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arXiv:physics/0602161 · Physics Essays

Becoming Classical: A Possible Cosmological Influence on the Quantum-Classical Transition.

C. L. Herzenberg

Published Dec 1, 2006• 8 citations
arXivHTMLPDF

Abstract

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using an uncertainty in position estimated from the spread in velocities associated with its size, the criterion that the uncertainty in position should be smaller than the extension of the object leads to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.

DOI
10.4006/1.3028869

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Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using an uncertainty in position estimated from the spread in velocities associated with its size, the criterion that the uncertainty in position should be smaller than the extension of the object leads to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using the criterion that the uncertainty in position should be smaller than the size of an object together with estimates based on the range of Hubble velocities extending through the object lead to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.
Recently, what appears to be a fundamental limit associated with the size of an object that separates the quantum behavior characterizing small objects from the classical behavior characterizing large objects has been derived from the Hubble velocity spread in an extended object. This threshold is now examined further and interpreted in terms of diffusion processes in stochastic quantum mechanics. This limiting size that separates quantum behavior from classical behavior is shown to correspond approximately to the diffusion distance of the object over the Hubble time.
Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum system can be explored in one approach by considering an object at rest in space with a universal Hubble expansion taking place away from it, and developing a Schroedinger type governing differential equation incorporating an intrinsic expansion speed. Wave function solutions to this governing equation exhibit pronounced central localization. The extent of concentration of probability depends on mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses are concentrated into much smaller regions. To develop a criterion for classicality, we consider that if the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, then quantum behavior could be expected; whereas if the region of high probability density for the location of the center of mass is smaller than the size of the object, the object would behave in a more classical manner. The resultant size threshold for classicality accords with results of other studies examining these issues based on uncertainty relations and wave packets. This size threshold is informative for the case of compact extended objects and, as the constraint applies to the center of mass of the system, does not lead to inconsistencies for quantum correlations between distant entangled quantum objects. While local decoherence may lead to classicality under a variety of conditions, cosmologically induced classicality would appear to cause fundamental limitations on quantum behavior in our universe.
We consider an object at rest in space with a universal Hubble expansion taking place away from it. We find that a governing differential equation developed from the Schroedinger equation leads to wave functions which turn out to exhibit pronounced central localization. The extent of concentration of probability depends on the mass; objects with small masses tend to behave in a delocalized manner as ordinary quantum objects do in a static space, while quantum objects with large masses have wave functions that are largely concentrated into much smaller regions. This in turn suggests the possibility that classical behavior is being induced in quantum objects by the presence of the Hubble expansion. If the size of the localized region of concentrated probability density is larger than the size of the corresponding extended object, quantum behavior might be expected; whereas classical behavior might be expected for cases in which the region of high probability density is smaller than the size of the object. The resulting quantum-classical boundary due to Hubble expansion may be expressed in terms of a relationship between the size and mass of an object, or may be expressed in terms of a threshold moment of inertia.