Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem
Author(s)
Mohamed S. El Naschie*
ABSTRACT
We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.
We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.
KEYWORDS
Double Eigenvalues, Weyl Scaling, Magueijo-Smolin Energy Formula, Dark Energy, Einstein’s Relativity, E-Infinity Theory
Double Eigenvalues, Weyl Scaling, Magueijo-Smolin Energy Formula, Dark Energy, Einstein’s Relativity, E-Infinity Theory
Cite this paper
Naschie, M. (2015) Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem. Journal of Modern Physics, 6, 384-395. doi: 10.4236/jmp.2015.64042.
Naschie, M. (2015) Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem. Journal of Modern Physics, 6, 384-395. doi: 10.4236/jmp.2015.64042.
References
[1] S. Perlmutter et al.: Supernova Cosmology Project Collaboration. “Measurements of Omega and Lambda from 42 High-Redshift Supernova.” Astrophys. J. 517, pp. 565 – 585. Astro-ph/9812133, 1999. [2] R. Panek: Dark Energy: The Biggest Mystery in The Universe. The Smithsonian Magazine.
http://www.smithsonianmagazine.com/science-nature/Dark-Energy-April, 2010. [3] Mohamed S. El Naschie: On a new elementary particle from the disintegration of the symplectic 't Hooft-Veltman-Wilson fractal spacetime. World Journal of Nuclear Science and Technology,4(4), 2014, pp. 216-221. [4] Mohamed S. El Naschie:Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics. 4(1), pp. 80-90, 2014. [5] M. A. Helal, L. Marek-Crnjac, Ji-Huan He: Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology Open Journal of Microphysics,3(4), pp. 141-145, 2013. [6] L. Marek-Crnjac, Ji-Huan He: An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics,3(4), 2013, pp. 464-471. [7] Mohamed S. El Naschie:A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics,3(4), pp. 483-493, 2013. [8] Mohamed S. El Naschie: From classical gauge theory back to Weyl scaling via E-infinity spacetime. Chaos, Solitons& Fractals, 38(4), 2008, pp. 980-985. [9] Mohamed S. El Naschie: Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science,1(2), 2011, pp. 50-53. [10] L. Amendola and S. Tsujikawa: Dark energy: Theory and observations. Cambridge University Press, Cambridge 2010. [11] M.S. El Naschie: A resolution of the cosmic dark energy via quantum entanglement relativity theory. Journal of Quantum Information Science, 3(1), 2013, pp. 23-26. [12] J.J. Thomsen: Vibration and Stability: Advanced Theory, Analysis and Tools. Springer, Berlin, Germany, 2003. (See in particular pp. 59 for composite Eigenvalue problems, Dunkerley and Southwell’s formulas). [13] M.S. El Naschie: Coupled oscillation and mode locking of quantum gravity fields, scale relativity and E-infinity space. Chaos, Solitons& Fractals, 12(1), 2001, pp. 179-192. [14] M.S. El Naschie: On Cotterill-Castigliano’s principle, Rayleigh-Timonsenko quotient and post buckling analysis. ZAMM (Journal of Applied Mathematics & Mechanics), T32-T34, 61, 1981. (See in particular equation No. 13 and Fig 1 for a proposed physical experiment). [15] T. Tamai: The Southwell and The Dunkerley Theorems. In ‘Summation Theorems in Structural Stability’, International Centre for Mechanical Sciences, Springer, Berlin, Germany, 354, 1995, pp. 141-185. [16] M.S. El Naschie and A. H. Mansouri: On the ultimate load of circular plates under eccentric radial pressure. Journal of Engineering Science of the University of Riyadh, Saudi Arabia, 6(1), 1980, pp. 103-106. [17] M.S. El Naschie and S. Al Athel: Some extensions of the theorem of Dunkerley. Proceedings of the Eighth Canadian Congress of Applied Mechanics., June 7-12, 1981, pp. 513-514. [18] M.S. El Naschie: Plastic buckling loads and the theorem of Dukerley. In ‘Stress, Stability and Chaos’. McGraw Hill International editions, London, 1990, pp. 370-373. [19] M.S. El Naschie and A. Mansouri: On the design of reinforced concrete columns. Journal of Engineering Science of the University of Riyadh, Saudi Arabia, 6(1), 1980, pp. 101-102. [20] E-Infinity Group: E-Infinity Communications Nos. 1 to 