An Uncertainty relation of space-time

Sasakura, Naoki

doi:10.1143/PTP.102.169

An Uncertainty relation of space-time

Naoki Sasakura
(
- Kyoto U.
)

Mar, 1999

12 pages

Published in:

Prog.Theor.Phys. 102 (1999) 169-179

e-Print:

hep-th/9903146 [hep-th]

DOI:

10.1143/PTP.102.169

Report number:

KUNS-1566

View in:

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Abstract:

We propose an uncertainty relation of space-time. This relation is characterized by GhT \lesssim \delta V, where T and \delta V denote a characteristic time scale and a spatial volume, respectively. Using this uncertainty relation, we give qualitative estimations for the entropies of a black hole and our universe. We obtain qualitative agreements with the known results. The holographic principle of 't Hooft and Susskind is reproduced. We also discuss cosmology and give a relation to the cosmic holographic principle of Fischler and Susskind. However, as for the maximal entropy of a system with an energy E, we obtain the formula \sqrt{EV/Gh^2}, with V denoting the volume of the system, which is distinct from the Bekenstein entropy formula ER/h with R denoting the length scale of the system.

uncertainty relations: space-time
black hole: entropy
cosmological constant
holography
energy: density
thermodynamics
quantum gravity

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