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 The Logic of Quantum Mechanics, 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 states that the system has a well-defined value p, of a physical magnitude P, and q₁, q₂, …, q_n describe all possible values of an incompatible quantity Q, then the uncertainty principle entails that p⋅q_i is false for any i. Yet, assuming that p obtains, (ascertained by measurement, say) we cannot conclude, as we classically would, that q₁∨q₂∨…∨q_n is false. In fact, while p⋅q_i is a quantum logical contradiction, q₁∨q₂∨…∨q_n is a quantum logical tautology. 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 general 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. Though intended to strengthen the analogy with logic, Putnam’s operational definition of the quantum-logical operators 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, when Putnam had already 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. Though this seemed an attractive way to retain ’internal’ realism while forgoing metaphysical realism, upon realizing that, in some cases, different perspectives are not empirically equivalent Putnam became dissatisfied with perspectivism.