90. E-infinityenergyblogspot.com. [21] M. Kaku: Strings, Conformal Fields and M-Theory. Springer, New York, USA, (2000). [22] M. Duff: The world in eleven dimensions. IOP Publishing, Bristol, UK. (1999). [23] Mohamed S. El Naschie: Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy Journal of Modern Physics,4(10), 2013, pp. 1417-1428. [24] Mohamed S. El Naschie:Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy World Journal of Condensed Matter Physics,4(2), pp. 74-77, 2014. [25] M.S. El Naschie: A topological Magueijo-Smolin varying speed of light theory, the accelerated cosmic expansion and the dark energy of pure energy. Applied Mathematics, 5, 2014, pp. 1780-1790. [26] Mohamed S. El Naschie:Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity Journal of Quantum Information Science,4(2), 2014, pp. 83-91. [27] M.S. El Naschie: Logarithmic running of ‘tHooft-Polyakov monopole to dark energy. International Journal of High Energy Physics, 1(1), 2014, pp. 1-5. [28] M.S. El Naschie: The quantum gravity Immirzi parameter—A general physical and topological interpretation. Gravitation and Cosmology, 19(3), 2013, pp. 151-155. [29] M.S. El Naschie: To dark energy theory from a Cosserat-like model of spacetime. Problems of Nonlinear Analysis in Engineering Systems, 20(1-41), 2014, pp. 79-98. [30] M.S. El Naschie: A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons& Fractals, Vol. 19, No. 1, 2004, pp. 209-236. [31] Ji-Huan He: A tutorial review on fractal spacetime and fractional calculus. Int. Journal of Theoretical Physics, 53, 2014, pp. 3698-3718. [32] A. Connes: Noncommutative Geometry. Academic Press, San Diego, USA, 1994. [33] M.S. El Naschie: The theory of Cantorian spacetime and high energy particle physics (An informal review). Chaos, Solitons& Fractals, 41(5), 2009, pp. 2635-2646. [34] M.S. El Naschie, Ji-Huan He, L. Marek-Crnjac, S. I. Nada and M.A. Helal: Golden mean computer for high energy physics. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Physics. 2(2), p. 80-92 (2012). [35] R. Carrigan et al: Particles and Forces At The Heart of The Matter. Scientific American, Freeman, New York, 1986. [36] L. Marek-Crnjac: The mass spectrum of high energy elementary particles via El Naschie’s E-infinity golden mean nested oscillators and the DunkerleySouthwell eigenvalue theorems and KAM. Chaos, Solitons& Fractals, 18(1), 2003, pp. 125-133
[1] S. Perlmutter et al.: Supernova Cosmology Project Collaboration. “Measurements of Omega and Lambda from 42 High-Redshift Supernova.” Astrophys. J. 517, pp. 565 – 585. Astro-ph/9812133, 1999. [2] R. Panek: Dark Energy: The Biggest Mystery in The Universe. The Smithsonian Magazine.
http://www.smithsonianmagazine.com/science-nature/Dark-Energy-April, 2010. [3] Mohamed S. El Naschie: On a new elementary particle from the disintegration of the symplectic 't Hooft-Veltman-Wilson fractal spacetime. World Journal of Nuclear Science and Technology,4(4), 2014, pp. 216-221. [4] Mohamed S. El Naschie:Pinched Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics. 4(1), pp. 80-90, 2014. [5] M. A. Helal, L. Marek-Crnjac, Ji-Huan He: Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology Open Journal of Microphysics,3(4), pp. 141-145, 2013. [6] L. Marek-Crnjac, Ji-Huan He: An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics,3(4), 2013, pp. 464-471. [7] Mohamed S. El Naschie:A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics,3(4), pp. 483-493, 2013. [8] Mohamed S. El Naschie: From classical gauge theory back to Weyl scaling via E-infinity spacetime. Chaos, Solitons& Fractals, 38(4), 2008, pp. 980-985. [9] Mohamed S. El Naschie: Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science,1(2), 2011, pp. 50-53. [10] L. Amendola and S. Tsujikawa: Dark energy: Theory and observations. Cambridge University Press, Cambridge 2010. [11] M.S. El Naschie: A resolution of the cosmic dark energy via quantum entanglement relativity theory. Journal of Quantum Information Science, 3(1), 2013, pp. 23-26. [12] J.J. Thomsen: Vibration and Stability: