Copenhagen and Contingency

[I]f certain equally plausible conditions, rather than the actually occurring and highly contingent historical ones, had prevailed and the interpretation of quantum mechanics had initially taken a very different route from the Copenhagen one around 1925-1927, would our worldview of fundamental microprocesses necessarily have been brought back, by the “internal” logic of science, to our currently accepted picture of an inherently and irreducibly indeterministic nature? Could our present understanding of the behavior of the fundamental laws of nature in terms of an inherently indeterministic nature have been replaced by the apparently diametrically opposed view of absolute determinism? This book argues that the answer to the first question is no and to the second question an emphatic yes. This is not to deny that there were already serious conceptual problems for classical physics. (Cushing, 1994, p. xiif.)

Cushing’s story presupposes some conceptual distinctions. The first looks rather innocent. A scientific theory is composed of a formalism and an interpretation;

“formalism means a set of equations and a set of calculational rules for making predictions that can be compared with experiment. … The physical interpretation refers to what the theory tells us about the underlying structure of these phenomena (i.e., the corresponding story about the furniture of the world – an ontology.” (Ibid., p.

9) One might, however, wonder whether this distinction is really adequate because the Bohm theory after all contains a second equation, the pilot-wave equation or the guidance condition, and additional concepts, the quantum potential and the particle positions, at such places where standard quantum theory has just certain intepretatory rules. Admittedly, one does not have to solve the pilot-wave equation and – apart from some more recent proposals (Valentini, 1996, Albert, 2000) – the particle positions are unobservable in principle, such that the second equation and the Bohmian positions might be counted under the interpretation. But this spoils, it seems, the whole philosophical advantage of the Bohm theory to be simply a theory about particles in motion, and one obtains a theory that is interpretable as if particles were in motion.

Cushing’s concept of formalism, to my mind, is so construed that empirically equivalent theories share the same formalism. This does not seem to meet what the underdetermination thesis was all about because it implicitly exempts the formalism from criticism, or at least it automatically directs all doubts and struggles to the interpretation only.

The second distinction already paves the way towards a philosophical predilection for the Bohm interpretation. “Empirical adequacy consists essentially in getting the numbers right. … An explanation is provided by a successful formalism with a set of equations and rules for its application.” (Cushing, 1994, p. 10) While the deductive-nomological or the covering law model yield successful explanations by unification or reduction, they cannot produce understanding.

[Understanding] is possible once we have an interpretation of the formalism that allows us to grasp the character of an the relations among the phenomena. This is typically associated with an interpretation that can plausibly be defended as a realistic one. … My argument here really begins from the intuition

… that understanding of physical processes involves a story that can, in principle, be told on an event-by-event basis. This exercise often makes use of picturable physical mechanisms and processes. (Ibid., p. 11)

To pick two of Cushing’s examples, Boyle’s law and the EPRB-correlations are empirically adequate descriptions which are explained by the formalisms of statistical mechanics and quantum mechanics respectively; but an explanation is only given by the kinetic theory of gases and the Bohm interpretation respectively. There are also two contingently necessary conditions for understanding.

‘Causality’ and ‘locality’ are logically distinct concepts, with causality being the more central in my scheme of understanding. The actual nonlocality demanded by nature turns out to be of a fairly benign variety: we cannot signal with it … We are able to construct a less incomprehensible, more nearly picturable, representation of the physical universe with Bohm than with Copenhagen. We do have the option of giving up locality while maintaining a visualizable causality. The choice is our to make on purely pragmatic grounds. The origins of the uneasiness about nonlocality may be more psychological than logical. … “If the price of avoiding non-locality is to make an intuitive explanation impossible, one has to ask whether the cost is not too great.”³² My evident sympathy with views such as those on contact action expressed by Maxwell earlier clearly put me into the camp of what has been termed the mechanistic view of physical processes. (Ibid., p. 21f.)

