American Journal of Modern Physics

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Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real

Received: Sep. 28, 2013    Accepted:     Published: Dec. 10, 2013
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Abstract

The objective of the present paper is to argue that based on the reality of the observed increased rate of cosmic expansion, Unruh’s temperature, Hawking’s negative vacuum energy and Rindler’s wedge must also be a physical reality. We present first a brief derivation of the missing dark energy density of the universe which is in absolute agreement with the most recent accurate cosmological measurements and observations. The derivation is based upon a Rindler space setting, the associated wedge horizon and Unruh temperature. That way the topological ordinary energy is found to be half of the topological Unruh fluctuation mass m(O) = φ3 multiplied with the square of the topological speed of light c2 = φ2 where φ = 2 /(√5+ 1). This is exactly equal to the area of the spear-like hyperbolic triangular part of the Rindler wedge. The corresponding physical ordinary energy density is thus E(O) = (1/2)( φ3)( φ2) mc2 = (φ5/2)( mc2), where φ5 is Hardy’s probability of quantum entanglement. The topological dark energy density on the other hand is equal half of the topological Kaluza-Klein five dimensional mass m(D) = 5 multiplied with c2 = φ2. This in turn is exactly equal to the circular segment part of the wedge which together with the hyperbolic triangular entangled area forms the complete Lorentzian invariant triangular area of the wedge. Consequently the physical dark energy density which is uncorrelated, i.e. disentangled is given by E(D) = (1/2)(5)( φ2)( mc2) = (5 φ2 /2)( mc2) in full agreement with observation. Adding E(O) and E(D) one finds E(Einstein) = mc2 in full agreement with all our previous derivations. From the above we argue that since measurements, observations and theory have shown the increased expansion to be real and because the present derivation of the same results is based on Rindler’s space and Unruh’s temperature, it follows as a logical necessity that Unruh’s temperature, Hawking’s fluctuation and Rindler’s wedge are all physically real and can be measured, at least in principle.

DOI 10.11648/j.ajmp.20130206.23
Published in American Journal of Modern Physics ( Volume 2, Issue 6, November 2013 )
Page(s) 357-361
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Hawking Vacuum Fluctuation, Unruh Temperature, Rindler Wedge, Dark Energy, Quantum Gravity, Cantorian Spacetime, Hyperbolic Fractal Geometry

References
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[2] L. Amendola and S. Tsujikawa: Dark Energy – Theory and Observations. Cambridge University Press, Cambridge (2010).
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[4] A.G. Riess et al: Observation evidence from supernova for an accelerating universe and cosmological constants. The Astronomical Journal. Vol. 116, P. 1009, 1998. Doi: 10.1086/300499.
[5] A.G. Riess et al: The farthest known supernova: Support for an accelerating universe and a glimpse of the epoch of deceleration. Astrophysical Journal, Vol. 560, 2001, pp. 49-71. Doi: 10.1086/322438.
[6] BP Schmidt et al: The high-Z supernova search: measuring cosmic deceleration and global curvature of the universe using type 1a supernovae. The Astrophysical Journal, Vol. 507, No. 1, 1998, pp. 46
[7] E.J. Copeland, M. Sami and S. Tsujikawa: Dynamics of dark energy, 2006. arXiv: hep-th/0603057V3.
[8] R. Panek: "Dark Energy": The biggest mystery in the universe. 2010. http:/www.smithsonianmagazine.com/science.Nature/darkenergy.
[9] Planck-spacecraft. Wikipedia, 2012. http://en.wikipedia.org/wiki/Planck.
[10] M.S. El Naschie: A unified Newtonian-relativistic quantum resolution of the supposedly missing dark energy of the cosmos and the constancy of the speed of light. Int. J. Mod. Nonlinear Theory & Appli., Vol. 2, No. 1, 2013, pp. 55-59.
[11] L. Marek-Crnjac, M.S. El Naschie and Ji-Huan He: Chaotic fractals at the root of relativistic quantum physics and cosmology. Int. J. of Mod. Nonlinear Theory & Appli., Vol. 2, No. 1A, 2013, pp78-88.
[12] C. Toni: Dark matter, dark energy and the fate of Einstein’s theory of gravity. AMS Graduate Student Blog. Mathgrablog.williams,edu/dark-matter-darkenergy=fate-einstein-theory=gravity/
[13] M.S. El Naschie: Quantum entanglement: where dark energy and negative gravity plus accelerated expansion of the universe comes from. J. of Quant. Info. Sci., Vol. 3, 2013, pp. 57-77.
[14] WMAP Collaboration. E.Komatsu et al. "Seven Years Wilkinson Microwave Anisotropy probe (WMAP) Observations: Cosmological interpretation." Astrophys. J. suppl 192 (2011) 18, arxiv: 1001.4538 [astro-ph.co].
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[18] W. Rindler: Relativity (Special, General and Cosmological). Oxford University press, Oxford. 2004.
[19] M.S. El Naschie: The hyperbolic extension of Sigalotti-Hendi-Sharif Zadeh’s golden triangle of special theory of relativity and the nature of dark energy. J. Mod. Phys., Vol. 4, No. 3, 2013, pp. 354-356.
[20] M.S. El Naschie and Atef Helal: Dark energy explained via the Hawking-Hartle quantum wave and the topology of cosmic crystallography. Int. J. Astron. & Astrophys, Vol. 3, No. 3, 2013, pp. 318-343.
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  • APA Style

