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Calibration to a Reference Determines when Schrödinger's Cats Die

Ken Krechmer

Published Dec 5, 2023• 0 citations
Publisher

Abstract

In 1935 E. Schrödinger proposed a thought experiment to illustrate his concerns with superpositions in quantum measurements. It appears in his experiment that a cat is both alive and dead. This paradoxical superposition has not been explained before. The following identifies that calibration to a reference, currently assumed to be only empirical in measurement theory, explains the paradox of Schrödinger's cats.

DOI
10.32388/f05d6y.5

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In 1935 E. Schrödinger proposed a thought experiment to illustrate his concerns with superpositions in quantum measurements. It appears in his experiment that a cat is both alive and dead. This paradoxical superposition has not been explained before. The following identifies that calibration to a reference, currently assumed to be only empirical in measurement theory, explains the paradox of Schrödinger's cats.
E. Schrödinger proposed a thought experiment to illustrate the discontinuity, not fully understood, that appears in quantum mechanics when a measurement process occurs. The cats in his thought experiment appear to be both alive and dead. This unreasonable appearance has not been satisfactorily explained before. Calibration, which is required in metrology, is not treated in physics theory. This paper illustrates how calibration to a non-local time standard explains the alive and dead appearance of Schrödinger's cats.
E. Schrödinger proposed a thought experiment to illustrate the discontinuity, not currently explained, that appears in quantum mechanics when a measurement occurs. Schrödinger's cats in his thought experiment appear to be both alive and dead. This unreasonable appearance has not been satisfactorily explained before. Calibration, which is required in metrology, is not included in physics theory. Schrödinger's thought experiment is explained by including calibration in measurement theory.
. It is pointed out that the conclusions drawn from a recent quantum interference experiment with light suggest an operational resolution of the Schrödinger cat paradox. On this occasion in honor of Prof. E.T. Jaynes, we recall that he devoted some of his research efforts to the interpretation of quantum mechanics, which led him to propose several experimental tests. Although the ‘neoclassical’ theory he developed was found not to be confirmed by experiment, it nevertheless played a role in encouraging us to think critically about quantum mechanics and to carry out new experiments. This short contribution is concerned with a well-known quantum problem of interpretation. The quantum paradox known as Schrödinger's cat, in which the cat is cast in a linear superposition of the state of being alive and the state of being dead, has been debated since the beginnings of quantum mechanics. Whereas most physicists are ready to concede the existence of superposition states for a microscopic quantum system like an atom, such states appear to be ruled out for a macroscopic system like a cat by common experience. The question then arises at which level classical concepts take over from quantum mechanical ones. In a very clear and readable discussion of this and other paradoxes Glauber has pointed out that the noise inevitably associated with the amplification process accompanying the measurement of a microscopic system leaves the cat in a mixed state rather than a pure one.
Erwin Schrodinger first described the thought-experiment which has since become known as 'the paradox of Schrodinger's cat' 51 years ago. In recent years, popular accounts of quantum mechanics have tended to adopt one or other of the philosophically most extreme solutions to this paradox, i.e. the consciousness hypothesis or the many worlds interpretation. The author attempts to redress the balance by describing what he takes to be the orthodox solution to the paradox which explains the paradox, without recourse to such counterintuitive notions as a cat simultaneously dead and alive or a universe continually splitting into multiple worlds, as being due to a misapplication of the quantum formalism.
Abstract Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead and alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events.
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.