Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology

ABSTRACT

Using Dvoretzky’s theorem in conjunction with Bohm’s picture of a quantum particle inside a guiding quantum wave akin to De Broglie-Bohm pilot wave we derive Einstein’s famous formula*E = mc*^{2} as the sum of two parts *E(O) = mc*^{2}/22 of the quantum particle and *E(D) = m c*^{2} (21/22) of the quantum wave where m is the mass, c is the speed of light and E is the energy. In addition we look at the problem of black holes information in the presence of extra dimensions where it seems initially that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. Again this surprising result is a consequence of the same well known theorem on measure concentration due to I. Dvoretzky. We conclude that there are only two real applications of the theorem and we expect that many more applications in physics and cosmology will be found in due course.

Using Dvoretzky’s theorem in conjunction with Bohm’s picture of a quantum particle inside a guiding quantum wave akin to De Broglie-Bohm pilot wave we derive Einstein’s famous formula

KEYWORDS

Spacetime Extra Dimensions, Dvoretzky’s Theorem, Information Paradox, E-Infinity Theory, Counterintuitive Geometry, Dark Energy of the Quantum Wave, ‘tHooft-Susskind Black Holes, Wave-Particle Duality, De Broglie-Bohm Pilot Wave

Spacetime Extra Dimensions, Dvoretzky’s Theorem, Information Paradox, E-Infinity Theory, Counterintuitive Geometry, Dark Energy of the Quantum Wave, ‘tHooft-Susskind Black Holes, Wave-Particle Duality, De Broglie-Bohm Pilot Wave

Cite this paper

Naschie, M. (2015) Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology.*Open Journal of Microphysics*, **5**, 11-15. doi: 10.4236/ojm.2015.52002.

Naschie, M. (2015) Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology.

References

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https://www.researchgate.net/post/In_GR_can_we_always_choose_the_local_speed_of_light_to_be_

everywhere_smaller_that_the_coordinate_speed_of_light_Can_this_be_used_in_a_theory

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http://dx.doi.org/10.1016/j.chaos.2005.11.079

[12] El Naschie, M.S. (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 & Astrophysics, 5, 243-247.

http://dx.doi.org/10.4236/ijaa.2015.54027

[13] El Naschie, M.S. (2015) A Resolution of the Black Hole Information Paradox via Transfinite Set Theory. World Journal of Condensed Matter Physics, 5, 249-260.

http://dx.doi.org/10.4236/wjcmp.2015.54026

[14] 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

[15] Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego.

[16] Levy, S., Ed. (1997) Flavors of Geometry. Cambridge University Press, Cambridge, UK.

[17] 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

[18] El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of Nano Spacetime Singularity Reactor. Natural Science, 7, 210-225.

http://dx.doi.org/10.4236/ns.2015.74024

[19] El Naschie, M.S. (1997) Remarks on Super Strings, Fractal Gravity, Nagasawa’s Diffusion and Cantorian Spacetime. Chaos, Solitons & Fractals, 8, 1873-1886.

[20] El Naschie, M.S. (2014) Why E Is Not Equal mc2. Journal of Modern Physics, 5, 743-750.

http://dx.doi.org/10.4236/jmp.2014.59084

[1] Frolov, V.P. and Zelnikov, A. (2011) Introduction to Black Hole Physics. Oxford University Press, Oxford.

http://dx.doi.org/10.1093/acprof:oso/9780199692293.001.0001

[2] Bardeen, J.M., Carter, B. and Hawking, S.W. (1973) The Four Laws of Black Hole Mechanics. Communications in Mathematical Physics, 31, 161-170.

http://dx.doi.org/10.1007/BF01645742

[3] Bekenstein, J.D. (1980) Black-Hole Thermodynamics. Physics Today, 33, 24-31.

http://dx.doi.org/10.1063/1.2913906

[4] Meisner, C.W., Thorne, K.S. and Wheeler, J.A. (1973) Gravitation. W.H. Freeman & Company, San Francisco.

[5] Weinberg, S. (2008) Cosmology. Oxford University Press, Oxford.

[6] Susskind, L. and Lindesay, J. (2005) Black Holes, Information and the String Theory Revolution (The Holographic Universe). World Scientific, New Jersey.

[7] Susskind, L. (2008) The Black Hole War. Back Bay Books, New York.

[8] Horowitz, G.T., Ed. (2012) Black Holes in Higher Dimensions. Cambridge University Press, Cambridge, UK.

http://dx.doi.org/10.1017/CBO9781139004176

[9] Wheeler, A. (1990) Information, Physics, Quantum: The Search for Links. In: Zurek, W., Ed., Complexity Entropy and the Physics of Information, Addison-Wesley, New York, 3-18.

[10] ‘tHooft, G. (2015) G. ‘tHooft Asks a Question about General Relativity on ResearchGate, Questions and Answers. October.

https://www.researchgate.net/post/In_GR_can_we_always_choose_the_local_speed_of_light_to_be_

everywhere_smaller_that_the_coordinate_speed_of_light_Can_this_be_used_in_a_theory

[11] 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

[12] El Naschie, M.S. (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 & Astrophysics, 5, 243-247.

http://dx.doi.org/10.4236/ijaa.2015.54027

[13] El Naschie, M.S. (2015) A Resolution of the Black Hole Information Paradox via Transfinite Set Theory. World Journal of Condensed Matter Physics, 5, 249-260.

http://dx.doi.org/10.4236/wjcmp.2015.54026

[14] 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

[15] Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego.

[16] Levy, S., Ed. (1997) Flavors of Geometry. Cambridge University Press, Cambridge, UK.

[17] 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

[18] El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of Nano Spacetime Singularity Reactor. Natural Science, 7, 210-225.

http://dx.doi.org/10.4236/ns.2015.74024

[19] El Naschie, M.S. (1997) Remarks on Super Strings, Fractal Gravity, Nagasawa’s Diffusion and Cantorian Spacetime. Chaos, Solitons & Fractals, 8, 1873-1886.

[20] El Naschie, M.S. (2014) Why E Is Not Equal mc2. Journal of Modern Physics, 5, 743-750.

http://dx.doi.org/10.4236/jmp.2014.59084