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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Hawking Vacuum Fluctuation, Unruh Temperature, Rindler Wedge, Dark Energy, Quantum Gravity, Cantorian Spacetime, Hyperbolic Fractal Geometry
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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
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
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
@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} }
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 -