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A contextual Planck parameter and the classical limit in quantum cosmology

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Title: A contextual Planck parameter and the classical limit in quantum cosmology
Authors: Barrow, JD
Magueijo, J
Item Type: Journal Article
Abstract: We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, lP, but for those larger than lQ=(l2PH−1)1/3, where H is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.
Issue Date: 19-Feb-2021
Date of Acceptance: 13-Jan-2021
URI: http://hdl.handle.net/10044/1/101367
DOI: 10.1007/s10701-021-00433-0
ISSN: 0015-9018
Publisher: Springer
Journal / Book Title: Foundations of Physics: an international journal devoted to the conceptual and fundamental theories of modern physics, biophysics, and cosmology
Volume: 51
Issue: 1
Copyright Statement: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publication Status: Published
Article Number: ARTN 22
Appears in Collections:Physics
Theoretical Physics



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