Unpacking Space-Time Quanta: Snyder’s Algebra Meets Bekenstein’s Bound

Author: (1) Ahmed Farag Ali, Essex County College and Department of Physics, Faculty of Science, Benha University. Table of Links Abstract and Introduction Space-time quanta and Becken Universal bound Shape of space-time quanta Symmetry of space-time quanta Space-time quanta and Spectral mass gap Phenomenological implications 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. Author: (1) Ahmed Farag Ali, Essex County College and Department of Physics, Faculty of Science, Benha University. Author: Author: (1) Ahmed Farag Ali, Essex County College and Department of Physics, Faculty of Science, Benha University. Table of Links Abstract and Introduction Abstract and Introduction Space-time quanta and Becken Universal bound Space-time quanta and Becken Universal bound Shape of space-time quanta Shape of space-time quanta Symmetry of space-time quanta Symmetry of space-time quanta Space-time quanta and Spectral mass gap Space-time quanta and Spectral mass gap Phenomenological implications Phenomenological implications Conclusion, Acknowledgments, and References 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. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv