A Fractal Rindler-Regge Triangulation in the Hyperbolic Plane and Cosmic de Sitter Accelerated Expansion

A Fractal Rindler-Regge Triangulation in the Hyperbolic Plane and Cosmic de Sitter Accelerated Expansion

A Fractal Rindler-Regge Triangulation in the Hyperbolic Plane and Cosmic de Sitter Accelerated Expansion

Mohamed S. El Naschie

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Department of Physics, University of Alexandria, Alexandria, Egypt

Email: Chaossf@aol.com

Copyright © 2015 by author and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Received 1 December 2014; accepted 24 March 2015; published 25 March 2015

ABSTRACT

The well known finite elements Regge calculus is transformed to a triangulation in the hyperbolic plane using fractal Rindler wedges as tiling elements. The final result is an expanding de Sitter hyperbolic, i.e. Gauss-Bolyai-Lobachevsky universe with dark energy and ordinary energy densities in full agreement with cosmic observations and measurements. In the course of obtaining this vital result, the work addresses fundamental points connected to a host of subjects, namely Hardy’s quantum entanglement, an extension of Turing’s machine to a transfinite version, the phenomenon of measure concentration in the context of Banach-like spaces with high dimensionality as well as the pioneering work on the relation between quantum entanglement and computational efficiency.

Keywords:

Component, Hyperbolic Regge Calculus, Finite Elements in Cosmology, de Sitter Universe, E-Infinity Theory, Transfinite Turing Golden Mean Computer, Rindler Triangulation, Endophysics, Anti-Bethes Poof, Topological Quantum Entanglement, Gauss-Bolyai-Lobachevsky Geometry

1. Introduction

Regge calculus is a powerful finite element-like method in four dimensions applied to solve Einstein’s highly nonlinear equations [1] -[13] . The method was further developed, modified and extended to a quantum gravity theory by many researchers [3] . In recent times the work of J. Ambjorn and R. Loll [13] deserves special attention [1] - [3] [13] . It was against this background that the present work was planned and executed by transforming Regge calculus to a fractal hyperbolic theory [14] which is used to solve the mystery of accelerated cosmic expansion and the associated dark energy believed to be an expression of a non-vanishing cosmological constant [14] - [24] . In short, the spacetime of our theory is a hyperbolic fractal where quantum entanglement is replaced by a Hardy type natural topological zero measure entanglement [22] following E-infinity theory [24] - [35] .

The paper is subdivided for efficient reading as follows: After the Introduction we review in Section 2 some important dualities between inverse electroweak couplings and the various energy sections as well as the extension of Turing’s machine to a transfinite version via a highly structured golden mean ring as a number system [34] - [48] . Section 3 is a condensed account of the Regge “finite element” method and its adaption to the present work [35] . In Section 4 we discuss the ideas and hunches leading to a hyperbolic expanding de Sitter universe [35] . Subsequently in Section 5 the fundamental results are wrapped up with the analogy presented earlier in Section 2 [49] - [60] . Finally in Section 6 we present a short recapitulation of the paper and the relevance of quantum entanglement enhanced computation [61] - [63] .

The present work is by no means self contained but we rely on an adequate list of references to fill in the inevitable gaps in a condensed presentation [20] - [63] .

2. E-Infinity Dualities between Various Cosmic Energy Sections and Electroweak Couplings―The Transfinite Turing Machine

Let us consider here a most instructive and somewhat surprising duality between the coupling constant of the electroweak interaction (i.e., , and) [25] - [40] and the four fundamental sections of cosmic energy (i.e. pure dark energy 74%, dark matter 22%, ordinary energy 3% and ordinary matter 1%) [14] - [24] . The values mentioned above for  are the exact E-infinity theoretical value which are very close to the experimental one [25] - [32] and also satisfies the reconstruction equation of  where, = P (Hardy’s quantum entanglement) and  [22] . Inserting in the said equation one finds [28] [33]

(1)

where  is the E-infinity Clebsch factor [25] - [27] [39] and, where  is Hardy’s probability of quantum-topological zero measure entanglement [22] , could be expressed in terms of ‘tHooft’s order parameter of dimensional regularization, namely  to give. On the other hand, the integer value of  namely  could be found using the same reconstruction formula but after replacing  and  by the following values [14] - [24]

(2)

In addition the E-infinity transfinite value the Clebsch factor [39] must be made rational, i.e.

(3)

We note on passing that the Clebsch factor is needed because the electroweak is based on three different Lie symmetry groups U(1), SU(2) and SU(3) [39] [40] which are made compatible by this very same factor. Inserting in our renormalization equation one finds

(4)

where 22 + 4 = 26 is the dimensionality of the Veneziano-Nambu bosonic string space [39] . It is also noteworthy that [11] [12] [19] [20]

(5)

and similarly

(6)

