Before continuing, I should offer the following caveat. What is to follow is a very rough draft of a paper I threw together. The paper was inspired by another I authored on a similar theme for a PoS class. The following neglects many details and instead provides for a rough outline of a larger, much closer analyzed and ambitious paper I suspect I will write in the near future. So, this post is but an approximation of what is to come. Nevertheless, if the post engenders discussion on any topics pertaining to quantum mechanics, scientific methodology, philosophy of science, verificationism, logical positivism, whatever, and attracts critical first assessments, then it will have served its purpose.
Logical Positivism and the Copenhagen Interpretation of Quantum Mechanics
“The rise of quantum theory in the years 1900 to 1927 is surely one of the major advances in the history of science- perhaps even one of the greatest intellectual advances ever made by mankind” (Hund 1974, p. 5). The mathematical formulation of modern quantum mechanics consists of a complete and logically consistent framework of mathematical deductions (see, for instance, von Neumann 1955). However, an ordered series of mathematical deductions, no matter how complete or logically consistent, is not a physical theory. In order to obtain the status of a physical theory, the mathematical formalism or, more precisely, the mathematical representations, must be assigned certain, specifiable experimental conditions so as to allow for the determination of measurement procedures which may aid in the confirmation and disconfirmation of hypotheses and in the identification of new and fruitful avenues of investigation. Of course, the experimental data produced by the measurement procedures necessitate interpretation, and that interpretation will run up through the mathematical structure resulting in our view of the theory and its overall implications for our system of the world.
The most popular interpretation of quantum mechanics among physicists today is the Copenhagen Interpretation [CI] (Tegmark 1998)1. The CI formed gradually in 1920s in Copenhagen, Denmark, through the work of Niels Bohr, Werner Heisenberg, Max Born, John von Neumann, and others (Cushing 1994; Heisenberg 1958; Jammer 1974). Contemporaneous to the development of the CI was the development of logical positivism, as represented by the Vienna and Berlin Circles2. Logical positivism, it has been commonly argued, is a philosophically dead programme (see, for instance, Passmore 1967, pp. 52 – 57). However, as recent trends in post-Kuhnian philosophy of science indicate, logical positivism remains a profitable philosophical enterprise. One reason for holding to the continuing value of logical positivism is the influence verificationism had on the formulation of the CI. More precisely, Niels Bohr, the primary architect of the CI, was himself influenced by logical positivism, as seen in his response- discussed below- to Einstein’s criticisms to the probabilistic nature of the CI. In the end, the success of the CI may be seen as a practical justification of a general and broad verificationist epistemology. Moreover, insofar as logical positivism rejects realism concerning scientific theories and the CI is an instrumentalist interpretation of quantum mechanics, an ancillary conclusion will be that some form of the scientific anti-realist view of instrumentalism remains a viable position on scientific theories.
To speak of a single logical positivist programme is inaccurate. Logical positivism is a more or less loose collection of philosophical theses- some of which are incompatible- which have their genesis in the scientific inclinations of the Vienna Circle members (on this see Friedman 1999 and Uebel 2009). However, one may identify two broadly unifying themes within logical positivism: (1) a verificationist epistemology and (2) an instrumentalist stance toward scientific theories.
The naive definition of verificationism may be stated as follows: a statement is meaningful if and only if it is verifiable. First, as formulated, this definition is too simple and subject to a much too easy criticism: In order to verify or falsify a statement, it seems that one must already know what that statement means. Second, “meaningful” and “verifiable” are ambiguous, and it is not at all clear in what sense the logical positivists intended to use the terms. Furthermore, even when the logical positivists avoid the simple criticism above by disambiguating “meaning” and “verification” (see, for instance, Pap 1962, pp. 6 – 37; Carnap 1936; Ayer 1946, Introduction to the 2nd edition; Dummett 1992, pp. 129 – 156), further, more intractable difficulties remain (Hempel 1959, pp. 108 – 129). While for our purposes we may forgo consideration of the problems of verificationism and their proposed solutions, it is prudent to state a more acceptable, albeit imprecise definition of verificationism: a sentence is meaningful if and only if it is truth-apt; a sentence is truth-apt if and only if it is verifiable; and a sentence is verifiable if and only if it is capable, in principle, of experiential test, whether via direct observation or through some indirect measurement procedure(s).
