http://www.mdpi.com/journal/entropy/special_issues/quantum_spaces/ Submission All papers should be submitted to entropy@mdpi.com with copy to the guest editor. To be published continuously until the deadline and papers will be listed together at the special websites. Both, research articles and review articles are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editors for announcment on this website. Submitted papers should not have been published previously, nor be under consideration for publication elsewhere. All papers are refereed through a peer-review process. A guide for authors, sample copies and other relevant information for submitting papers are available on the Instructions for Authors page. Entropy is an international peer-reviewed quarterly journal published by MDPI. Please visit the Instructions for Authors page before submitting a paper. Open Access publication fees are 800 CHF per paper. English correction fees (250 CHF) will be added in certain cases (1050 CHF per paper for those papers that require extensive additional formatting and/or English corrections.). http://www.mdpi.com/1099-4300/10/4/441/ 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. http://www.mdpi.com/1099-4300/10/4/441/ Tue, 14 Oct 2008 00:00:00 CEST Entropy 2008-10-14 10 4 Article 441 461 1099-4300 Spacetime Foam: From Entropy and Holography to Infinite Statistics and Nonlocality 2008-10-14 doi: 10.3390/e10040441 Y. Jack Ng http://www.mdpi.com/1099-4300/10/2/19/ 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. http://www.mdpi.com/1099-4300/10/2/19/ Wed, 19 Mar 2008 00:00:00 CET Entropy 2008-03-19 10 2 Article 19 32 1099-4300 Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables? 2008-03-19 doi: 10.3390/entropy-e10020019 Andrei Khrennikov