If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox
Author(s)
Mohamed S. El Naschie*
ABSTRACT
We start from a minimal number of generally accepted premises, in particular Hartle-Hawking quantum wave of the universe and von Neumann-Connes’ pointless and self referential spacetime geometry. We then proceed from there to show, using Dvoretzky’s theorem of measure concentration, that the total energy of the universe is divided into two parts, an ordinary energy very small part which we can measure while most of the energy is concentrated as the second part at the boundary of the holographic boundary which we cannot measure in a direct way. Finally the results are shown to imply a resolution of the black hole information paradox without violating the fundamental laws of physics. In this way the main thrust of the two opposing arguments and views, namely that of Hawking on the one side and Susskind as well as tHooft on the other side, is brought to a consistent and compatible coherent unit.
We start from a minimal number of generally accepted premises, in particular Hartle-Hawking quantum wave of the universe and von Neumann-Connes’ pointless and self referential spacetime geometry. We then proceed from there to show, using Dvoretzky’s theorem of measure concentration, that the total energy of the universe is divided into two parts, an ordinary energy very small part which we can measure while most of the energy is concentrated as the second part at the boundary of the holographic boundary which we cannot measure in a direct way. Finally the results are shown to imply a resolution of the black hole information paradox without violating the fundamental laws of physics. In this way the main thrust of the two opposing arguments and views, namely that of Hawking on the one side and Susskind as well as tHooft on the other side, is brought to a consistent and compatible coherent unit.
KEYWORDS
Dvoretzky Theory, Wave-Particle Duality, Von Neumann Pointless and Self Referential Geometry, Cantorian Spacetime, Hartle-Hawking Quantum Wave of the Universe, Dark Energy, Black Hole Information Paradox, Connes Noncommutative Geometry
Dvoretzky Theory, Wave-Particle Duality, Von Neumann Pointless and Self Referential Geometry, Cantorian Spacetime, Hartle-Hawking Quantum Wave of the Universe, Dark Energy, Black Hole Information Paradox, Connes Noncommutative Geometry
Cite this paper
El Naschie, M. (2015) If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox. International Journal of Astronomy and Astrophysics, 5, 243-247. doi: 10.4236/ijaa.2015.54027.
El Naschie, M. (2015) If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox. International Journal of Astronomy and Astrophysics, 5, 243-247. doi: 10.4236/ijaa.2015.54027.
References
[1] Hartle, J.B. and Hawking, S.W. (1983) Wave Function of the Universe. Physics Review D, 28, 2960-2975.
http://dx.doi.org/10.1103/PhysRevD.28.2960 [2] Hawking, S. and Penrose, R. (1996) The Nature of Space and Time. Princeton University Press, Princeton, New Jersey. [3] Misner, C., Thorne, K. and Wheeler, J. (1973) Gravitation. Freeman, New York. [4] Hawking, S. (1993) Hawking on the Big Bang and Black Holes. World Scientific, Singapore. [5] Gibbons, G.W. and Hawking, S.W. (1993) Euclidean Quantum Gravity. World Scientific, Singapore.
http://dx.doi.org/10.1142/1301 [6] Hawking, S. and Israel, W. (1990) 300 Years of Gravitation. Cambridge University Press, Cambridge, UK. [7] Tayler, E.F. and Wheeler, J.A. (1966) Spacetime Physics. W.H. Freeman Company, New York, USA. [8] Amendola, L. and Tsujikawa, S. (2010) Dark Energy: Theory and Observation. Cambridge University Press, Cambridge, UK.
http://dx.doi.org/10.1017/CBO9780511750823 [9] Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego, USA. [10] He, J.-H. (2014) A Tutorial Review on Fractal Spacetime and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718.
http://dx.doi.org/10.1007/s10773-014-2123-8 [11] El Naschie, M.S. (1998) Von Neumann Geometry and E-Infinity Quantum Spacetime. Chaos, Solitons & Fractals, 9, 2023-2030. [12] El Naschie, M.S. (2014) The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. American Journal of Astronomy & Astrophysics, 2, 72-77.
http://dx.doi.org/10.11648/j.ajaa.20140206.13 [13] Moskowitz, C. (2015) Stephen Hawking Hasn’t Solved the Black Hole Paradox Just Yet. Scientific American, 27 August 2015. [14] El Naschie, M.S. (2006) Fractal Black Holes and Information. Chaos, Solitons & Fractals, 29, 23-35.
http://dx.doi.org/10.1016/j.chaos.2005.11.079 [15] El Naschie, M.S. (2013) Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrodinger Quantum Wave. Journal of Modern Physics, 4, 591-596.
http://dx.doi.org/10.4236/jmp.2013.45084 [16] El Naschie, M.S. (2013) What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy and Astrophysics, 3, 205-211.
http://dx.doi.org/10.4236/ijaa.2013.33024 [17] Susskind, L. and Lindesay, J. (2005) Black Holes, Information and the String Theory Revolution. World Scientific, Singapore. [18] Susskind, L. (2008) The Black Hole War. Back Bay Books, New York. [19] ‘t Hooft, G. (1985) On the Quantum Structure of a Black Hole. Nuclear Physics B, 256, 727-745.
http://dx.doi.org/10.1016/0550-3213(85)90418-3 [20] El Naschie, M.S. (2014) From E = mc2 to E = mc2/22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entangled Origin. Journal of Quantum Information Science, 4, 284-291.