In other words, let us suppose the meaningfulness of a sentence is under consideration. Following William James, we must inquire ‘‘what concrete differences will its being true [or false] make in any one’s actual life? What experiences [may] be different from those which would obtain if the belief were false? How will the truth be realized? What, in short, is the truth’s cash-value in experiential terms” (James 1907, p. 200-201)? In other words, the desire is for broad, intersubjective observable criteria for the application and truth assessment of sentences. If a sentence fails to establish in the analysis intersubjective observable criteria- or bridging hypotheses which tie the sentence to observable criteria-, then the sentence is not truth-apt, and thus not meaningful.
In general, verificationsim led to the identification and rejection of so-called metaphysical statements. In particular, verificationism led to the dissolution of perennial philosophical problems such as the problem of the external world. Here logical positivists took two approaches. The first approach, which A.J. Ayer (1946) and early Rudolf Carnap (1959, pp. 60 – 81) adopted, reduced talk of the reality of objects to talk of sense-data, from which physical objects are a logical construction. The other approach, which Otto Neurath (Cat 2009) and later Carnap adopted, is to reduce talk of the reality of objects to talk of physicalism, that is, that rather than sense-data, what we experience is physical objects. A bridge between these two approaches may be seen in Moritz Schlick (1959, pp. 82 – 107), who reduced talk of “reality” to talk of observation as such. That is, we may speak of objects as real if by “real” we mean “observable” or, broadly, detectable in some measurement or observation procedure. In other words, we may simply translate “real” as “observed” or “observable.” Whichever approach one takes3, I think Schlick’s position is basically correct: We may say that which is real is that which is observable, and conclude that talk of things-in-themselves or substances in which our experiences inhere, e.g., is entirely unnecessary. Nevertheless, for the positivists verificationism is the preeminent guide to scientific methodology- whether one construes to observe physical objects or sense-data- and determines the adoption of scientific theories. The adoption of a scientific theory, then, is not a matter of truth or the elucidation of fundamental reality, but rather a matter of instrumental utility. It is a matter of framing hypotheses which imply past observations and which predict future observations under specifiable conditions, which in turn serve to confirm or disconfirm these hypotheses. That is to say, one theory is better than another to the extent that it is more fruitful in suggesting empirical generalizations under which we may subsume an ever expanding spectrum of phenomena and in aiding in the formulation of further predictive hypotheses.
The Copenhagen Interpretation of Quantum Mechanics
The origin of quantum theory began with the inability of classical physics to account for the observed energy spectrum of black body radiation and the experimental data which confirmed the atomic theory of matter (Jammer 1966). Through the work of Max Planck and Albert Einstein in the early 1900s, it soon became productive to understand light as consisting of discrete packets of energy, photons, which in collision with electrons produced energy radiation (the observed light spectra of heated bodies). Subsequent experimental data revealed an ever more complex subatomic world. From 1913 with the publication of Niels Bohr’s mathematical model of the hydrogen atom and improvements to it through the work of Arnold Sommerfeld and Werner Heisenberg and many others, including Paul Dirac, Max Born, Louis de Broglie, Erwin Schrodinger, and John von Neumann, to name only a few, the basic mathematical structure that we have today of quantum mechanics was formed (Fong 1962; Omnes 1999; Cushing 1994). The problem remained, however: How ought we to interpret the body of experimental data and mathematical formalisms?
From October 24th to the 29th in 1927 the Fifth Solvay Congress took place. In attendance were the greatest names in physics at the time: Albert Einstein, Marie Curie, Max Planck, Henry Lorentz, Wolfgang Pauli, Erwin Schrodinger, Niels Bohr, Max Born, and Werner Heisenberg (not a complete list). The official program of the Solvay Congress was “Electrons and Photons,” but the participants soon realized that this meeting would set the stage for a definitive discussion regarding the interpretation of the new quantum mechanics (Jammer 1974).
The debate (known as the Bohr-Einstein debate) that ensued consisted of two principal factions: the realists and the anti-realists, represented by Einstein and Bohr, respectively. Initially, as Max Jammer writes, “Bohr cherished the hope that the positivistic element in the complementarity interpretation would make Einstein change his mind” (1974, p. 109). However, unbeknownst to Bohr and his colleagues, Einstein since turned away from his earlier Machian influences and adopted a more realist position (Frank 1947, p. 215). In fact, the realists were of the opinion that in principle Bohr and his colleagues were gravely mistaken and that a series of thought experiments would elucidate the mistake. The expectations for success on both sides were palpable.
[More here to come.]
After the conference, and after Einstein’s criticisms were answered in detail by Bohr, much to Einstein’s chagrin, Bohr’s interpretation was deemed the most plausible in light of the experimental evidence (Cushing 1994). What resulted was what is known today as the Copenhagen Interpretation of quantum mechanics. While to identify a single CI may in fact be a mistake4, one may identify three theses which form the central core of any CI (Heisenberg 1958; Cushing 1994; Hund 1974; Jammer 1974):
(1) The wave function is a complete description of the wave/particle duality. That is, the wave function establishes completely the possible information available from which to predict quantum phenomena.
(2) When a measurement procedure is conducted, the wave function collapses. That is, quantum particles are assigned classical values when (and only when) a measurement procedure is performed. For example, before a measurement is performed, a particle’s position is indeterminate and is constrained by the statistical wave function within a given space. After a measurement is performed, the possibilities of the particle’s position collapses and we may assign a definite value within specifiable, experimentally determined margins of error.
(3) Indeterminacy. If one measures one value, then one cannot measure another value with any measurable degree of accuracy. That is, there exists an uncertainty relationship between classical values, such as position and velocity, in quantum mechanical systems.
EPR and Bohr’s Response
(1) – (3) entail the violation of heretofore deeply established scientific principles of determinacy, which for many is unacceptable. For example, Einstein and his colleagues believed that nature operated according to deterministic processes, and if one could not predict an outcome with a measurable degree of accuracy, then it is because of a lack of knowledge, not because of the nature of the physical processes themselves. In order to emphasize the criticism, Einstein and fellow physicists, Boris Podolsky and Nathan Rosen, published a paper (hereafter EPR) wherein, through a detailed thought experiment, they sought to show either that measurements in one quantum system affect measurements in another or that the wave function is not complete, which is to say either (3) or (1), and by implication (2), above is incorrect.
In nuce, the argument in EPR is as follows. Einstein begins his thought experiment by assuming locality (the thesis that there is no action at a distance). He then assumes that system S1 at previous time t interacted with system S2. Einstein continues that via a measurement of S1 one may assign a state vector ϴ or Є (but not both) to observables in S2 without physically interfering with S2. Therefore, S2 is either in the same physical state as S1 at t whether we assign ϴ or Є to it or S2 is in a different state. If the latter, then the physical state of S2 at t is dependent upon the physical state of S1 at t. If the former, then since one can describe similar physical states with ϴ or Є, then ϴ or Є cannot be a complete description of that physical state; that is, we must be able to assign other hidden values which discriminate between similar physical states. In either case, either the wave function which describes S1 and S2 is incomplete or locality is violated, which relativity entails is impossible (Einstein, et al., 1935, pp. 770 – 780).
[Expound upon locality / non-locality here.]
Bohr’s response to EPR evinces his positivistic influences. In “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” (1935), Bohr argues that Einstein’s assumption that S2 was in the same physical state at t- irrespective of whether it was assigned ϴ or Є- is meaningless. The ascription of a physical state may occur only within the context of the total experimental data. In Einstein’s thought experiment the experimental context included data concerning S1 and S2, in which case measurements of S1 can affect S2, and vice versa. Moreover, Bohr’s response to Einstein entails non-locality, which Einstein assumes is impossible. For Bohr, to speak of a physical state and state vectors which describe that state is meaningless outside of the measurement procedures used to assign state vectors to observables. However plausible Einstein’s initial assumptions may at first blush appear, Einstein’s argument begs the question in the assumption of locality and the existence of hidden variables. In fact, in 1964, Bohr’s response was confirmed by the physicist John Bell in a series of experiments wherein he assumed a locality assumption similar to Einstein’s and showed that such an assumption in fact restricts the probabilities for the measurement outcomes and that the experimentally confirmed probabilities of specified quantum physical systems violate Einstein’s assumptions.
