Optimal uncertainty relations in a modified Heisenberg algebra
Name
PhysRevD.94.123505.pdf
Size
1.11 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Abdelkhalek, Kais
Chemissany, Wissam
Fiedler, Leander
Mangano, Gianpiero
Schwonnek, René
Date Issued
December 2016
Journal
Physical Review D
Publisher
American Physical Society
Citation
Abdelkhalek, Kais et al. “Optimal Uncertainty Relations in a Modified Heisenberg Algebra.” Physical Review D 94.12 (2016): n. pag. © 2016 American Physical Society
Version
Final published version
Abstract
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations that are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows us to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min entropy is exactly 1 bit.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1103/PhysRevD.94.123505
