This content originally appeared on HackerNoon and was authored by Phenomenology
:::info Author:
(1) Ahmed Farag Ali, Essex County College and Department of Physics, Faculty of Science, Benha University.
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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:
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\ 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:
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\ When we compare Eq. (3) with Eq. (6), we get:
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\ that completely describes the quanta of space-time. Notice here that Hκ depends only on π and is independent of κ and nature constants.
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:::info This paper is available on arxiv under CC BY 4.0 DEED license.
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This content originally appeared on HackerNoon and was authored by Phenomenology
Phenomenology | Sciencx (2024-07-31T15:10:51+00:00) Unpacking Space-Time Quanta: Snyder’s Algebra Meets Bekenstein’s Bound. Retrieved from https://www.scien.cx/2024/07/31/unpacking-space-time-quanta-snyders-algebra-meets-bekensteins-bound/
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