From the preceding elementary analysis, it is obvious even to non-mathematicians that the mathematical scheme behind this calculation is trying to tell us something which transcends mathematics in the common naïve understanding as a mere tool and elevate it to something indistinguishable from physics, albeit the physics of what G. ‘tHooft calls the elementary building block of space, time and matter [41] . Let us attempt in good faith to translate what is superficially numbers to what is equally superficially means physics. Since 75% corresponds to  we feel strongly inclined to view pure dark energy as being of electromagnetic origin at the energy scale of the electroweak unification. Next  corresponds to the weak force and again at the electroweak unification. Proceeding with our educated guesswork, it would seem quite evident that ordinary energy and matter must be clearly connected to the strong interaction  and the quantum gravity coupling  [25] - [30] . Considering that the topology required by high energy physics is not the classical “tame” topology but the Cantor set ramified “wild topology” [28] - [33] , the preceding guesswork was not “wild” at all. However, the next guesswork may be closer to scientific speculation than to scientific-mathematical deduction. The point concerns the division of ordinary energy into non-luminous matter and luminous matter. Following the statistical analysis of cosmic energy measurement, it seems that 74% should be nearer to 73% while 22% is reported to be 23% [42] . This is not grave because we could discuss these things away once we take the next set of data seriously. These are 3.6% for non-luminous matter and 0.4% for luminous matter [42] . We can for instance see 0.4% as the difference between the core Hausdorff dimension  and the scaling dimension of ‘tHooft fractal dimensional regularization spacetime  [17] . That means. Concentrating now on the larger picture we could say from reading the preceding dualities road map that the ordinary energy and matter inhabits Einstein’s four dimensional spacetime, i.e. 3 + 1 = 4 dimensions with a corresponding about 4% energy density [14] - [24] . Dark matter on the other hand is uniquely connected to the compactified 26 − 4 = 22 dimensions of bosonic string spacetime. This leaves from our canonical 100 dimensions exactly 100 − (22 + 4) = 74 dimensions for pure dark energy to roam in [19] - [22] . The word is too complex to have been at the beginning and we say that with the outmost due respect to all religions who believe to the contrary. The number must have been there first because one, two, three seems infinitely simpler than a word although we admit that this depends crucially upon what we mean by the word ‘word’. However, this is not entirely true because the integers are a very special kind of numbers and they may be infinite but there seems to be much larger infinity than this simple infinite number. It is here where our golden mean based number system constituting a transfinite version of A. Turing’s machine [34] [43] , a golden mean computer if you want [43] , is infinitely more efficient to handle quantum problems in high energy physics and cosmology. In fact, this number theoretical wonder weapon is subtly related to our choice of units and it can be shown on deep reflection that Hans Bethe’s famous spoof [44] is not really a spoof. We actually mean that the most convenient choice of units is a natural requirement of accurate quantum and micro physics expressed properly in the language of the most irrational number f in all its combinations. In this sense, a part of naïve conception of number coincidence or numerology of the customary loose sense in which this word is misused although if we encounter such “numerology” [44] - [52] then it is just the pattern of a not yet understood fundamental physical or cosmological phenomena. That is also where the circle closes because fundamental physics and cosmology are fundamental mathematics [49] - [60] . In this sense, Sir A.S. Eddington’s rational intuition was far ahead of his and our mastery of pure mathematical reasoning at the time [52] [56] - [60] .

3. From Transfinite Triangulation in the Hyperbolic Plane to Dark Energy

In what follows, we give a concise outline for a general theory of quantum relativity and dark energy based on an exact transfinite extension of Regge triangulation calculus in the Poincare-Beltrami hyperbolic plane [39] . In our present theory, not only the basic idea is very easy to grasp but also the actual computation is surreal in its simplicity [14] . We suggest starting by recalling the geometrical shape of a circular region covered by triangular tiles which are a crossbreed between those used in Klein’s modular curve and those utilized in Penrose tiling [19] [20] [39] . Compactifying these shapes would mean that we are approaching a fractal Penrose universe or in more stringent mathematical terminology, our circular region becomes an exact realization of a fiber bundle manifold [39] or in the language used by A. Connes, a noncommutative x quotient space [36] . It is thus neither difficult to imagine nor mathematical to reason that the following applies to the topology and geometry we are dealing with:

1) In the center of our Regge “finite elements” tessellation [1] - [5] , the triangular tiles are rather ordinary classical shapes with straight sides. However, as we move from the center of the Beltrami-Poincaré plane outwardly the triangular straight lines start to deform and shrink hyperbolically [35] [39] .

2) The circular boundary lies naturally at infinity and the area of the hyperbolic triangle tends towards a classical zero.

3) Adding uniform randomness to the so obtained fractal Regge tiling covering of the hyperbolic plane will result in a topology endowed with the golden mean inherited from the two legitimate parents, namely the Mauldin-Williams random triadic Cantor sets [28] - [34] and the golden mean proportioned kite and dart of Penrose’s universe [28] - [34] [39] .

4) Having went as far as we did, our basic spacetime blocks will be looked upon not as mere hyperbolic triangles but as a Rindler triangle, i.e. Rindler wedge with the familiar spear form containing the correlated part of spacetime, i.e. the entangled part while the moon section rear part contains the uncorrelated part of space which amounts to about 95.5% of the total “area” of the Rindler wedge [14] [35] .