Advanced Theory, Analysis and Tools. Springer, Berlin, Germany, 2003. (See in particular pp. 59 for composite Eigenvalue problems, Dunkerley and Southwell’s formulas). [13] M.S. El Naschie: Coupled oscillation and mode locking of quantum gravity fields, scale relativity and E-infinity space. Chaos, Solitons& Fractals, 12(1), 2001, pp. 179-192. [14] M.S. El Naschie: On Cotterill-Castigliano’s principle, Rayleigh-Timonsenko quotient and post buckling analysis. ZAMM (Journal of Applied Mathematics & Mechanics), T32-T34, 61, 1981. (See in particular equation No. 13 and Fig 1 for a proposed physical experiment). [15] T. Tamai: The Southwell and The Dunkerley Theorems. In ‘Summation Theorems in Structural Stability’, International Centre for Mechanical Sciences, Springer, Berlin, Germany, 354, 1995, pp. 141-185. [16] M.S. El Naschie and A. H. Mansouri: On the ultimate load of circular plates under eccentric radial pressure. Journal of Engineering Science of the University of Riyadh, Saudi Arabia, 6(1), 1980, pp. 103-106. [17] M.S. El Naschie and S. Al Athel: Some extensions of the theorem of Dunkerley. Proceedings of the Eighth Canadian Congress of Applied Mechanics., June 7-12, 1981, pp. 513-514. [18] M.S. El Naschie: Plastic buckling loads and the theorem of Dukerley. In ‘Stress, Stability and Chaos’. McGraw Hill International editions, London, 1990, pp. 370-373. [19] M.S. El Naschie and A. Mansouri: On the design of reinforced concrete columns. Journal of Engineering Science of the University of Riyadh, Saudi Arabia, 6(1), 1980, pp. 101-102. [20] E-Infinity Group: E-Infinity Communications Nos. 1 to 90. E-infinityenergyblogspot.com. [21] M. Kaku: Strings, Conformal Fields and M-Theory. Springer, New York, USA, (2000). [22] M. Duff: The world in eleven dimensions. IOP Publishing, Bristol, UK. (1999). [23] Mohamed S. El Naschie: Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy Journal of Modern Physics,4(10), 2013, pp. 1417-1428. [24] Mohamed S. El Naschie:Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy World Journal of Condensed Matter Physics,4(2), pp. 74-77, 2014. [25] M.S. El Naschie: A topological Magueijo-Smolin varying speed of light theory, the accelerated cosmic expansion and the dark energy of pure energy. Applied Mathematics, 5, 2014, pp. 1780-1790. [26] Mohamed S. El Naschie:Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity Journal of Quantum Information Science,4(2), 2014, pp. 83-91. [27] M.S. El Naschie: Logarithmic running of ‘tHooft-Polyakov monopole to dark energy. International Journal of High Energy Physics, 1(1), 2014, pp. 1-5. [28] M.S. El Naschie: The quantum gravity Immirzi parameter—A general physical and topological interpretation. Gravitation and Cosmology, 19(3), 2013, pp. 151-155. [29] M.S. El Naschie: To dark energy theory from a Cosserat-like model of spacetime. Problems of Nonlinear Analysis in Engineering Systems, 20(1-41), 2014, pp. 79-98. [30] M.S. El Naschie: A review of E-infinity and the mass spectrum of high energy particle physics. Chaos, Solitons& Fractals, Vol. 19, No. 1, 2004, pp. 209-236. [31] Ji-Huan He: A tutorial review on fractal spacetime and fractional calculus. Int. Journal of Theoretical Physics, 53, 2014, pp. 3698-3718. [32] A. Connes: Noncommutative Geometry. Academic Press, San Diego, USA, 1994. [33] M.S. El Naschie: The theory of Cantorian spacetime and high energy particle physics (An informal review). Chaos, Solitons& Fractals, 41(5), 2009, pp. 2635-2646. [34] M.S. El Naschie, Ji-Huan He, L. Marek-Crnjac, S. I. Nada and M.A. Helal: Golden mean computer for high energy physics. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Physics. 2(2), p. 80-92 (2012). [35] R. Carrigan et al: Particles and Forces At The Heart of The Matter. Scientific American, Freeman, New York, 1986. [36] L. Marek-Crnjac: The mass spectrum of high energy elementary particles via El Naschie’s E-infinity golden mean nested oscillators and the DunkerleySouthwell eigenvalue theorems and KAM. Chaos, Solitons& Fractals, 18(1), 2003, pp. 125-133