Putnam, Hilary (1926–2016)

4. The philosophy of quantum mechanics

Heisenberg’s uncertainty principle imposes a limit on the precision with which the values of certain pairs of physical parameters, such as position and momentum, or two spin components, can be measured simultaneously. On the Copenhagen interpretation, this principle implies that it is meaningless to ascribe simultaneous sharp values to such pairs of physical parameters, whether or not they are actually being measured. Since, however, when any one magnitude is measured separately, a sharp value is obtained, it appears that it is measurement itself which creates the transition, better known as the collapse, from the indeterminate to the well-defined state. If so, measurement does not reflect a state objectively existing prior to measurement, but points to a state of its own creation (see Quantum measurement problem). Both the inference from the impossibility of measurement to the meaninglessness of concepts and the non-classical understanding of measurement, offend the realist. In "Is Logic Empirical?" (1968; reprinted as "The Logic of Quantum Mechanics" in 1975a) Putnam proposed overcoming these difficulties by adopting a nonclassical logic first suggested in the context of quantum mechanics (QM) by Birkhoff and von Neumann in 1936, and developed by Finkelstein in the 1960s. The suggested logic is non-distributive – from p⋅(q1∨q2) we cannot, in general, conclude that p⋅q1∨p⋅q2. If p-s states that the system has a well-defined value p-s, of a physical magnitude P, and q1, q2, …, qn describe all possible values of an incompatible quantity Q, then the uncertainty principle entails that p.qi is false for any i. Yet, assuming that p-s obtains, (ascertained by measurement, say) we cannot conclude, as we classically would, that q1∨q2∨…∨qn is false. In fact, while p⋅qi is a quantum logical contradiction, q1∨q2∨…∨qn is a quantum logical tautology! Quantum logic is thus compatible with the claim that the magnitude Q always has a well-defined value, which its measurement will reveal, and no collapse is called for (see Quantum mechanics, interpretation of; Quantum logic). In light of the traditional gulf between factual and logical truth, the idea that logic can be revised on the basis of empirical considerations is revolutionary. Putnam saw this situation as analogous to the merging of physics and geometry into an interdependent whole in the framework of the theory of relativity.

Quantum logic raises several questions. First, it is not clear that it is a logic, a way of reasoning, rather than a calculus that happens to fit the structure of the Hilbert space of QM. Second, the idea that one can save realism by rejecting classical logic, generally seen as constitutive of realism, seems paradoxical. In particular, Putnam’s operational definition of the quantum-logical operators, though intended to strengthen the analogy with logic, has a verificationist flavor and thus obscures the connection to realism. Third, work on the foundations of QM by theorists such as Kochen and Specker, and Bell, put unbearable strain on the realist interpretation of QM (see Bell’s theorem). Indeed, in "Quantum Mechanics and the Observer" (1978; reprinted in Putnam 1983), written when Putnam had moved away from his early realism, he assumed a verificationist understanding of quantum logic. The main point of that paper, however, is to argue for yet another interpretation of QM – perspectivism, attributed by Putnam to von Neumann. Like quantum logic, perspectivism is a way of avoiding the collapse of the wave-function upon measurement. Collapse, on this interpretation, is not a physical process but an epiphenomenon created by the shift from one perspective to another. Thus, when a system M performs a measurement on another system S, we can either view M as interfering with S from without, inducing a collapse of the wave-function of S, or view S and M as a unified system obeying QM, and the external observer as interfering with it and making its wave-function collapse. Ultimately, Putnam argues, different perspectives are empirically equivalent and congruent with the predictions of QM; hence, they are equally legitimate. But perspectives exclude each other in the sense that statements belonging to different perspectives cannot be combined to form a quantum state. Realism can be sustained within each perspective, but not across perspectives. At the time, this seemed an attractive way of retaining 'internal’ realism while forgoing 'metaphysical realism' (see section 7; see also Realism and antirealism) but internal realism was short lived. Furthermore, upon realizing that, in some cases, different perspectives are not empirically equivalent Putnam became dissatisfied with perspectivism.

Putnam continued to pursue realist ways of understanding QM. The version that has seemed most appealing to him since the abandonment of perspectivism is the GRW theory put forward by Giancarlo Girardi, Alberto Rimini and Tullio Weber, and further developed by Roderick Tomulka. Like its ancestor, David Bohm's theory, the GRW version of QM provides a realist interpretation that does not suffer from the measurement problem. It proposes that the deterministic evolution governed by the Schrödinger equation is interrupted by rare random events of spontaneous collapse that become highly probable only when the quantum system is coupled to a macroscopic system, as it happens when a measurement is made. The worry that the GRW theory, like Bohm's theory, cannot be made Lorentz invariant, and is thus in conflict with the Special Theory of Relativity, has been alleviated to some extent by Tomulka's construction of a relativistic version of the GRW theory. The lack of empirical support still makes this approach tentative.