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Journal of Applied Mathematics and Physics

Schrödinger’s Cat Paradox Resolution Using GRW Collapse Model: Von Neumann Measurement Postulate Revisited

Jaykov Foukzon, Alex Potapov, Менькова Елена Романовна, Подосенов Станислав Александрович

Published Jan 1, 2017• 2 citations
Publisher

Abstract

In his famous thought experiment, Schrôdinger (1935) imagined a cat that measures the value of a quantum mechanical observable with its life.Since Schrödinger's time, no any interpretations or modifications of quantum mechanics have been proposed which give clear unambiguous answers to the questions posed by Schrödinger's cat of how long superpositions last and when (or whether) they collapse?In this paper appropriate modification of quantum mechanics is proposed.We claim that canonical interpretation of the wave function 1 2 cat live cat death cat c c = +.

DOI
10.4236/jamp.2017.52044

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In his famous thought experiment, Schrôdinger (1935) imagined a cat that measures the value of a quantum mechanical observable with its life.Since Schrödinger's time, no any interpretations or modifications of quantum mechanics have been proposed which give clear unambiguous answers to the questions posed by Schrödinger's cat of how long superpositions last and when (or whether) they collapse?In this paper appropriate modification of quantum mechanics is proposed.We claim that canonical interpretation of the wave function 1 2 cat live cat death cat c c = +.
In his famous thought experiment, Schrôdinger (1935) imagined a cat that measures the value of a quantum mechanical observable with its life.Since Schrödinger's time, no any interpretations or modifications of quantum mechanics have been proposed which give clear unambiguous answers to the questions posed by Schrödinger's cat of how long superpositions last and when (or whether) they collapse?In this paper appropriate modification of quantum mechanics is proposed.We claim that canonical interpretation of the wave function 1 2 cat live cat death cat c c = +.
In his famous thought experiment, Schrodinger(1935) imagined a cat that measures the value of a quantum mechanical observable with its life. Since Schrodinger’s time,no any interpretations or modifications of quantum mechanics have been proposed which gives clear unambiguous answers to the questions posed by Schrodinger’s cat of how long superpositions last and when (or whether) they collapse?In this book appropriate modification of quantum mechanics is proposed.We claim that canonical interpretation of the wave function ψ=с1ψ1+с2ψ2 is correct only when the wave function supports ψ1 and ψ2 essentially overlap. When these ones have separated supports we claim that canonical interpretation of the wave function ψ is no longer valid for a such cat state.Possible solution of the Schrodinger’s cat paradox is considered. We pointed out that the collapsed state of the cat always shows definite and predictable outcomes even if the cat also consists of a superposition:|cat>=с1|alive cat>+с2|death cat>.Using new quantum mechanical formalism the EPRB-paradox is considered.We find that the EPRB-paradox can be resolved by nonprincipal and convenient relaxing of the Einstein’s locality principle.
A new quantum mechanical formalism based on the probability representation of quantum states is proposed. This paper in particular deals with the special case of the measurement problem, known as Schrödinger's cat paradox. We pointed out that Schrödinger's cat demands to reconcile Born's rule. Using new quantum mechanical formalism we find the collapsed state of the Schrödinger's cat always shows definite and predictable outcomes even if cat also consists of a superposition cat  c 1 live cat  c 2 death cat |c 1 | 2  |c 2 | 2  1. Using new quantum mechanical formalism the EPRB-paradox is considered successfully. We find that the EPRB-paradox can be resolved by nonprincipal and convenient relaxing of the Einstein's locality principle. Content Part I.Schrödinger's cat paradox resolution using GRW collapse model. Von Neumann measurement postulate revisited.
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.
The Schrödinger's Cat paradox was proposed in 1935 by Edwin Schrodinger, one of the founders of quantum mechanics, as an attempt to visualize the macroscopic realization of a quantum superposition state. A cat is placed in a sealed box together with a vial of poison. A two-state particle (e.g. an electron) is sent into a detector in the box resulting either in a broken or an intact vial and a dead or live cat, respectively. The main problem consists in whether the superposition state of a microscopic particle can be transferred upon the macroscopic cat, that is, whether the cat can exist in a superposition state, being simultaneously dead and alive. Since the standard Copenhagen interpretation is unable to assign any reality to the quantum superposition state, the paradox finds no resolution within the regime of this interpretation. Von Neumann's insistence on the uniform treatment of both microscopic (quantum) and macroscopic (classical) objects according to the laws of quantum mechanics provides a more consistent framework for the resolution of the paradox. In particular, the discovery of the phenomenon of decoherence, whereby the disappearance of the quantum interferences at the macro level is accounted for, suggests the onset of an extremely efficient interference relaxation process (10-23 s) upon the interaction of the two state particle with the detector. As a result, Schrodinger's cat can exist macroscopically either as dead or alive and never as a combination of both. Decoherence not only aids the resolution of the Schrodinger's Cat paradox but also sheds light upon the mechanisms by which the macro-world emerges from the microscopic quantum realm.