http://dx.doi.org/10.4236/jqis.2014.44023 [21] El Naschie, M.S. (2004) A Review of E-Infinity and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 209-236.
http://dx.doi.org/10.1016/S0960-0779(03)00278-9 [22] El Naschie, M.S. (2015) Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy. International Journal of High Energy Physics, 2, 13-21.
http://dx.doi.org/10.11648/j.ijhep.20150201.12 [23] Ball, K. (1997) An Elementary Introduction to Modern Convex Geometry. In: Levy, S., Ed., Flavors of Geometry, Cambridge University Press, Cambridge, 1-58. [24] Baryshev, Y. and Teerikorpe, P. (2002) Discovery of Cosmic Fractals. World Scientific, Hackensack. [25] Kauffman, L.H. (1987) Self-Reference and Recursive Form. Journal of Social and Biological Structures, 10, 53-72.
http://dx.doi.org/10.1016/0140-1750(87)90034-0
[1] Hartle, J.B. and Hawking, S.W. (1983) Wave Function of the Universe. Physics Review D, 28, 2960-2975.
http://dx.doi.org/10.1103/PhysRevD.28.2960 [2] Hawking, S. and Penrose, R. (1996) The Nature of Space and Time. Princeton University Press, Princeton, New Jersey. [3] Misner, C., Thorne, K. and Wheeler, J. (1973) Gravitation. Freeman, New York. [4] Hawking, S. (1993) Hawking on the Big Bang and Black Holes. World Scientific, Singapore. [5] Gibbons, G.W. and Hawking, S.W. (1993) Euclidean Quantum Gravity. World Scientific, Singapore.
http://dx.doi.org/10.1142/1301 [6] Hawking, S. and Israel, W. (1990) 300 Years of Gravitation. Cambridge University Press, Cambridge, UK. [7] Tayler, E.F. and Wheeler, J.A. (1966) Spacetime Physics. W.H. Freeman Company, New York, USA. [8] Amendola, L. and Tsujikawa, S. (2010) Dark Energy: Theory and Observation. Cambridge University Press, Cambridge, UK.
http://dx.doi.org/10.1017/CBO9780511750823 [9] Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego, USA. [10] He, J.-H. (2014) A Tutorial Review on Fractal Spacetime and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718.
http://dx.doi.org/10.1007/s10773-014-2123-8 [11] El Naschie, M.S. (1998) Von Neumann Geometry and E-Infinity Quantum Spacetime. Chaos, Solitons & Fractals, 9, 2023-2030. [12] El Naschie, M.S. (2014) The Measure Concentration of Convex Geometry in a Quasi Banach Spacetime behind the Supposedly Missing Dark Energy of the Cosmos. American Journal of Astronomy & Astrophysics, 2, 72-77.
http://dx.doi.org/10.11648/j.ajaa.20140206.13 [13] Moskowitz, C. (2015) Stephen Hawking Hasn’t Solved the Black Hole Paradox Just Yet. Scientific American, 27 August 2015. [14] El Naschie, M.S. (2006) Fractal Black Holes and Information. Chaos, Solitons & Fractals, 29, 23-35.
http://dx.doi.org/10.1016/j.chaos.2005.11.079 [15] El Naschie, M.S. (2013) Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrodinger Quantum Wave. Journal of Modern Physics, 4, 591-596.
http://dx.doi.org/10.4236/jmp.2013.45084 [16] El Naschie, M.S. (2013) What Is the Missing Dark Energy in a Nutshell and the Hawking-Hartle Quantum Wave Collapse. International Journal of Astronomy and Astrophysics, 3, 205-211.
http://dx.doi.org/10.4236/ijaa.2013.33024 [17] Susskind, L. and Lindesay, J. (2005) Black Holes, Information and the String Theory Revolution. World Scientific, Singapore. [18] Susskind, L. (2008) The Black Hole War. Back Bay Books, New York. [19] ‘t Hooft, G. (1985) On the Quantum Structure of a Black Hole. Nuclear Physics B, 256, 727-745.
http://dx.doi.org/10.1016/0550-3213(85)90418-3 [20] El Naschie, M.S. (2014) From E = mc2 to E = mc2/22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entangled Origin. Journal of Quantum Information Science, 4, 284-291.
http://dx.doi.org/10.4236/jqis.2014.44023 [21] El Naschie, M.S. (2004) A Review of E-Infinity and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 209-236.
http://dx.doi.org/10.1016/S0960-0779(03)00278-9 [22] El Naschie, M.S. (2015) Banach Spacetime-Like Dvoretzky Volume Concentration as Cosmic Holographic Dark Energy. International Journal of High Energy Physics, 2, 13-21.
http://dx.doi.org/10.11648/j.ijhep.20150201.12 [23] Ball, K. (1997) An Elementary Introduction to Modern Convex Geometry. In: Levy, S., Ed., Flavors of Geometry, Cambridge University Press, Cambridge, 1-58. [24] Baryshev, Y. and Teerikorpe, P. (2002) Discovery of Cosmic Fractals. World Scientific, Hackensack. [25] Kauffman, L.H. (1987) Self-Reference and Recursive Form. Journal of Social and Biological Structures, 10, 53-72.
http://dx.doi.org/10.1016/0140-1750(87)90034-0