Details
| Original language | English |
|---|---|
| Article number | 123505 |
| Journal | Physical Review D |
| Volume | 94 |
| Issue number | 12 |
| Publication status | Published - 5 Dec 2016 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Physical Review D, Vol. 94, No. 12, 123505, 05.12.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Optimal uncertainty relations in a modified Heisenberg algebra
AU - Abdelkhalek, Kais
AU - Chemissany, Wissam
AU - Fiedler, Leander
AU - Mangano, Gianpiero
AU - Schwonnek, René
PY - 2016/12/5
Y1 - 2016/12/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85002243995&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.94.123505
DO - 10.1103/PhysRevD.94.123505
M3 - Article
AN - SCOPUS:85002243995
VL - 94
JO - Physical Review D
JF - Physical Review D
SN - 2470-0010
IS - 12
M1 - 123505
ER -