5) The genesis from classical triangular geometry to that of hyperbolic geometry may be likened to a very far extent with that of the logistic map which starts by period doubling classical bifurcation [48] [50] [52] but at approximately l = 3.8 we have triple bifurcation leading according to Zarkovski’s number theory to a quasi chaotic region [50] following the title of the famous J. Yorke paper “Period three implies chaos” and from l = 4.23606 onwards we enter into a hyperbolic region [48] [50] [52] . It is incredible how generic this behaviour is when we consider that the Hausdorff dimensions of ‘tHooft’s fractal regularization space is 4 − k = 3.81966011 while the core of E-infinity Cantorian spacetime is characterized by a Hausdorff dimension expectation of exactly D = 4.23606, i.e. D = l = 4.23606 of the logistic map [57] . Needless to say that in all of our physical analysis quantum entanglement is de facto replaced by the notion of a zero measure topological Hardy type entanglement [22] .

6) Also as we move away from the center with our normal triangle, we leave behind us slowly but surely an exo-physical universe and approach an endo-physical one [53] [54] . At infinity we cannot reconcile experiment with theory except when we recognize the exo-endo duality as uncovered in the pioneering work of D. Finkelstein, O.E. Roessler, H. Primas and their schools [53] [54] .

7) Most importantly, we must realize that as our random space grows more “hyperbolic” it does not acquire a negative curvature but against naïve expectation, the curvature corresponding to the entire hyperbolic projection is not negative but positive.

8) Based on the above we have to conclude that our space corresponds to a de Sitter universe [39] .

9) The preceding scenario of a de Sitter space entails not only an expanding but an accelerated expansion of the spacetime described above.

10) Taking points one to nine, we conclude that the cosmological constant is non-zero and that our universe is self similar hyperbolic fractal and that with a 95.5% volume concentration at the surface of the spacetime manifold. This is actually a mathematical theorem on volume measure concentration of convex highly dimensional Banach-like spaces.

4. Discussion and Our Initial Hunch That E-Infinity Leads to an Expanding Hyperbolic de Sitter University

It is quite instructive and rather helpful to a proper understanding of the hyperbolic fractal nature of our alleged de Sitter universe to explain how we arrived at what must have been just a hunch and foggy idea, at least initially. Any idea, no matter how simple is produced by a highly complex and as yet not really understood perceptive, combinatorial and imaginative brain process, but in the present case it may well have started by the author noticing the similarity between the Rindler wedge and the Regge triangulation used in recent times intensively in a computer oriented theory by Ambjorn and Loll [13] . In addition, we know that a normal triangle is fat in the spherical case but thin in the hyperbolic case. Therefore in the limit the area tends to zero. Furthermore as we could describe a flat space as space with a trivial axiom for parallel lines and a spherical space as zero parallel lines space, a hyperbolic space has infinitely many parallel lines just as a Cantorian space has infinitely many dimensions. The only point which may not be straight forwards in our largely hand waving but accurate arguments is that we are claiming “Rindler” tiling space will be globally a de Sitter space although on account of its hyperbolicity, it should have a negative curvature, an anti de Sitter space [39] . However, noting the intrinsic randomness coupled with the Poincare-Beltrami projection and the basic averaging used, our space is not simply hyperbolic space but actually a very high dimensional Banach-like Cantorian fractal [14] [35] which is projected on the hyperbolic plane to give us this unique structure. In the case of any doubt, the reader needs to ponder the simplicity of the exact expressions of the Rindler areas involved. These are the arrow like area which is equal to the density of ordinary energy of the exo-physical universe [53] [54] and is given by [18] -[20]

(7)

and the circular section area behind the arrow which is equal to the total ark energy density of an endo-physical universe [53] [54] , namely [18] - [20]

(8)

If the proof of the pudding is in the eating, as a common English proverb says, then the above result and the associated energy-mass relationship [18] - [20]

(9)

are sufficient proof for us that Einstein’s formula is confirmed rather than refuted by the absence of measurable dark energy and the observation of accelerated cosmic expansion as well as our present reinterpretation of E = mc² as the sum of the measurable energy of the quantum particle E(O) and the energy of the quantum wave E(D) which we cannot measure because of the Hartle-Hawking collapse of Wheeler-Dewitt wave function of the cosmos [12] [39] . For the avoidance of any possible misunderstanding, we stress again that our dissection not only presupposes Einstein’s beautiful formula but in conjunction with the cosmic endo-physical measurement, it confirms E = mc² theoretically and experimentally beyond a trace of a doubt.

5. Analogies between Analogies and into Deep 5 Dimensional de Sitter Waters

From the preceding analysis, we see that a most intriguing duality or maybe what we could call analogies among analogies as befitting a self affine universe exists, which we could represent as earlier in Section 2:

(10)

However, this is not yet where things end for there are some even deeper interrelationships not only between time and matter but also between mater expressed as mass and space as well as spacetime dimensionality. It turns out that a unit of dimensionless energy corresponds to a unit of Cantorian spacetime and that tangible and directly detectable mass (m) enters into our equations as a three dimensional, i.e. space-like Cantor set given by the treble intersection. This means “measurable” mass is the inverse of the core Hausdorff dimension  of our Cantorian de Sitter spacetime. By contrast dark matter enters into our equation as a five dimensional topological mass m = 5. Recalling that the interval topological speed of light is given by, we see that we must have two kinds of energy densities, namely

(11)

and

(12)

which then leads to the two expressions for ordinary energy  and dark energy. Naturally and provided we remember that  is the Hausdorff dimension of the zero set while  is the Hausdorff dimension of the empty set, both expressions, i.e. and  could be viewed as having been grown out of a five dimensional Kaluza-Klein theory with the only difference that  is a multiplicative, i.e., while  is additive, i.e. as explained in great detail in previous publications [17] - [22] [43] .

