisms) possessing recording devices (memory) and which are capable of responding to their environment. (Everett 2012, 77)

27 Feyerabend's labels this proposition as ‘thesis I’. The term ‘contextual theory of meaning’ appears in (Feyerabend 1960a) to denote the idea that ‘the meaning of our words is a function of the (theoretical) context in which they occur’; and is used in Feyerabend (1962) to denote the idea that ‘the meaning of a term is not an intrinsic property of it, but is dependent upon the way in which the term has been incorporated into a theory’. Preston (1997, 25–30) and Oberheim (2006, 58–63) have variously argued how ‘thesis I’ and the ‘contextual theory of meaning’ are related. Since these details do not really matter to our discussion, we equate them here.

28 This is a much stronger claim than the usual ‘theory-ladeness’ of observation: as Feyerabend puts it, according to the contextual theory ‘[l]ogically speaking, all [i.e. everyday-experience and theoretical] terms are “theoretical”’ (Feyerabend 1958, 164. fn 23).

29 Cf. the previous quotation.

30 This may suggest a solution to Feyerabend's puzzling claim, which still bestirs scholars, made in the context of the later debate about incommensurability and theory change with Smart, Sellars and Putnam:

In his paper Professor Putnam creates the impression that I am mainly interested in meanings and that I am eager to find change where others see stability. This is not so. As far as I am concerned even the most detailed conversations about meanings belong in the gossip columns and have no place in the theory of knowledge.

while the claim is not free of hyperbole, the solution to the puzzle is Feyerabend's contention that philosophers working in philosophy of science (‘the theory of knowledge’) do not help to make progress in the sciences by simply advancing new ‘theories of meaning’ on philosophical grounds. Rather, progress in the sciences can only be had by entering the scientific discourse. (For an interpretation of Feyerabend's philosophy highlighting the aim of improving science, see Oberheim and Hoyningen-Huene 2000, 373–374). Feyerabend's measurement scheme is such an instance; and here, as we have seen, his contribution involves no ‘meaning’ talk whatsoever.

31 We thank Jos Uffink for raising this point.

32 Paul Feyerabend, ‘On the quantum theory of measurement’. undated manuscript, HF 08-33-26, Herbert Feigl papers, University Archive, University of Minnesota (referenced in Feyerabend 2020, 254, fn 11).

Additional information

Funding

Daniel Kuby was supported by the Volkswagen Foundation. Patrick Fraser was supported in part by the Social Sciences and Humanities Research Council.