Logical Positivism and Niels Bohr
Bohr’s response to EPR (and his responses to Einstein’s criticisms during the 1927 Solvay Congress) reveals an overt positivistic influence. Many scholars have discussed the influence of the logical positivists on Bohr’s (and Heisenberg’s) scientific understanding (see, for instance, Jammer 1974; Beller 1999; Cushing 1994, pp. 28, 29). However, other scholars have noted that Bohr’s philosophical influences were rather more varied (see, for instance, Petersen 1968; Folse 1985; Jammer 1966, pp. 166 – 180). An honest assessment of the relevant historical evidence, however, reveals multiple lines of philosophical influence. Nevertheless, enough evidence exists to warrant the conclusion that Bohr was rather heavily influenced by logical positivism, in particular verificationism.
In June 1936, from the 21st to the 26th, Bohr hosted the 2nd International Congress for the Unity of Science in Copenhagen at his honorary mansion in Carlsberg (Faye 2008). In attendance was Otto Neurath, C.G. Hempel, Karl Popper, Phillip Frank, Jorgen Jorgensen, the leading expositor of logical positivism in Denmark at the time, and other Danish scientists and philosophers who were sympathetic to the positivist program. Faye reports that Hans Reichenbach, Moritz Schlick, and Rudolf Carnap also expressed a desire to attend (indeed, a paper of Schlick’s was read at the conference), but were for various reasons unable.
Bohr also had other interactions with logical positivists before the 1936 conference. Two years prior Jorgensen gave six lectures on epistemology, two of which Bohr attended. At the conference was Neurath, who would later write to Carnap (Faye 2008, p. 4):
“Bohr. Idiosyncratic. An intense man. Came to two lectures and joined the discussion enthusiastically … Basic line: he does not want to be considered a metaphysician. And he is able to express himself relatively non-metaphysically, when he is careful. Yet obviously there lies a certain tendency in the selection of problems, insofar as the question of life, etc. is discussed, as well as in the stress on uncertainty. In addition, his printed remarks are full of crass metaphysics. But he possesses certain basic attitudes which agree with mine, e.g., that in science one cannot clear up everything at once, but that the individual scientific-logical actions have to pay a price, as it were. An idea of compensation, which with him naturally tends to be connected with the uncertainty relation. Obviously tries to come into agreement with us. But since his circle confirms him in his habit to express himself somewhat unclearly, one would have to be able to work on him for a long time, which he would be prepared to do.”
Obviously, Neurath found much in common with Bohr. In fact, after the lectures Bohr handed Neurath a copy of his Atomic Theory and the Description of Nature along with a letter which apparently stated Bohr’s agreement and common cause with the positivist program (Faye 2008). A striking fact further confirms logical positivism’s influence on Bohr: Prior to 1935 Bohr apparently held that measurements of quantum states disturbed the particles under observation so as to prevent determining precisely state vectors. In other words, Bohr seems to have considered the particles to have had determinate variables before any observation was made of them (Faye 1991). In fact, Faye contends that this stance of Bohr’s may have influenced Einstein’s argument in EPR (Faye 2008, p. 7). Nevertheless, after 1935, and after various exchanges with positivists, Bohr seems to have changed his view on the matter. Perhaps the publication of EPR compelled Bohr to make his position more consistent with the experimental data so that he could respond to Einstein’s criticisms. For in his reply to EPR Bohr was clear when he argued that one could talk meaningfully of a quantum particle only within specifiable measurement procedures. In other words, the measurement procedures determined the conditions under which one could apply values such as position, spin, velocity, etc., thus, in the absence of measurement procedures, in that one talks of hidden variables, one can only be construed as inserting metaphysical presuppositions. Otto Neurath was not the only member of the Vienna Circle with whom Bohr corresponded. In a letter dated January 9, 1936, regarding the Bohr-Einstein debate, Philipp Frank (then professor of physics and philosophy at the University of Prague) informed Bohr that he (Frank) understood Bohr to have expressed a verificationist view of quantum observables while Einstein expressed a realist view and inquired if this was correct. Bohr responded in a letter dated January 14, 1936: “I am very glad to hear from your kind letter that you have given such care to the papers of Einstein and myself concerning the question of reality. I also think that you have caught the sense of my efforts very well” (Faye 2008, p. 9).