6. Conclusion

The classical Regge method of relativity is transformed using Gauss-Bolyai-Lobachevsky hyperbolic geometry to the context of quantum relativity and cosmology to give information about the accelerated cosmic expansion and the associated dark energy density. The task was achieved by transforming the method to the hyperbolic plane and using Rindler-like triangles to form a random self similar fractal tiling akin to that of Klein-Penrose. The final conclusion is that our model effectively represents a fractal de Sitter universe with ordinary measurable exo-physical energy density of  and a complimentary endo-physical dark energy [48] [49] density which cannot be measured directly and amounts to. We stress that all the preceding results could not be arrived at without the experimentally verified magnificent result of L. Hardy that a two quantum particle entanglement is given by  where  and the interpretation that this is due to zero measure topological entanglement [22] . In fact, we are tempted to speculate on the imaginative but quite realistic idea that computational efficiency may be related to entanglement and consequently to a hidden golden mean number system [61] [62] .

References

1. Regge, T. (1961) General Relativity without Coordinates. Il Nuovo Cimento Series 10, 19, 558-571.
2. Regge, T. and Wheeler, J.A. (1957) Stability of Schwarzschild Singularity. Physics Review, 108, 1063. http://dx.doi.org/10.1103/PhysRev.108.1063
3. Misner, C., Thorne, K. and Wheeler, J. (1973) Gravitation. Freeman, New York.
4. El Naschie, M.S. (2007) The Fibonacci Code Behind Superstrings and P-Branes. An Answer to M. Kaku’s Fundamental Question. Chaos, Solitons & Fractals, 31, 537-547.http://dx.doi.org/10.1016/j.chaos.2006.07.001
5. El Naschie, M.S. (2013) The Quantum Gravity Immirzi Parameter―A General Physical and Topological Interpretation. Gravity and Cosmology, 19, 151-153.http://dx.doi.org/10.1134/S0202289313030031
6. El Naschie, M.S. (2005) Einstein’s Dream and Fractal Gravity. Chaos, Solitons & Fractals, 24, 1-5. http://dx.doi.org/10.1016/j.chaos.2004.09.001
7. El Naschie, M.S. (2001) Fisher’s Scaling and Dualities at High Energy in E-infinity Spaces. Chaos, Solitons & Fractals, 12, 1557-1561. http://dx.doi.org/10.1016/S0960-0779(00)00127-2
8. Argyris, J., Ciubotariu, C. and Weingartner, W.E. (1999) Progress in Physical Concepts and Strings and Superstring Theory―Thirty Years of String Theory. Chaos, Solitons & Fractals, 10, 225-256. http://dx.doi.org/10.1016/S0960-0779(98)00320-8
9. Marek-Crnjac, L. and El Naschie, M.S. (2013) Chaotic Fractal Tiling for the Missing Dark Energy and VenezianoModel. Applied Mathematics, 4, 22-29.http://dx.doi.org/10.4236/am.2013.411A2005
10. Sidharth, B.G. (2006) Strings and Planck Oscillator. Chaos, Solitons & Fractals, 30, 300-311. http://dx.doi.org/10.1016/j.chaos.2006.01.114
11. El Naschie, M.S. (2014) Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘t Hooft’s 4-ε Fractal Spacetime. American Journal of Astronomy & Astrophysics, 2, 34-37.http://dx.doi.org/10.11648/j.ajaa.20140203.12
12. El Naschie, M.S. (2013) Dark Energy of the Quantum Hawking-Hartle Wave of the Cosmos from the Holographic Boundary and Lie Symmetry Groups―Exact Computation and Physical Interpretation. Fractal Spacetime and Noncommutative Geometry in Quantum High Energy Physics, 3, 11-20.
13. Jurkiewicz, A.J. and Loll, R. (2008) The Self-Organizing Quantum Universe. Scientific American, 24-31.
14. El Naschie, M.S. (2013) A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, 3, 483-493. http://dx.doi.org/10.4236/ijaa.2013.34056
15. Supernova Cosmology Project Collaboration, Perlmutter, S., Aldering, G., Goldhaber, G., Knop, R.A., Nugent, P., Castro, P.G., et al. (1999) Measurements of Omega and Lambda from 42 High-Redshift Supernova. Astrophysical Journal, 517, 565-585.
16. Panek, R. (2010) Dark Energy: The Biggest Mystery in the Universe. The Smithsonian Magazine. http://www.smithsonianmagazine.com/science-nature/Dark-Energy-April.
17. El Naschie, M.S. (2014) 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, 216-221. http://dx.doi.org/10.4236/wjnst.2014.44027
18. El Naschie, M.S. (2014) Material Einstein Space-Time Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics, 4, 80-90.http://dx.doi.org/10.4236/ijaa.2014.41009
19. Helal, M.A., Marek-Crnjac, L. and He, J-H. (2013) The Three 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, 141-145.http://dx.doi.org/10.4236/ojm.2013.34020
20. Marek-Crnjac, L. and He, J-H. (2013) An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics, 3, 464-471. http://dx.doi.org/10.4236/ijaa.2013.34053
21. Auffray, J.P. (2014) E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment. Journal of Modern Physics, 5, 1427-1436.http://dx.doi.org/10.4236/jmp.2014.515144
22. El Naschie, M.S. (2011) Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science, 1, 50-53.http://dx.doi.org/10.4236/jqis.2011.12007
23. Amendola, L. and Tsujikawa, S. (2010) Dark Energy: Theory and Observations. Cambridge University Press, Cambridge.
24. El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26.http://dx.doi.org/10.4236/jqis.2013.31006
25. El Naschie, M.S. (2006) Elementary Prerequisites for E-Infinity (Recommended Background Readings in Nonlinear Dynamics, Geometry and Topology). Chaos, Solitons & Fractals, 30, 579-605. http://dx.doi.org/10.1016/j.chaos.2006.03.030
26. El Naschie, M.S. (2008) Extended Renormalizations Group Analysis for Quantum Gravity and Newton’s Gravitational Constant. Chaos, Solitons & Fractals, 35, 425-431.http://dx.doi.org/10.1016/j.chaos.2007.07.059
27. El Naschie, M.S. (2008) Transfinite Harmonization by Taking the Dissonance out of the Quantum Field Symphony. Chaos, Solitons & Fractals, 36, 781-786.http://dx.doi.org/10.1016/j.chaos.2007.09.018
28. 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
29. El Naschie, M.S. (2006) Elementary Number Theory in Superstring Loop Quantum Mechanics, Twistors and E-Infi- nity High Energy Physics. Chaos, Solitons & Fractals, 27, 297-330. http://dx.doi.org/10.1016/j.chaos.2005.04.116
