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arXiv:1206.5189

Re-assessment of the state of Schroedinger's cat, final version

Art Hobson

Published Jun 21, 2012• 0 citations
arXivHTMLPDF

Abstract

The quantum state of Schroedinger's cat is usually incorrectly described as a superposition of "dead" and "alive," despite an argument by Rinner and Werner that, locally, the cat should be considered to be in a mixture of non-superposed states. Here, it is rigorously proven that the cat is not in a superposition. This is central to the measurement problem. Nonlocal two-photon interferometry experiments throw further light on the measurement state by probing the effect of a variable phase factor inserted between its superposed terms. These experiments demonstrate that both subsystems really are in locally mixed states rather than superpositions, and they tell us what the measurement state superposition actually superposes. They show that measurement transfers the coherence in Schroedinger's nuclear superposition neither to the cat nor to the nucleus, but only to the correlations between them. This explains the collapse process--but not its subsequent irreversible dissipation--within the context of unitary dynamics with no need for external entities such as the environment, a human mind, other worlds, or collapse mechanisms.

DOI
10.48550/arxiv.1206.5189

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The quantum state of Schroedinger's cat is usually incorrectly described as a superposition of "dead" and "alive," despite an argument by Rinner and Werner that, locally, the cat should be considered to be in a mixture of non-superposed states. Here, it is rigorously proven that the cat is not in a superposition. This is central to the measurement problem. Nonlocal two-photon interferometry experiments throw further light on the measurement state by probing the effect of a variable phase factor inserted between its superposed terms. These experiments demonstrate that both subsystems really are in locally mixed states rather than superpositions, and they tell us what the measurement state superposition actually superposes. They show that measurement transfers the coherence in Schroedinger's nuclear superposition neither to the cat nor to the nucleus, but only to the correlations between them. This explains the collapse process--but not its subsequent irreversible dissipation--within the context of unitary dynamics with no need for external entities such as the environment, a human mind, other worlds, or collapse mechanisms.
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 entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the phase is fixed at zero for perfect correlations, nonlocality experiments cover the full range of superposition phases and can thus show precisely what entangled states superpose. For two-state systems, these experiments reveal that the measurement state is not a superposition of two macroscopically different detector states but instead a superposition of two coherent correlations between distinct detector states and corresponding system states. In the measurement situation (i.e. at zero phase), and assuming the Schrodinger's cat scenario, the entangled state can be read as follows: An undecayed nucleus is perfectly correlated with an alive cat, AND a decayed nucleus is perfectly correlated with a dead cat, where "AND" indicates the superposition. This is not paradoxical.
This paper resolves the problem of definite outcomes, also known as "Schrodinger's cat" and the "problem of wavefunction collapse." It's the problem of understanding how nature goes from a coherent superposition of possible outcomes to a single definite outcome. This "measurement problem" has not to my knowledge been solved. The analysis stems from an insight into entanglement demonstrated in two nonlocality experiments involving pairs of momentum-entangled photons. These show that an entangled state of two subsystems is not a superposition of products of paired states, but instead a superposition of correlations between paired states. The "premeasurement state" is just such a superposition with the proviso that one subsystem is the detector of the other subsystem. This state is not a paradoxical superposition of macroscopic detector states; it is instead a superposition of correlations between detector states and microscopic quantum states. Thus, Schrodinger's cat isn't "smeared" between dead and alive but instead represents a nonlocal superposition of correlations between states of the cat and states of the nucleus: This is what we want. We also critique one previously claimed resolution of the measurement problem and seven previously claimed proofs that the measurement problem is unsolvable.
The fully entangled Schrodinger cat state obtained immediately upon measurement of a superposed two state quantum system by a detector is often said to paradoxically predict macroscopically different outcomes simultaneously. However, nonlocal interferometry experiments and their accompanying quantum theoretical analyses, testing momentum entangled photon pairs over the full range of phases, demonstrate that the cat state does not fit this description. This state instead represents two nonlocally coherent correlations between its subsystems. Even if the detector is a cat, this state is not paradoxical. Furthermore, standard quantum theory correctly predicts the experimentally observed nonparadoxical outcomes. Thus both quantum theory and quantum experiments show there is no Schrodinger cat paradox associated with measurement. This resolves the problem of definite outcomes and, with it, the measurement problem. Upon entanglement with a detector, superpositions collapse nonlocally and unitarily to one definite macroscopic outcome. No special collapse postulate is needed.
Schrödinger's cat paradox has persisted for nearly a century as a demonstration of the apparent absurdity of quantum superposition when extended to macroscopic scales. This technical note demonstrates that the paradox dissolves entirely within the CAT'S Theory framework through the triadic invariant Reality = Pattern × Intent × Presence (P × I × Pr). We argue that the cat is neither "both alive and dead" nor the victim of mysterious collapse. Instead, superposition represents a state where Presence (Pr) has not yet instantiated, yielding P × I × 0 = 0 (potential but not actual). Measurement does not "cause" collapse through mysterious observer effects; it provides the Presence component required for actualization. This resolution eliminates the need for Multiple Worlds or hidden variables while maintaining consistency with quantum mechanical predictions.