Thus, given the evidence gleaned from Bohr’s interactions with Jorgen Jorgensen and members from the Vienna Circle, his response to EPR and, previously, to Einstein at Solvay in 1927, one may conclude that verificationism played an important role in the formation of the Copenhagen Interpretation of quantum mechanics.
While other philosophical programs besides logical positivism influenced Bohr, notably American pragmatism and the subjectivism of Kierkegaard (Jammer 1966, pp. 166 – 172), verificationism played more than an important role in Bohr’s scientific thinking. Bohr did not hold that quantum mechanics revealed the ‘fundamental nature of reality’. Rather, he held that quantum theory was a tool with which scientists could order and predict experimental results. For Bohr, then, a distinction between observable and unobservable is to be made. Classical descriptions are made with deterministic state vectors. That is, macroscopic objects (planets or billiard balls, e.g.) maintain deterministic positions and velocities relative to a frame of reference whether or not measurements are performed. In quantum theory, while classical descriptions are retained (see, for instance, Heisenberg 1958)- indeed, must be retained- determinacy is not. Contrary to Einstein (and many others), the CI rejects ascriptions of classical values to unobservables. This is not to say that the CI contends that what is not measured does not exist, to the contrary. To quote Carl Friedrich von Weizsäcke, a student of Niels Bohr: “What is observed certainly exists; about what is not observed we are still free to make suitable assumptions. We use that freedom to avoid paradoxes” (1985, p. 82).
[Need much more here.]
In treating unobservables, as von Weizsäcke’s quote implies, the CI need only ensure the avoidance of contradictory conclusions. For instance, consider the infamous Schrodinger’s cat paradox. In the paradox, a cat is confined to a small metallic box in which lies a chamber containing a radioactive atom. If the atom decays, then a detector will sense the decay and release a poisonous gas which will have the effect of killing the cat. If, as the CI explicitly maintains, quantum actions are uncertain and the state function remains probabilistic on the wave function, then the cat is neither definitely alive nor definitely dead. This, of course, is paradoxical (thus the description of a paradox!) since if the cat were alive, then it would have always remained so, and likewise if the cat were dead, deterministically. That is, it seems that the statistical interpretation of the wave function entails that the cat is both alive and dead. The proponent of the CI need only respond, however, that the wave function represents a probabilistic distribution of all the possible states of a quantum event and our measurement of the event collapses it to a determinate valued. Hence, given the range of possibilities for the cat’s life, it is approximately ½ probable that the cat is dead and ½ probable that the cat is alive, and when a measurement occurs (in this case, opening the box to look or the reading of the radioactive detector), we will observe either a live cat or a dead cat- never neither, never both.
The empirical success of modern quantum theory is unrivaled and the Copenhagen Interpretation has, since its initial formulation, remained widely accepted. Of course, mere popularity does not justify an interpretation. Instead, as the Bohr-Einstain debate and Bohr’s responses (and later Bell’s work) show, the CI satisfies the experimental data and mathematical formulations of quantum mechanics. Bohr’s instrumentalism comports well with the instrumentalism of the logical positivists and the influences of the latter on the former are well-established, and, insofar as Bohr’s instrumentalism shaped and formed the CI, one may conclude that the CI remains a more or less instrumentalist interpretation of quantum mechanics. While verificationism has generally been considered to be hopelessly problematic, insofar as particle physics is concerned, it remains valuable. Hence, insofar as verificationism remains vital to important parts of physics, philosophers of science should reconsider its importance within the philosophy of science in particular and epistemology in general.
[Not happy with the conclusion; of course, it is a work in progress.]
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