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Physics Essays

New adventures with Schrödinger's cat: The role of statistical uncertainty in stabilizing measurement

Phil Maguire, Rebecca Maguire

Published Jun 1, 2017• 2 citations
Publisher

Abstract

We reopen Erwin Schrodinger's thought experiment involving a cat in an informationally impenetrable box. A common view is that the cat enters a superposition of alive/dead because of a lack of observation, leading to uncertainty about the state of the cat. We, on the other hand, argue that the cat only enters a superposition if everything about the cat is known prior to the box being closed. The superposition results from a lack of uncertainty inside the box. Rather than interpreting this state of affairs as a live and dead cat interacting with each other, we suggest that the more natural interpretation is that of an inability to precisely position events within spacetime due to the lack of uncertainty. We clarify how stable measurement depends on a diversified portfolio of statistical uncertainty, and how the lack of such uncertainty in Schrodinger's box precludes stabilization.

DOI
10.4006/0836-1398-30.2.232

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We reopen Erwin Schrodinger's thought experiment involving a cat in an informationally impenetrable box. A common view is that the cat enters a superposition of alive/dead because of a lack of observation, leading to uncertainty about the state of the cat. We, on the other hand, argue that the cat only enters a superposition if everything about the cat is known prior to the box being closed. The superposition results from a lack of uncertainty inside the box. Rather than interpreting this state of affairs as a live and dead cat interacting with each other, we suggest that the more natural interpretation is that of an inability to precisely position events within spacetime due to the lack of uncertainty. We clarify how stable measurement depends on a diversified portfolio of statistical uncertainty, and how the lack of such uncertainty in Schrodinger's box precludes stabilization.
Abstract Chapter 15 deals with various unresolved issues, such as how measurements are to be described, whether they induce collapse of linear superpositions, and if so, what the result should be. Another is whether quantum mechanics applies to macroscopic measuring devices, and if not, why not. Some of these issues are addressed via the Schrödinger cat-in-the-box experiment, in particular whether the cat is ever half alive and half dead; analogs of the corresponding Schrödinger-cat state (not involving a cat) have been studied experimentally. For Schrödinger, it was ridiculous to apply quantum mechanics to macroscopic situations, nevertheless, it has been explored by many physicists. Whether measurements induce collapse and whether collapse arises in various formulations/interpretations of quantum mechanics is examined in the context of generic measuring instruments known as pointer devices. Various conclusions have been reached, though consensus has not, despite only one interpretation having been verified experimentally.
This preprint introduces a novel thought experiment—two sealed double-slit apparatuses, one with which-path detectors and one without—to resolve Schrödinger's cat paradox using only classical logic and standard quantum formalism. The interference pattern (or lack thereof) on each screen is determined by the experimental operational setup, not by later observation. Macroscopic objects like the cat reside in a quantum mixed state, not a quantum superposition state—which must be a pure state—even in a closed box. These concepts form the foundation of the Logical Interpretation of Quantum Mechanics, a minimalist approach that preserves Aristotle's laws of thought, requires no supplementary postulates, and resolves paradoxes (measurement problem, EPR, cat) as linguistic artifacts. The interpretation aligns fully with quantum predictions and recognizes indistinguishability as the primary source of quantum behavior.
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.
Schrodinger's famous cat has long been misunderstood. According to quantum theory and experiments with entangled systems, an entangled state such as the Schrodinger's cat state is neither a superposition of states of either subsystem nor a superposition of compound states of the composite system, but rather a nonlocal superposition of correlations between pairs of states of the two subsystems. The entangled post-measurement state that results from an ideal measurement is not paradoxical, but is merely a coherent superposition of two statistical correlations at "zero phase angle," i.e. at 100% positive correlation. Thus the state of the radioactive nucleus and Schrodinger's cat is as follows: an undecayed nucleus is 100% positively correlated with an alive cat, and (i.e. superposed with) a decayed nucleus is 100% positively correlated with a dead cat. The superposition consists merely in the fact that both correlations are simultaneously true. Despite many published statements to the contrary, this superposition is not paradoxical. It is in fact what one expects intuitively.
The physicist Erwin Schrödinger described, back in 1935, one aspect of this strange phenomenon. He placed his cat in a sealed box with a piece of radioactive material which might or might not send out a sub-atomic particle. If it did, the Geiger counter was designed to trigger a release of poisonous gas in the box, and thereby kill his cat. The counter was set up to be triggered just enough to give a 50-50 chance of a particle being detected, and therefore the cat an even chance of being poisoned or not. (In those days, this sort of experiment was acceptable, particularly as it was only a thought experiment.) Radioactive behaviour is unpredictable (except in a general, statistical probability kind of way). There is no rule for working out whether or not the Geiger counter will be triggered. If the sub-atomic event does not occur, the cat lives. Otherwise, it dies. Just as a photon (in that famous experiment from ‘real-life’ physics) will quite happily go through both of two parallel slits in a screen – until someone tries to measure or detect it, at which point what the physicists call ‘the collapse of the wave function’ takes place – the particle can both trigger the poison gas and not trigger the poison gas. That is, until someone looks, Schrödinger’s idea is that his cat, for a while, is both alive and dead!