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Entropy
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Quantum Spaces: Where Locality Is not Necessary, Causality Might not...
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Quantum Spaces: Where Locality Is not Necessary, Causality Might not Be, but Entropy Certainly Is

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (30 April 2008)

Special Issue Editor

Dr. Paola Zizzi

E-Mail Website
Guest Editor
Department of Pure and Applied Mathematics, University of Padova, Via Belzoni 7, 35131 Padova, Italy
Interests: quantum gravity; quantum cosmology; quantum information
Special Issues, Collections and Topics in MDPI journals

Keywords

  • quantum gravity
  • noncommutative geometry
  • locality
  • microcausality
  • information entropy

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Published Papers (2 papers)

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21 pages, 267 KiB  
Article
Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality
by Y. Jack Ng
Entropy 2008, 10(4), 441-461; https://doi.org/10.3390/e10040441 - 14 Oct 2008
Cited by 62 | Viewed by 13671
Abstract
Due to quantum fluctuations, spacetime is foamy on small scales. The degree of foaminess is found to be consistent with holography, a principle prefigured in the physics of black hole entropy. It has bearing on the ultimate accuracies of clocks and measurements and [...] Read more.
Due to quantum fluctuations, spacetime is foamy on small scales. The degree of foaminess is found to be consistent with holography, a principle prefigured in the physics of black hole entropy. It has bearing on the ultimate accuracies of clocks and measurements and the physics of quantum computation. Consistent with existing archived data on active galactic nuclei from the Hubble Space Telescope, the application of the holographic spacetime foam model to cosmology requires the existence of dark energy which, we argue, is composed of an enormous number of inert “particles” of extremely long wavelength. We suggest that these “particles” obey infinite statistics in which all representations of the particle permutation group can occur, and that the nonlocality present in systems obeying infinite statistics may be related to the nonlocality present in holographic theories. We also propose to detect spacetime foam by looking for halos in the images of distant quasars, and argue that it does not modify the GZK cutoff in the ultra-high energy cosmic ray spectrum and its contributions to time-offlight differences of high energy gamma rays from distant GRB are too small to be detectable. Full article
(This article belongs to the Special Issue Quantum Spaces: Where Locality Is not Necessary, Causality Might not Be, but Entropy Certainly Is)
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14 pages, 188 KiB  
Article
Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?
by Andrei Khrennikov
Entropy 2008, 10(2), 19-32; https://doi.org/10.3390/entropy-e10020019 - 19 Mar 2008
Cited by 51 | Viewed by 11260
Abstract
The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to [...] Read more.
The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space). These investigations were started hundred of years ago by J. Boole (who invented Boolean algebras). The complete solution of the problem was obtained by Soviet mathematician Vorobjev in 60th. Surprisingly probabilists and statisticians obtained inequalities for probabilities and correlations among which one can find the famous Bell’s inequality and its generalizations. Such inequalities appeared simply as constraints for probabilistic compatibility. In this framework one can not see a priori any link to such problems as nonlocality and “death of reality” which are typically linked to Bell’s type inequalities in physical literature. We analyze the difference between positions of mathematicians and quantum physicists. In particular, we found that one of the most reasonable explanations of probabilistic incompatibility is mixing in Bell’s type inequalities statistical data from a number of experiments performed under different experimental contexts. Full article
(This article belongs to the Special Issue Quantum Spaces: Where Locality Is not Necessary, Causality Might not Be, but Entropy Certainly Is)
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