30. El Naschie, M.S. (2006) Intermediate Prerequisites for E-Infinity Theory. Chaos, Solitons & Fractals, 30, 622-628. http://dx.doi.org/10.1016/j.chaos.2006.04.042
31. El Naschie, M.S. (2006) Advanced Prerequisites for E-Infinity Theory. Chaos, Solitons & Fractals, 30, 636-641. http://dx.doi.org/10.1016/j.chaos.2006.04.044
32. El Naschie, M.S. (2006) Topics in the Mathematical Physics of E-Infinity Theory. Chaos, Solitons & Fractals, 30, 656-663. http://dx.doi.org/10.1016/j.chaos.2006.04.043
33. El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (an Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646.http://dx.doi.org/10.1016/j.chaos.2008.09.059
34. El Naschie, M.S., Olsen, S, He, J-H., Marek-Crnjac, L., Nada, S.I. and Helal, M.A. (2012) On the Need for Fractal Logic in High Energy Quantum Physics. Fractal Spacetime & Noncommutative Geometry in Quantum & High Energy Physics, 2, 80-92.
35. El Naschie, M.S. (2013) The Hyperbolic Extension of Sigalotti-Hendi-Sharifzadeh’s Golden Triangle of Special Theory of Relativity and the Nature of Dark Energy. Journal of Modern Physics, 4, 354-356. http://dx.doi.org/10.4236/jmp.2013.43049
36. Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego.
37. El Naschie, M.S. (2008) From Classical Gauge Theory Back to Weyl Scaling via E-Infinity Spacetime. Chaos, Solitons & Fractals, 38, 980-985.http://dx.doi.org/10.1016/j.chaos.2008.05.017
38. Marek-Crnjac, L. (2003) The Mass Spectrum of High Energy Elementary Particles via El Naschie’s E-Infinity Golden Mean Nested Oscillators and the Dunkerly Southwell Eigenvalue Theorems and KAM. Chaos, Solitons & Fractals, 18, 125-133.http://dx.doi.org/10.1016/S0960-0779(02)00587-8
39. Penrose, R. (2004) The Road to Reality. Jonathan Cape, London.
40. He, J-H. (2005) Transfinite Physics. China Culture & Science Publishing, Beijing.
41. ‘t Hooft, G. (1997) In Search of the Ultimate Building Blocks. Cambridge University Press, Cambridge.
42. Wikipedia-Matter (2014) Pie Charts Showing the Fractions of Energy in the Universe. Contributed by Different Sources. http://en.wikipedia.org/wiki/Matter
43. El Naschie, M.S., He, J-H., Nada, S.I., Marek-Crnjac, L. and Helal, M. (2012) Golden Mean Computer for High Energy Physics. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 2, 80-92.
44. Beck, G, Bethe, H. and Riezler, W. (1931) Remarks on Quantum Theory of the Absolute Zero Temperature. Die Naturwissenschaften, 2, 38-39. (In German)
45. El Naschie, M.S. (2006) The Unreasonable Effectiveness of the Electron-Volt Units System in High Energy Physics and the Role Played by. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 119-128. >http://html.scirp.org/file/4-1300139x59.png" class="200" />. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 119-128. http://dx.doi.org/10.1515/IJNSNS.2006.7.2.119
46. El Naschie, M.S. (2006) On the Vital Role Played by the Electron-Volts Units System in High Energy Physics and Mach’s Principle of “Denkökonomie”. Chaos, Solitons & Fractals, 28, 1366-1371. http://dx.doi.org/10.1016/j.chaos.2005.11.001
47. Zhong, T. (2009) From the Numeric of Dynamics to the Dynamics of Numeric and Visa Versa in High Energy Particle Physics. Chaos, Solitons & Fractals, 42, 1780-1783.http://dx.doi.org/10.1016/j.chaos.2009.03.079
48. El Naschie, M.S. (2007) On the Topological Ground State of E-Infinity Spacetime and the Super String Connection. Chaos, Solitons & Fractals, 32, 468-470.http://dx.doi.org/10.1016/j.chaos.2006.08.011
49. Devaney, R.L. (1989) Chaotic Dynamical Systems. Addison-Wesley, New York.
50. Bhatia, N.P. and Egerland, W. (1988) A Refinement of Sarkovski’s Theorem. Proceedings of the American Mathematical Society, 102, 965-972.
51. MacGregor, M.H. (2007) The Power of Alfa (α)-Electron Elementary Particle Generation With α-Quantized Lifetime and Masses. World Scientific, Singapore.
52. Li, T. and Yorke, J. (1975) Period Three Implies Chaos. The American Mathematical Monthly, 82, 985-992. http://dx.doi.org/10.2307/2318254
53. Rössler, O.E. (1998) Endophysics, World Scientific, Singapore.http://dx.doi.org/10.1142/3183
54. El Naschie, M.S. (2001) On a General Theory for Quantum Gravity. In: Diebner, H., Druckrey, T. and Weibel, P., Eds., Science of the Interface, GenistaVerlag, Tübingen.
55. Addison, P.S. (1997) Fractals and Chaos: An Illustrated Course. Institute of Physics, Bristol.
56. El Naschie, M.S. (1991) Peano Dynamics as a Model for Turbulence and Strange Nonchaotic Behaviour. Acta Physica Polonica A, 80, 1-13.
57. El Naschie, M.S. (2007) Feigenbaum Scenario for Turbulence and Cantorian E-Infinity Theory of High Energy Particle Physics. Chaos, Solitons & Fractals, 32, 911-915.http://dx.doi.org/10.1016/j.chaos.2006.08.014
58. El Naschie, M.S. (2002) Determining the Temperature of Microwave Background Radiation from the Topology of Geometry of Spacetime. Chaos, Solitons & Fractals, 14, 1121-1126.http://dx.doi.org/10.1016/S0960-0779(02)00172-8
59. El Naschie, M.S. (2009) On Zero Dimensional Points Curvature in the Dynamics of Cantorian-Fractal Spacetime Setting and High Energy Particle Physics. Chaos, Solitons & Fractals, 41, 2725-2732. http://dx.doi.org/10.1016/j.chaos.2008.10.001
60. El Naschie, M.S. (2005) ‘t Hooft Ultimate Building Blocks and Spacetime as an Infinite Dimensional Set of Transfinite Discrete Points. Chaos, Solitons & Fractals, 25, 521-524.http://dx.doi.org/10.1016/j.chaos.2005.01.022
61. Pati, A.K. and Brauenstein, S.L. (2009) Role of Entanglement in Quantum Computation. Indian Institute of Science Journal (Special Issue), 89, 295.
62. Pati, A.K. (2006) Entanglement Guides Quantum Computation. In: Goswami, D., Ed., Quantum Coupling, Back Action, AIP Publication, College Park, Vol. 864, 114-126.
63. Agrawal, P. and Pati, A.K. (2006) Perfect Teleportation and Superdense Coding with W-State. Physics Review A, 74, Article ID: 062320.http://dx.doi.org/10.1103/PhysRevA.74.062320

Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor

Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor

Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor

 Download as PDF (Size:724KB)  HTML   XML  PP. 210-225  

DOI: 10.4236/ns.2015.74024     

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Mohamed S. El Naschie

Affiliation(s)

Department of Physics, University of Alexandria, Alexandria, Egypt.

ABSTRACT

The present paper is basically a synthesis resulting from incorporating Kerr spinning black hole geometry into E-infinity topology, then letting the result bares on the vacuum zero point Casimir effect as well as the cosmic dark energy and dark matter density. In E-infinity theory a quantum particle is represented by a Hausdorff dimension Φwhere Φ =2/(√5+1) . The quantum wave on the other hand is represented by Φ² . To be wave and a particle simultaneously intersection theory leads us to (Φ) (Φ)²= Φ³ which will be shown here to be twice the value of the famous Casimir force of the vacuum for a massless scalar field. Thus in the present work a basically topological interpretation of the Casimir effect is given as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so called missing dark energy density of the cosmos. From the view point of the present work Casimir pressure is a local effect acting on the Casimir plates constituting the local boundary condition while dark energy is nothing but the global combined effect of infinitely many quantum waves acting on the Möbius-like boundary of the holographic boundary of the entire universe. Since this higher dimensional Möbius-like boundary is one sided, there is no outside to balance the internal collective Casimir pressure which then manifests itself as the force behind cosmic expansion, that is to say, dark energy. Thus analogous to the exact irrational value of ordinary energy density of spacetime E(O)=(Φ⁵/2) mc² we now have P (Casimir) = (Φ³/2)(ch/d²) where c is the speed of light, m is the mass, h is the Planck constant and d is the plate separation. In addition the new emerging geometry combined with the topology of E-infinity theory leads directly to identifying dark matter with the quasi matter of the ergosphere. As a direct consequence of this new insight E=mc² which can be written as E = E (O) + E (D) where the exact rational approximation is E (O)=mc²/22 is the ordinary energy density of the cosmos and the exact rational approximation E (D)=mc²/(21/22) is the corresponding dark energy which could be subdivided once more albeit truly approximately into E(D)=mc²/(5/22) +mc²/(16/22)  where 5 is the Kaluza Klein spacetime dimension, 16 are the bosonic extra dimensions of Heterotic superstrings and 5/22 □ 22% is approximately the density of the dark matter-like energy of the ergosphere of the Kerr geometry. As for the actual design of our nano reactor, this is closely related to branching clusters of polymer, frequently called lattice animals. In other words we will have Casimir spheres instead of Casimir plates and these spheres will be basically nano particles modelling lattice animals. Here D= 4 will be regarded as spacetime dimensionality while D=6 of percolations are the compactified super string dimensions and D=8 is the dimension of a corresponding super space.

