Abstract
Stringy corrections to the ordinary Heisenberg uncertainty relations have been known for some time. However, a proper understanding of the underlying new physical principle modifying the ordinary Heisenberg uncertainty relations has not yet emerged. The author has recently proposed a new scale relativity theory as a physical foundation of string and M theories. In this work the stringy uncertainty relations, and corrections thereof, are rigorously derived from this new relativity principle without any ad-hoc assumptions. The precise connection between the Regge trajectory behavior of the string spectrum and the area quantization is also established.
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REFERENCES
C. Castro, “Hints of a new relativity principle from p-brane quantum mechanics,” hep-th/ 9912113; J. Chaos, Solitons and Fractals 11, 1721 (2000); “The search for the origins of M theory: Loop QM and bulk/boundary duality,” hep-th/9809102. S. Ansoldi, C. Castro, and E. Spallucci, Class. Quant. Grav. 16, 1833 (1999); hep-th/9809182.
W. Pezzaglia, “Dimensionally democratic calculus and principles of polydimensional physics,” gr-qc/9912025.
C. Castro, A. Granik, and Mohammed S. El Naschie, “Why we live in 3 dimensions,” hep-th/ 0004152.
C. Castro, “Is quantum spacetime infinite-dimensional?,” hep-th/0001134; J. Chaos, Solitons and Fractals 11, 1663 (2000).
L. Nottale, Fractal Spacetime and Microphysics, Towards the Theory of Scale Relativity (World Scientific, Singapore, 1992); La relativite/ dans tous ses etats (Hachette Literature, Paris, 1999).
D. Amati, M. Ciafaloni, and G. Veneziano, Phys. Letts. B 197, 81 (1987). D. Gross and P. Mende, Phys. Lett. B 197, 129 (1987).
L. Garay, Int. J. Mod. Phys. A 10, 145 (1995).
A. Kempf and G. Mangano, “Minimal length uncertainty and ultraviolet regularization,” hep-th/9612084.
G. Amelino-Camelia, J. Lukierski, and A. Nowieki, “k-deformed covariant phase space and quantum gravity uncertainty relations,” hep-th/9706031.
R. Adler and D. Santiago, “On a generalization of quantum theory: Is the Planck constant really constant?,” hep-th/9908073.
C. Castro and Alex Granik, “How the new scale relativity resolves some quantum paradoxes,” J. Chaos, Solitons and Fractals 11, 2167 (2000).
M. El Naschie, J. Chaos, Solitons and Fractals 10 (2-3), 567 (1999).
G. Ord, J. Chaos, Solitons and Fractals 10 (2-3), 499 (1999).
M. Pitkannen, “p-Adic TGD: Mathematical ideas,” hep-th/9506097; A. Khrennikov, “Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena,” quant-ph/0003016; M. Altaisky and B. Sidharth, J. Chaos, Solitons and Fractals 10 (2-3), 167 (1999). V. Vladimorov, I. Volovich, and E. Zelenov, p-Adic Numbers in Mathematical Physics (World Scientific, Singapore, 1994). L. Brekke and P. Freund, Phys. Rep. 231, 1-66 (1993). G. Ghoshal and A. Sen, “Tachyon condensation and brane descent relations in p-adic string theory,” hep-th/0003278.
C. Castro, “An elementary derivation of the black-hole area-entropy relation in any dimension,” hep-th/0004018.
L. Smolin and S. Kaufmann, “Combinatorial dynamics in quantum gravity,” hep-th/ 9809161.
H. Brandt, J. Chaos, Solitons and Fractals 10 (2-3), 267 (1999).
A. Aurilia, S. Ansolodi, C. Castro, and E. Spallucci, in preparation.
Z. Osiewicz, “Clifford/Hopf algebra and bi-universal Hopf algebra,” q-alg/9709016.
E. Witten, Nuc. Phys. B 268, 253 (1986).
B. Zwiebach, Nuc. Phys. B 390, 33 (1993).
S. Adler, Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, New York, 1995).
Rovelli, “The century of the incomplete revolution: searching for general relativistic quantum field theory,” hep-th/9910131.
S. Mahid, Foundations of Quantum Group Theory (Cambridge University Press, 1995); Int. J. Mod. Phys. A 5, 4689 (1990). I. C. Biedenharn and M. A. Lohe, Quantum Groups and q-Tensor Algebras (World Scientific, Singapore, 1995).
C. Castro, Found. Phys. Lett. 10, 273 (1997).
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Castro, C. The String Uncertainty Relations Follow from the New Relativity Principle. Foundations of Physics 30, 1301–1316 (2000). https://doi.org/10.1023/A:1003640606529
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DOI: https://doi.org/10.1023/A:1003640606529