Those readers who dislike the Bohm theory might be tempted to quickly subsume it under the mechanicist world-view of 19th century physics. Against these allegations advocates of the Bohm theory could reasonably emphasize that it is anything but a mechanical theory in the Newtonian sense and that is contains, in virtue of its empirical equivalence with standard quantum mechanics, strongly non-deterministic traits which might be interpreted as a form of quantum chaos.³³

Cushing does not give a priori grounds for preferring the Bohmian ontology of particles in motion rather than Copenhagen talk about measurement results, but he leaves the choice up to pragmatic criteria of theory preference. Although accordingly the ontology of physical theory is conditioned by pragmatic criteria and factual choice, Cushing with Quine rejects a Carnapian conception of ontology as linguistic framework (1950). While the latter approach might provide ‘explanations’ it cannot confer ‘understanding’ – as the concept is defined by Cushing.

We have reached one of the crossroads of post-positivist philosophy and thus the philosophical discussion has to slow down and check the right of way. The first to start is the relation of pragmatic criteria and historical contingency. Investigating

32 Quoted from (Bohm, Hiley, and Kaloyerou, 1987, p. 331); italics by Cushing.

33 See (Dürr, Goldstein, Zanghí, 1992b).

Cushing’s case study will remind us of the holistic character of history and teach us how pragmatic criteria transform in time and between theories. The second to follow is holism philosophically conceived. Reasonable criteria for a proper ontology of a single scientific theory should – on pain of relapsing into Carnap’s frameworks (too) narrowly understood – be able to accommodate other fundamental theories as well.

Otherwise intertheoretical inconsistencies across theories might become conflicts between different metaphysical views even before Kuhnian anomalies abound. Third, let me just stress that Cushing’s conception of mechanism is intimately linked to the Bohmian particle picture, and thus favors a very particular type of ontology. There are other mechanist and realist accounts, according to which particle paths in the Bohmian theory do not qualify as causal processes. Most interesting is Wesley Salmon’s (1984) avowedly mechanistic account of the causal structure of the world, although its author has been quite reluctant to take a stand on quantum mechanics (Cf. Stöltzner, 1999b and Salmon’s comment). To Salmon, a realist explanation is reached by successful reduction to causal processes at a lower level, but these processes are not necessarily deterministic. This shows that the far-reaching identification of realism and determinism typically advocated by Bohmians – but not only by them – is quite problematic. Might thus historical contingency not be a surprisingly effective hideout for metaphysical convictions? And might not large part of the equal rights case depend on accepting this identification?

As Cushing is skeptical about pragmatic criteria, he investigates the influence of contingent historical events on the development of quantum mechanics and finds, expectedly, the Forman thesis along the way. The stage for it is set after dropping some names as “philosophical precedents for the concept of indeterminism in nature.”

(Ibid., p. 96) The list, which contains Charles-Bernard Renouvier, Émile Boutroux, Henri Poincaré, and Harald Høffding, but not Exner, is even less compelling than Forman’s “subterranean anticausality current.” (Forman, 1971, p. 67). No wonder that

“philosophical trends alone did not determine the course of quantum mechanics in the early part of the century.” (Cushing, 1994, p. 97) Cushing modifies Forman’s outlook by two distinctions.

[P]sychological factors play a larger … role in the specific formulation of a theory while sociological ones can be crucial for the acceptance and propagation of an already-formulated theory. Such

“external” psychological or social factors are not solely responsible for the content of science. Science has also its own “internal” demands and constraints that must also be accommodated. I argue that the

“internal” factors were most important for the emergence of the formalism of quantum mechanics,

“external” ones for the nature of the interpretation that was accepted. (Ibid., p. 100)

The approximate identification of internal factors and formalism is necessary to tame historical contingencies to the interpretation and prevent bad effects on the quantum mechanical formalism which standard quantum mechanics and the Bohm theory have in common. From Forman’s standpoint it is surprising why the influence of the milieu should halt at the border between formalism and interpretation. And accordingly Cushing distinguishes

a strong Forman thesis, which would claim a major causal role of the cultural milieu in determining the very form and content of a scientific theory, as opposed to a weak Forman thesis, which would see the cultural milieu as sometimes playing an important part in the acceptance and propagation of an

external nature of the factors that are responsible for creating and shaping the theory itself. (Ibid., p.

100)

While Forman advocates the strong thesis, Cushing limits himself to the weak version.

Consequently the quantum formalism was largely unaffected by the milieu and rationally justified, even before 1927.

But initially two formalisms emerged the equivalence of which was proven only afterwards, though quickly afterwards. There was the wave mechanics route favored by the heterogeneous continuity group (Einstein, deBroglie, Schrödinger) and the matrix mechanics route elaborated by the quite uniform Göttingen and Copenhagen groups (Bohr, Heisenberg, Pauli, Jordan, and Born). Not being part of the German milieu, deBroglie “did believe that one theory should best conform to nature. He felt that classical Hamilton-Jacobi theory provided an embryonic theory of the union of waves and particles, all in a manner consistent with a realist (continuous) theory of matter.” (Ibid., p. 104) After some early interest for Bergson and Poincaré, deBroglie derived support from the philosophy of Émile Meyerson. In was the Austrian Schrödinger who developed deBroglie’s ideas into wave mechanics. At first sight Schrödinger’s theory seemed to support the visualizability requirement of classical theory and “one might expect that the scientific community would have been inclined to take the more conservative of the alternatives on offer.” (Ibid., 107) But matters turned out in favor of matrix mechanics.

I read in Cushing’s account basically three internal factors. First, wave mechanics and matrix mechanics quickly proved to be equivalent formulations quite in line with Heisenberg’s and de Broglie’s joint conviction that there could be only one true theory of quantum phenomena. Second, Born’s stochastic interpretation of the wave function showed that the Schrödinger theory was not so classical as it initially appeared. Third, on the matrix mechanics route “[d]iscontinuities, not causality as such, were initially the key issue.” (Ibid., p. 108) The failed application of the old quantum theory to molecules had already convinced experts that the old picturable electron orbitals were meaningless. This was the “crisis” of the Bohr-Sommerfeld scheme. “The failure of the Bohr-Kramers-Slater theory [moreover] … in 1925 indicated to Bohr that a complete renunciation of the usual space-time methods of visualization of the phenomena would be necessary for further progress.” (Ibid., p.

109) As Beller (1999) convincingly argues, Born’s peculiar consequence was to strive for a theory of particles almost at any cost. But, so Cushing and Beller hold likewise, all these physical arguments were not conclusive to win the case for matrix mechanics not least because it was initially formulated without any interpretative commentary at all. “Heisenberg [merely] believed that a successful mathematical formalism of a physical theory … was of a piece or whole and that it could not be modified in any essential way without destroying the entire structure.” (Cushing, 1994, p. 114)

But the challenge from wave mechanics increased; matrix mechanics was in severe “danger of losing the war on the calculational front.” (Ibid., p. 117) Schrödinger’s equation quickly became the most powerful tool in atomic physics, while Heisenberg’s algebraical methods were – and still are – so clumsy that certain calculations are hardly doable. This lasting difference seems to me further evidence to doubt Cushing’s claim that Schrödinger and Heisenberg were using the same formalism just because the theories were rapidly proven to give the same predictions.

Physicists would continue to prefer Schrödinger’s formalism even if equivalence held

only with a grain of salt; in quantum field theory calculations with inconsistent and thus uninterpretable formalisms abound for merely practical purposes. The more mathematically-minded would cite von Neumann’s (1932) uniqueness theorem as the deeper reason for the equivalence proof and relate that it is a nontrivial feature of finite-dimensional quantum mechanics that all representations are equivalent up to isomorphism. In the quantum field theoretical perspective it appears fruitful to distinguish both formalisms. Moreover, the date when this proof was actually given is an important, but historically contingent fact that influences the distinction between formalism and interpretation in quantum mechanics. Frederik Muller (1997) has recently argued that the equivalence proof taken literally did not concern the theories actually proposed in 1926 but the modified versions current as of 1932. Conversely, one could counterfactually imagine that equivalence would have been established only much later. In the absence of a general proof, Cushing’s concept of formalism would crucially depend upon the equivalence of the predictions actually made to date.