KEYWORDS

Casimir Effect, Dark Energy, E-Infinity, Cantorian Spacetime, Kerr Spacetime Geometry, Energy from the Ergosphere, Spinning Black Holes, Nano Spacetime Reactors, Kaluza-Klein Spacetime, Heterotic Superstrings

Cite this paper

El Naschie, M. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor. Natural Science, 7, 210-225. doi:10.4236/ns.2015.74024.

References

[1]	El Naschie, M.S. (2015) Three Quantum Particles Hardy Entanglement from the Topology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy—A Great Opportunity for Nanotechnology. American Journal of Nano Research and Applications, 3, 1-5.
[2]	El Naschie, M.S. (2014) Casimir-Like Energy as a Double Eigenvalue of Quantumly Entangled System Leading to the Missing Dark Energy Density of the Cosmos. International Journal of High Energy Physics, 1, 55-63.
[3]	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.
[4]	Slezak, M. (2015) Quantum Wave Function Gets Real. New Scientist, 225, 14. http://dx.doi.org/10.1016/S0262-4079(15)60242-1
[5]	El Naschie, M.S. (2015) Dark Energy and Its Cosmic Density from Einstein’s Relativity and Gauge Fields Renormalization Leading to the Possibility of a New ‘tHooft Quasi Particle. The Open Astronomy Journal, 8, 1-17. http://dx.doi.org/10.2174/1874381101508010001
[6]	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.
[7]	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 Entanglement Origin. Journal of Quantum Information Science, 4, 284-291. http://dx.doi.org/10.4236/jqis.2014.44023
[8]	El Naschie, M.S. (2014) The Hidden Quantum Entanglement Roots of E = mc2 and Its Genesis to E = mc2/22 Plus mc2(21/22) Confirming Einstein’s Mass-Energy Formula. American Journal of Electromagnetics and Applications, 2, 39-44. http://dx.doi.org/10.11648/j.ajea.20140205.11
[9]	El Naschie, M.S. (1999) From Implosion to Fractal Spheres. A Brief Account of the Historical Development of Scientific Ideas Leading to the Trinity Test and Beyond. Chaos, Solitons & Fractals, 10, 1955-1965. http://dx.doi.org/10.1016/S0960-0779(99)00030-2
[10]	El Naschie, M.S. and Al Athel, S. (2000) Estimating the Eigenvalue of Fast Reactors and Cantorian Space. Chaos, Solitons & Fractals, 11, 1957-1961. http://dx.doi.org/10.1016/S0960-0779(99)00069-7
[11]	El Naschie, M.S. (2000) On Nishina’s Estimate of the Critical Mass for Fussion and Early Nuclear Research in Japan. Chaos, Solitons & Fractals, 11, 1809-1818. http://dx.doi.org/10.1016/S0960-0779(99)00172-1
[12]	El Naschie, M.S. (2000) Remarks on Heisenberg’s Farm-Hall Lecture on the Critical Mass of Fast Neutron Fission. Chaos, Solitons & Fractals, 11, 1327-1333. http://dx.doi.org/10.1016/S0960-0779(99)00136-8
[13]	El Naschie, M.S. and Hussein, A. (2000) On the Eigenvalue of Nuclear Reaction and Self-Weight Buckling. Chaos, Solitons & Fractals, 11, 815-818. http://dx.doi.org/10.1016/S0960-0779(99)00106-X
[14]	El Naschie, M.S. (2000) Elastic Buckling Loads and Fission Critical Mass as an Eigenvalue of a Symmetry Breaking Bifurcation. Chaos, Solitons & Fractals, 11, 631-639. http://dx.doi.org/10.1016/S0960-0779(99)00063-6
[15]	El Naschie, M.S. (2000) On the Zel’dovich-Khuriton Critical Mass for Fast Fission. Chaos, Solitons & Fractals, 11, 819-824. http://dx.doi.org/10.1016/S0960-0779(99)00113-7
[16]	El Naschie, M.S. (2000) On the Eigenvalue of Transport Reaction Involving Fast Neutrons. Chaos, Solitons & Fractals, 11, 929-934. http://dx.doi.org/10.1016/S0960-0779(99)00066-1
[17]	El Naschie, M.S. (2000) Heisenberg’s Critical Mass Calculations for an Explosive Nuclear Reaction. Chaos, Solitons & Fractals, 11, 987-997. http://dx.doi.org/10.1016/S0960-0779(99)00110-1
[18]	El Naschie, M.S. (1998) Chaos and Fractals in Nano and Quantum Technology. Chaos, Solitons & Fractals, 9, 1793- 1802.
