In previous chapters we argued that the empirically successful formalism of quantum mechanics supports equally well two mutually incompatible general ontologies: the inherently indeterministic and generally accepted Copenhagen interpretation and Bohm's completely deterministic one. This underdetermination of the interpretation by the formalism is not simply an apparent one of two equivalent theories since there is no way to translate the terms of one of these ontologies into those of the other. This case could be seen as presenting a challenge to the scientific realist who seeks from successful scientific theories a true representation of the world. Furthermore, we suggest that the actual historical competition between these theories and the selection of Copenhagen over Bohm illustrate that such an historically contingent process is not meaningfully distinct from the rational reconstruction and logical judgment of the victorious theory. What is deemed successful and put on offer by the scientific community for the philosopher of science to justify after the fact is itself a contingent and nonunique product. UNDERDETERMINATION The origin of the underdetermination of scientific theories, what we refer to here as the so-called Duhem–Quine thesis, is typically located in Pierre Duhem's The Aim and Structure of Physical Theory (first published in 1906). There Duhem was quite explicit about what he took to be the basis for judging whether or not a given physical theory is acceptable.
In previous chapters we argued that the empirically successful formalism of quantum mechanics supports equally well two mutually incompatible general ontologies: the inherently indeterministic and generally accepted Copenhagen interpretation and Bohm's completely deterministic one. This underdetermination of the interpretation by the formalism is not simply an apparent one of two equivalent theories since there is no way to translate the terms of one of these ontologies into those of the other. This case could be seen as presenting a challenge to the scientific realist who seeks from successful scientific theories a true representation of the world. Furthermore, we suggest that the actual historical competition between these theories and the selection of Copenhagen over Bohm illustrate that such an historically contingent process is not meaningfully distinct from the rational reconstruction and logical judgment of the victorious theory. What is deemed successful and put on offer by the scientific community for the philosopher of science to justify after the fact is itself a contingent and nonunique product. UNDERDETERMINATION The origin of the underdetermination of scientific theories, what we refer to here as the so-called Duhem–Quine thesis, is typically located in Pierre Duhem's The Aim and Structure of Physical Theory (first published in 1906). There Duhem was quite explicit about what he took to be the basis for judging whether or not a given physical theory is acceptable.
Through the analysis of the interpretations of quantum mechanics and the theory of relativity, the paper aims to demonstrate the following thesis: the Duhem-Quine thesis \non empirical underdetermination can be extended to the claim that not only the empirical data, but also the empirical data together with the mathematical formalism of a physical \ntheory do not suffice to determine completely our theories of physical reality. As a consequence, beyond observational data and mathematical physics, cultural and social factors \nas well as the value-preferences of physicists also play role as constitutive elements of physical theories. For example, the indeterminist interpretations of quantum mechanics are not neutral but value-laden, and deterministic interpretations, which insist on classical determinism as a value, are also possible. On the other hand, the thesis of the underdetermination of physical reality by mathematical physics confirms neither radical relativism, nor extreme versions of sociology of science. On the contrary, the mathematical formalism to be interpreted is autonomous – and in this sense “objective” – to a great extent with respect to cultural, social and other non-scientific factors and, therefore, there is a firm consensus regarding it in science. \n
The dominance of the Copenhagen interpretation is the result of a historical accident (Cushing, 1994). At the Solvay conference in 1927, Louis de Broglie put forward the deterministic pilot wave theory, described later. Never slow to criticize, Pauli jumped up and demolished de Broglie’s proposal, and de Broglie was so discouraged by this that he did not develop his interpretation any further. The Copenhagen interpretation was then developed by Bohr, Heisenberg, Pauli and many others, as described in the previous chapter. It was strongly supported by von Neumann’s proof of the impossibility of hidden variables. Years later, in 1952, Bohm published a deterministic hidden variable theory, showing that there must be something wrong with von Neumann’s proof. The error was found by John Bell in 1966, as described in the last chapter, and he also showed how Pauli’s objections to de Broglie’s original idea can be answered. If this had been done at the conference in 1927, quantum mechanics could have been interpreted deterministically from the beginning. The essential mistake in the Copenhagen interpretation is to treat it as a complete account of the behaviour of each individual system. It is frequently claimed that it enables us to calculate, at least in principle, everything that can be measured. Thus Hooft (1997, p. 11) said that ‘The laws of quantum mechanics have been formulated very accurately. We know exactly how to compute anything we would like to know.’ Also Peierls (1997, p. 25) has said that quantum mechanics ‘had become a complete and consistent scheme capable of giving a unique answer to any questions relating to actual or possible observations’. Even if this were true, it would not imply that it is the final complete theory, for it is always possible that some new phenomenon might be found that cannot be calculated quantum-mechanically. However, it is not true: there are many phenomena such as the time of decay of a radioactive nucleus, or the direction a particle is scattered by a nucleus, that cannot be calculated, even in principle. Quantum mechanics is therefore an incomplete theory. We can only calculate the statistical properties of these systems, such as the half-life of a radioactive decay or the differential scattering cross-section that gives the probabilities that a particle is scattered through various angles. All measurements of quantum systems are of this statistical character. It might be thought that the possibility of making measurements on a single electron provides an exception to this. However, even in such cases the electron is continually bathed in a fluctuating background radiation from nearby atoms. Since this is variable, that electron is a member of an ensemble of electrons subject to different fluctuations. All these examples clearly demonstrate the statistical character of quantum mechanics. ‘I am rather firmly convinced’, Einstein (in Schilpp, 1949, pp. 666, 671) remarked, ‘that the essentially statistical character of contemporary quantum theory is solely to be ascribed to fact that this theory operates with an incomplete description of physical systems’. As a result, ‘the c-function is to be understood as the description not of a single system but of an ensemble of systems’. So, ‘if the statistical quantum theory does not pretend to describe the individual system completely, it appears unavoidable to look elsewhere for a complete description of the individual systems’. Thus ‘the difficulties of theoretical interpretation disappear, if one views the quantum-mechanical description as a description of an ensemble of systems’. If this is achieved, ‘the statistical theory would, within the framework of future physics, take an approximately analogous position to statistical mechanics within the framework of classical mechanics’. ‘Thus, essentially, nothing has changed since Galileo or Newton or Faraday concerning the status of the ‘‘observer’’ or our ‘‘consciousness’’ or of our ‘‘information’’ in physics’ (Popper, 1982, p. 46). Once this is accepted, the quantum paradoxes that plagued the Copenhagen interpretation are easily resolved, as described below. In any textbook of quantum mechanics problems such as the calculation of the energy levels of the hydrogen atom are solved as if that hydrogen atom is alone in the universe. As Feynman (1972) remarked, ‘when we solve a quantum-mechanical problem, what we really do is to divide the universe into two parts – the system in which we are interested and the rest of the universe. We then usually act as if the system in which we are interested comprised the whole universe.’ In fact, however, every hydrogen atom on which measurements are made is surrounded by other atoms and exposed to their radiations. Quantum mechanics somehow takes this into account and gives the average behaviour of an ensemble of hydrogen atoms. A more detailed theory takes these influences into account. One attempt to do this is stochastic electrodynamics, described in a later section.
Earlier in this century, the physics community was wracked with a great debate between the determinists and the indeterminists over the status of quantum theory. Determinists like Einstein and Bohm argued that quantum theory would eventually be superseded by a deterministic theory having new state variables. Indeterminists like Heisenberg and Schrodinger, speaking for the Copenhagen School, disagreed. They maintained that the indeterminism in quantum theory was not merely a temporary setback, an epistemological problem to be overcome by means of a better scientific theory, but an accurate ontological representation of the matter.
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
Abstract Nonrelativistic quantum mechanics (QM) works perfectly well for all practical purposes. Once one admits, however, that a successful scientific theory is supposed not only to make predictions but also to tell us a story about the world in which we live, a philosophical problem emerges: in the specific case of QM, it is not possible to associate with the theory a unique scientific image of the world; there are several images. The fact that the theory may be compatible with distinct ontologies, and that those ontologies may themselves be associated with a plurality of metaphysical approaches, gives rise to the problem of metaphysical underdetermination. This paper concludes that the available metametaphysical criteria fail to deliver objectivity in theory choice, and it puts forward its own criterion based on a tension between two methods of metaphysical inquiry: one that is closely related to science and another that is not.
This chapter repeats for quantum mechanics the comparison carried out for relativity in Chapter 5. Its thesis is that the same three interpretative families, neo-Kantian, empiricist and scientific realist, reappear in the philosophical reception of quantum mechanics, but in a more radical form, because the dispute now reaches the meaning of the quantum state, of probability and of measurement. The chapter first identifies what the formalism established in Chapter 4 leaves open and treats the Copenhagen framework as a point of departure rather than a unified doctrine. It then reconstructs the neo-Kantian interpretation (the Kantian affinities of Bohr’s complementarity, Cassirer, Grete Hermann and contemporary transcendental perspectives), the empiricist interpretation (Heisenberg’s observability principle, instrumentalism, Schlick, Frank, Reichenbach and van Fraassen’s constructive empiricism) and, on equal terms, the realist interpretation: Einstein and the EPR argument, Popper’s propensities, the de Broglie–Bohm theory, Bell’s beables and local causality, realist modal interpretations, and the Everett and collapse programmes. The realist family is the most developed of the three in quantum mechanics, but it is also internally plural: it affirms that the theory refers to a mind-independent reality while disagreeing about whether that reality consists of particles, fields, propensities, branching worlds or definite and possible properties. On this basis the chapter compares the three interpretations of causality and of stationary action. Causality appears as a relativized condition of objective description, as a statistical relation without surplus content, or as an objective but non-local structure; stationary action appears as a coordination axiom of quantum dynamics, as an empirically equivalent formulation, or as a real dynamical structure that in Bohm’s theory directly guides motion. The result confirms the pattern of Chapter 5 and identifies the precise point, the relation between quantum possibility and actuality, from which the BBMT bridge of Chapter 7 will start.