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PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association

A Formal Statement of Schrödinger's Cat Paradox

James H. McGrath

Published Jan 1, 1980• 2 citations
Publisher

Abstract

Schrödinger's argument about a “cat penned up in a steel chamber” is a timely challenge to those concerned with the philosophy of quantum theory; the argument prompts difficult decisions about correlated quantum mechanical systems, locality, reality and completeness. Here Schrödinger's own text is reproduced and, in view of the text, several plausible axioms and formal rules are chosen. Then, beginning with the axioms and using the rules, a contradiction is derived. This result establishes that Schrödinger's argument can be viewed as a paradox, a derivation of a contradiction from plausible assumptions. A final section of the paper refines the paradox and treats two possible resolutions as representative of a watershed issue in the foundations of quantum mechanics. Comments concerning the method of formalization were provided when I applied the method to the Einstein-Podolsky-Rosen argument (1978).

DOI
10.1086/psaprocbienmeetp.1980.1.192569

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Schrödinger's argument about a “cat penned up in a steel chamber” is a timely challenge to those concerned with the philosophy of quantum theory; the argument prompts difficult decisions about correlated quantum mechanical systems, locality, reality and completeness. Here Schrödinger's own text is reproduced and, in view of the text, several plausible axioms and formal rules are chosen. Then, beginning with the axioms and using the rules, a contradiction is derived. This result establishes that Schrödinger's argument can be viewed as a paradox, a derivation of a contradiction from plausible assumptions. A final section of the paper refines the paradox and treats two possible resolutions as representative of a watershed issue in the foundations of quantum mechanics. Comments concerning the method of formalization were provided when I applied the method to the Einstein-Podolsky-Rosen argument (1978).
Schrödinger's Cat has acquired many descriptions and interpretations since its introduction in 1935. This paper returns to Schrödinger's original text and separates what Schrödinger explicitly constructed from what is inferred from the construction. Schrödinger specified a steel chamber, “a tiny amount” of radioactive substance, a Geiger counter, relay, hammer, poison, a one-hour interval, equal possibilities that one atom decays or none does, and “the first atomic decay” as the decisive occurrence. He then described the wave function of the entire system as containing the living and dead cat “mixed or smeared in equal parts.” However, not knowing which of two mutually exclusive states is true, or being unable to rule out either, does not imply that both are physically true. The distinction involves not only Schrödinger's Cat but also Schrödinger's YOU—the observer outside the steel chamber who lacks information. Moreover, the causal chain from atomic decay to the cat's death contains additional physical and biological conditions. The original construction should therefore distinguish the physical cat, its quantum-mechanical description, and the information available to YOU.
Once upon a time the well-known paradoxes of quantum mechanics (one might even say the “traditional” paradoxes of quantum mechanics!—I refer here to paradoxes such as the Schrödinger cat and the Einstein-Podolsky-Rosen Paradox) seemed especially difficult because of the rather bizarre behavior of the wave packet under the von Neumann theory of measurement, to which behavior these paradoxical situations seemed to draw especial attention. Quite recently quantum theoretical accounts of the measurement process have been appearing which sidestep direct reference to such things as “contraction” of the wave packet (see, for example, Krips and Jauch). With this development it has become increasingly popular to take a “cool” approach to these paradoxes, arguing that the new approach to measurement provides a consistent, nonbizarre account of the physical situations and that the paradoxicality was due largely to intuitive blunders—even plausible intuitive blunders—accentuated (but also disguised) by the unfortunate features of the von Neumann approach to measurement. Both Krips and Jauch, for example, adopt this approach.
When it was first put forward, special relativity struck many people as counterintuitive and possibly inconsistent, as we saw when we considered the twin paradox in Chapter 17. Quantum mechanics had a similar effect, only to a much greater and longer lasting degree, from the time of its inception in the mid 1920s until the present. This reaction to quantum theory was not confined to an initial confusion that often accompanies a new subject, but remained a life-long puzzle for Einstein, to mention only the most prominent opponent of what he took to be the reigning orthodoxy. In this chapter we study a famous attempt by Einstein and two of his colleagues to show that quantum mechanics was, if not logically inconsistent, then at least an incomplete theory. This charge of incompleteness is just that raised by Schrödinger's cat paradox (Section 21.4). THE EPR PARADOX In 1935 Einstein, Boris Podolsky (1896–1966) and Nathan Rosen (1909–1995) (hereafter referred to as EPR) published a paper titled ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’. They take as their criterion for the completeness of a theory that it contains terms corresponding to every relevant entity found in reality. For example, in the classical description of a system, such as a planet going around the sun, there are symbols representing the position r , the momentum p and so forth for the various parts of the system.
Despite the spectacular success of quantum mechanics (QM) over the last 80 years in explaining phenomena observed at the atomic and subatomic level, the conceptual status of the theory is still a topic of lively controversy. Most of the discussion centers around two famous paradoxes (or, as some would have it, pseudoparadoxes) associated, respectively, with the names of Einstein, Podolsky, and Rosen (EPR) and with Schrodinger's cat. In this Viewpoint, I will concentrate on the paradox of Schrodinger's cat or, as it is often known (to my mind somewhat misleadingly), the quantum measurement paradox.