    Mohamed S. El Naschie. (2013). Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real. American Journal of Modern Physics, 2(6), 357-361. https://doi.org/10.11648/j.ajmp.20130206.23

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    ACS Style

    Mohamed S. El Naschie. Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real. Am. J. Mod. Phys. 2013, 2(6), 357-361. doi: 10.11648/j.ajmp.20130206.23

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    AMA Style

    Mohamed S. El Naschie. Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real. Am J Mod Phys. 2013;2(6):357-361. doi: 10.11648/j.ajmp.20130206.23

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  • @article{10.11648/j.ajmp.20130206.23,
      author = {Mohamed S. El Naschie},
      title = {Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real},
      journal = {American Journal of Modern Physics},
      volume = {2},
      number = {6},
      pages = {357-361},
      doi = {10.11648/j.ajmp.20130206.23},
      url = {https://doi.org/10.11648/j.ajmp.20130206.23},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmp.20130206.23},
      abstract = {The objective of the present paper is to argue that based on the reality of the observed increased rate of cosmic expansion, Unruh’s temperature, Hawking’s negative vacuum energy and Rindler’s wedge must also be a physical reality.  We present first a brief derivation of the missing dark energy density of the universe which is in absolute agreement with the most recent accurate cosmological measurements and observations.  The derivation is based upon a Rindler space setting, the associated wedge horizon and Unruh temperature.  That way the topological ordinary energy is found to be half of the topological Unruh fluctuation mass m(O) = φ3 multiplied with the square of the topological speed of light c2 = φ2 where  φ = 2 /(√5+ 1).  This is exactly equal to the area of the spear-like hyperbolic triangular part of the Rindler wedge.  The corresponding physical ordinary energy density is thus E(O) = (1/2)( φ3)( φ2) mc2 = (φ5/2)( mc2), where φ5 is Hardy’s probability of quantum entanglement.  The topological dark energy density on the other hand is equal half of the topological Kaluza-Klein five dimensional mass m(D) = 5 multiplied with c2 = φ2.  This in turn is exactly equal to the circular segment part of the wedge which together with the hyperbolic triangular entangled area forms the complete Lorentzian invariant triangular area of the wedge.  Consequently the physical dark energy density which is uncorrelated, i.e. disentangled is given by E(D) = (1/2)(5)( φ2)( mc2) = (5 φ2 /2)( mc2) in full agreement with observation.  Adding E(O) and E(D) one finds E(Einstein) = mc2 in full agreement with all our previous derivations. From the above we argue that since measurements, observations and theory have shown the increased expansion to be real and because the present derivation of the same results is based on Rindler’s space and Unruh’s temperature, it follows as a logical necessity that Unruh’s temperature, Hawking’s fluctuation and Rindler’s wedge are all physically real and can be measured, at least in principle.},
     year = {2013}
    }
    

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  • TY  - JOUR
    T1  - Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real
    AU  - Mohamed S. El Naschie
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    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
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    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20130206.23
    AB  - The objective of the present paper is to argue that based on the reality of the observed increased rate of cosmic expansion, Unruh’s temperature, Hawking’s negative vacuum energy and Rindler’s wedge must also be a physical reality.  We present first a brief derivation of the missing dark energy density of the universe which is in absolute agreement with the most recent accurate cosmological measurements and observations.  The derivation is based upon a Rindler space setting, the associated wedge horizon and Unruh temperature.  That way the topological ordinary energy is found to be half of the topological Unruh fluctuation mass m(O) = φ3 multiplied with the square of the topological speed of light c2 = φ2 where  φ = 2 /(√5+ 1).  This is exactly equal to the area of the spear-like hyperbolic triangular part of the Rindler wedge.  The corresponding physical ordinary energy density is thus E(O) = (1/2)( φ3)( φ2) mc2 = (φ5/2)( mc2), where φ5 is Hardy’s probability of quantum entanglement.  The topological dark energy density on the other hand is equal half of the topological Kaluza-Klein five dimensional mass m(D) = 5 multiplied with c2 = φ2.  This in turn is exactly equal to the circular segment part of the wedge which together with the hyperbolic triangular entangled area forms the complete Lorentzian invariant triangular area of the wedge.  Consequently the physical dark energy density which is uncorrelated, i.e. disentangled is given by E(D) = (1/2)(5)( φ2)( mc2) = (5 φ2 /2)( mc2) in full agreement with observation.  Adding E(O) and E(D) one finds E(Einstein) = mc2 in full agreement with all our previous derivations. From the above we argue that since measurements, observations and theory have shown the increased expansion to be real and because the present derivation of the same results is based on Rindler’s space and Unruh’s temperature, it follows as a logical necessity that Unruh’s temperature, Hawking’s fluctuation and Rindler’s wedge are all physically real and can be measured, at least in principle.
    VL  - 2
    IS  - 6
    ER  - 

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Author Information
  • Dept. of Physics, University of Alexandria, Egypt

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