At any rate, the Copenhagen group had to organize an interpretative defense against wave mechanics. It was based on combining two philosophical principles, positivism and finality, with organizational strength. To Göttingen-Copenhagen – so Beller’s more appropriate geography – positivism became the major regulative principle of theory construction. When exhibiting an operationalist attitude and rigorously eliminating all unobservables, matrix mechanicians conceived themselves widely as executing the very program which Einstein had once pursued in relativity theory. But the alleged prototype refused Heisenberg’s positivist company and retorted, according to Heisenberg’s (1971, p. 63) report, that “on principle, it is quite wrong to try founding a theory on observable magnitudes alone. It is the theory which decides what we can observe. … Only theory, that is, knowledge of natural laws, enables us to deduce the underlying phenomena from our sense impressions.” (quoted from Cushing, 1994, p. 110) And also Philipp Frank and Moritz Schlick had to see Einstein moving towards metaphysics.³⁴ Yet, Einstein’s philosophical convictions are quite intricate and they hardly acquiesce in the two-camp picture suggested by Cushing.

The second philosophical element of Göttingen-Copenhagen was the notorious finality claim.

Through his analysis of scattering processes with Schrödinger’s formalism, Born came to the opinion that even perfect initial information still led to uncertainty in the result and this implied, for him, a lack of causality. Why was the complementarity principle taken as being complete and the final word in forbidding even the in-principle possibility of a description of microphenomena that is both causal and pictured in a continuous space time? One response is that (thus far) experience has shown the validity of complementary pairs of descriptions and that belief in the ultimate necessity of complementarity rests on the subjective epistemological criterion of the need for classical concepts and on the indivisibility of atomic phenomena (i.e. Bohr’s act of faith). … For Bohr ‘causality’ meant the applicability of the exact laws of energy and momentum conservation. (Cushing, 1994, p. 112)

Bohr’s later theory of complementary pictures provided “a consistent story, but it does not eliminate, in principle, a causal account.” (Ibid., p. 108) By a mere declaration of faith Bohr ultimately claimed that these consistency arguments ruled out even the possibility of an alternative point of view. “These were not logical or in-principle

refutations, but strong, practical beliefs that became dogma.” (Ibid., p. 108) Now we have assembled all those commitments which, to Cushing’s mind, form the intersection of the interpretations of Heisenberg, Born, and others and can thus be considered as the Copenhagen interpretation: “complementarity, completeness of the description (in terms of the state vector or probability amplitude), a prohibition against any possible alternative causal description in a space-time background, and a positivistic attitude.”(Ibid., p. 31)

I doubt whether these three creeds are able to keep the Copenhagen interpretation together. One might even wonder to what extent the Copenhagen interpretation still historically existed as an independent position after John von Neumann’s Mathematical Foundations of Quantum Mechanics was published in 1932.³⁵ There the formalism was axiomatized, and the finality claim accordingly obtained a precise meaning and was based on explicit presuppositions in the form of a No-hidden variable theorem. Moreover, the brand name “Copenhagen Interpretation”

did not come up until the 1950s (Howard, 2002).

At any rate, Cushing’s thesis does not really depend upon the exact philosophical content of the finality claim because he also advances an argument about the contingent course of history. Referring to works of Beller (reaffirmed in Beller, 1999), Cushing holds that the conflict between Copenhagen and wave mechanics “can be characterized as one over superiority and professional dominance.” (Cushing, 1994, p. 117)

The Copenhagen group had the talent, organization, and drive to carry the day in establishing the hegemony of its view. Heisenberg’s uncertainty relation paper was a major step in accomplishing this.

The Copenhagen group worked in concert, while its opponents (Einstein, Schrödinger, deBroglie) pulled each in his own direction. … The Bohr Institute in Copenhagen had an enormous influence on an entire generation of leading theoretical physicists who passed through it. … As Ralph Kronig recalled, Bohr and his close colleagues were authority figures and a young person did not go against them. (Ibid., p. 117)

On the 1927 Solvay Congress, the united Göttingen-Copenhagen team won a great victory against deBroglie’s first pilot-wave theory which promised a resurgence of a causal and realist world view. Pauli brushed it aside by an example which de Broglie could rebut no other than by ad hoc arguments; a definitive answer to Pauli’s objections was obtained only by Bohm (1952). On the congress, “neither Einstein nor Schrödinger gave positive support to de Broglie’s ideas. De Broglie presented a conceptual mixture of waves and particles, which did not incline Schrödinger kindly toward it since, at this time, he wanted an interpretation based wholly upon the wave concept.” (Cushing, 1994, p. 118) In his speech to the congress, Einstein emphasized

“that any truly fundamental theory … should be a complete theory of individual processes (as opposed to yielding information about the statistics of ensembles only).

… Still, Einstein remained distrustful of this particular model of de Broglie. This was likely related to his own abortive attempt at a hidden-variables theory” (Ibid., p. 118f.) In May 1927, that is, just five months before the congress, Einstein had written a paper entitled “Bestimmt Schrödingers Wellenmechanik die Bewegung des Systems vollständig oder nur im Sinne der Statistik?” (Does Schrödinger’s Wave Mechanics Determine the Motion of a System Completely or Only in the Sense of Statistics?), but

35 This is, for instance, Peter Mittelstaedt’s opinion; private communication.

quickly withdrew it; the piece never appeared in print. The reason was most probably the “peculiar sort of ‘entanglement’ between independent systems that appears when they are described as a composite system in multidimensional configuration space.”

(Belousek, 1996, p. 443) According to Belousek’s detailed analysis,³⁶ Einstein’s manuscript bears some striking similarities with Bohm’s theory, a fact which, however, did not prevent Einstein from rejecting the latter as “too cheap.”³⁷ Belousek concludes quite in line with Cushing that “the failure of the ‘Bestimmt’ scheme engendered in Einstein’s thinking an overall skepticism toward the very possibility of a wave-particle synthetic completion of quantum mechanics that conditioned both his less than enthusiastic support for de Broglie’s theory and his outright rejection of Bohm’s theory.” (Ibid., p. 453)

Cushing is reluctant to apply a weak Forman strategy also to the fate of Bohm’s interpretation; let me briefly sketch how he story continues. In 1952, Bohm’s intellectual opponents were still the same deBroglie had faced in 1927, and they once again reacted in a decidedly negative way – von Neumann being a notable exception (Cf. Stöltzner, 1999d). Einstein still had concerns about locality, but he “had even deeper reasons for rejecting such hidden-variables approaches to a completion of quantum mechanics. Quite simply, they were not radical enough.” (Cushing, 1994, p.

147) The late Einstein counted on a unified field theory that represented a radical break with all remnants of classical mechanics. Similarly as in 1927 the internal reasons were not compelling, and so Cushing turns to historical contingency. Rejecting – reasonably – any influence of Marxist materialist ideology on Bohm’s interpretation, he cites Heisenberg’s contention that all opponents of the Copenhagen view wanted to return to the ontology of materialism, to a completely objective description of nature, rather than accepting Copenhagen’s subjective element in the description of atomic events.

At this point we realize the simple fact that natural science is not Nature itself but a part of the relation between Man and Nature, and therefore dependent on Man. The idealistic argument that certain ideas are a priori ideas, i.e., in particular come before all natural science, is here correct. (Heisenberg, 1955, p. 28, quoted from Cushing, 1994, p. 153)

This was the basis on which Heisenberg took the positivist tack that observationally equivalent theories, such as Bohm’s, just signify a difference of language. True, this sounds like a positivist meaning criterion. But as Cushing himself notices, already in the 1920s Heisenberg had rejected any underdetermination of theory, in stark contrast to the Viennese positivists. Moreover, if we compare Heisenberg’s charge against Bohm of relapsing into materialism with Frank’s (Section 8.4.), we see that Heisenberg just replaces one metaphysical world view with another. His emphasis on idealism and a priori ideas elevated, as it were, two anathemas of Logical Empiricists to lessons to be drawn from quantum mechanics and, finally, his insistence on the subjective-objective distinction was precisely that sort of dualist metaphysics which Mach’s neutral monism wanted to overcome (See Ch. 3). On such metaphysical a foundation, Heisenberg’s meaning criterion was anything but a genuine positivist argument.

36 See also (Howard, 1990).