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

Mohamed S. El Naschie

doi:doi:10.11648/j.ajmp.20130206.23

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

Mohamed S. El Naschie

Published in American Journal of Modern Physics (Volume 2, Issue 6)

Received: 28 September 2013 Published: 10 December 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.

Published in	American Journal of Modern Physics (Volume 2, Issue 6)
DOI	10.11648/j.ajmp.20130206.23
Page(s)	357-361
Creative Commons	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), 2013. 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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[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.
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[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.
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[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://article.sciencepublishinggroup.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
Y1  - 2013/12/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajmp.20130206.23
DO  - 10.11648/j.ajmp.20130206.23
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 357
EP  - 361
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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Mohamed S. El Naschie

Dept. of Physics, University of Alexandria, Egypt

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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://article.sciencepublishinggroup.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}
}

Copy | Download

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
Y1  - 2013/12/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajmp.20130206.23
DO  - 10.11648/j.ajmp.20130206.23
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 357
EP  - 361
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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