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Unpacking Space-Time Quanta: Snyder’s Algebra Meets Bekenstein’s Bound
by Phenomenology TechnologyJuly 31st, 2024
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We’re exploring Snyder’s space-time quanta and their relation to Bekenstein’s universal bound. Snyder’s algebra implies that non-commutative geometry relies on a fundamental minimal length, and Bekenstein’s bound provides a limit on the amount of information needed to describe a physical object. These findings help define the quanta of space-time and connect important concepts in quantum theory.
Author:
(1) Ahmed Farag Ali, Essex County College and Department of Physics, Faculty of Science, Benha University.
Table of Links
Space-time quanta and Becken Universal bound
Space-time quanta and Spectral mass gap
Conclusion, Acknowledgments, and References
II. SPACE-TIME QUANTA AND BEKENSETIN UNIVERSAL BOUND
In this section, we investigate the physical properties of space-time quanta implied by Snyder’s algebra. It is clear that Eq. (1) only vanishes if there is no fundamental minimal/quantum length (i.e κℓP l = 0). This means non-commutative geometry would vanish if there is no minimal/quantum length. On the contrary, we find that the GUP commutation relation in Eq. (2) vanishes. The time-energy commutation relation of Eq. (2) vanishes when:
where E = p0 and Eκ represents the maximum bound on energy. The position-momentum commutation relation Eq. (2) vanishes when:
On another side, Bekenstein found a universal bound [35–37] that defines the maximal amount of information that is necessary to perfectly and completely describes a physical object up to the quantum level. Bekenstein universal bound is given by:
When we compare Eq. (3) with Eq. (6), we get:
that completely describes the quanta of space-time. Notice here that Hκ depends only on π and is independent of κ and nature constants.
This paper is available on arxiv under CC BY 4.0 DEED license.
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