[19]	El Naschie, M.S. (2006) Nanotechnology for the Developing World. Chaos, Solitons & Fractals, 30, 769-773. http://dx.doi.org/10.1016/j.chaos.2006.04.037
[20]	El Naschie, M.S. (2007) The Political Economy of Nanotechnology and the Developing World. International Journal of Electrospun Nanofibrers and Applications, 1, 41-50.
[21]	El Naschie, M.S. (1998) Some Tentative Proposals for the Experimental Verification of Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 9, 143-144. http://dx.doi.org/10.1016/S0960-0779(97)00175-6
[22]	Johnston, H. (2012) Physicists Solve Casimir Conundrum. Physicsworld.com. 18 July 2012.
[23]	Rencroft, S. and Swain, J. (1998) What Is the Casimir Effect? Scientific American, 22 June 1998.
[24]	Wongjun, P. (2015) Casimir Dark Energy, Stabilization of the Extra Dimensions and Gauss-Bonnet Term. The European Physical Journal C, 75, 6. http://dx.doi.org/10.1140/epjc/s10052-014-3237-0
[25]	El Naschie, M.S. (2007) A Review of Applications and Results of E-Infinity Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 8, 11-20. http://dx.doi.org/10.1515/IJNSNS.2007.8.1.11
[26]	Smolin, L. (2001) The Strong and the Weak Holographic Principles. Nuclear Physics B, 601, 209-247. http://dx.doi.org/10.1016/S0550-3213(01)00049-9
[27]	El Naschie, M.S. (2006) Holographic Dimensional Reduction: Center Manifold Theorem and E-Infinity. Chaos, Solitons & Fractals, 29, 816-822. http://dx.doi.org/10.1016/j.chaos.2006.01.013
[28]	Misner, C., Thorne, K. and Wheeler, J.A. (1973) Gravitation. Freeman, New York.
[29]	El Naschie, M.S. (2003) Kleinian Groups in E-Infinity and Their Connection to Particle Physics and Cosmology. Chaos, Solitons & Fractals, 16, 637-649. http://dx.doi.org/10.1016/S0960-0779(02)00489-7
[30]	El Naschie, M.S. (2005) A Guide to the Mathematics of E-Infinity Cantorian Spacetime Theory. Chaos, Solitons & Fractals, 25, 955-964.
[31]	El Naschie, M.S. (2004) The Concepts of E-Infinity: An Elementary Introduction to the Cantorian-Fractal Theory of Quantum Physics. Chaos, Solitons & Fractals, 22, 495-511. http://dx.doi.org/10.1016/j.chaos.2004.02.028
[32]	El Naschie, M.S. (2003) Complex Vacuum Fluctuation as a Chaotic “Limit” Set of Any Kleinian Group Transformation and the Mass Spectrum of High Energy Particle Physics via Spontaneous Self Organization. Chaos, Solitons & Fractals, 17, 631-638. http://dx.doi.org/10.1016/S0960-0779(02)00630-6
[33]	El Naschie, M.S. (2003) Modular Groups in Cantorian E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 16, 353-366. http://dx.doi.org/10.1016/S0960-0779(02)00440-X
[34]	El Naschie, M.S. (1994) On Certain “Empty” Cantor Sets and Their Dimensions. Chaos, Solitons & Fractals, 4, 293- 296. http://dx.doi.org/10.1016/0960-0779(94)90152-X
[35]	He, J.H., Xu, L., Zhang, L.N. and Wu, X.H. (2007) Twenty-Six Dimensional Polytope and High Energy Spacetime Physics. Chaos, Solitons & Fractals, 33, 5-13. http://dx.doi.org/10.1016/j.chaos.2006.10.048
[36]	El Naschie, M.S. (1994) Is Quantum Space a Random Cantor Set with a Golden Mean Dimension at the Core? Chaos, Solitons & Fractals, 4, 177-179. http://dx.doi.org/10.1016/0960-0779(94)90141-4
[37]	El Naschie, M.S. (2008) Mathematical Foundation of E-Infinity via Coxeter and Reflection Groups. Chaos, Solitons & Fractals, 37, 1267-1268. http://dx.doi.org/10.1016/j.chaos.2008.02.001
[38]	El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508. http://dx.doi.org/10.1016/0960-0779(95)00052-6
[39]	El Naschie, M.S. (1995) On the Initial Singularity and the Banach-Tarski Theorem. Chaos, Solitons & Fractals, 5, 1391-1392. http://dx.doi.org/10.1016/0960-0779(95)99645-2
[40]	El Naschie, M.S. (1998) Cobe Satellite Measurement, Hyperspheres, Superstrings and the Dimension of Spacetime. Chaos, Solitons & Fractals, 9, 1445-1471. http://dx.doi.org/10.1016/S0960-0779(98)00120-9
[41]	El Naschie, M.S. (2001) Infinite Dimensional Branes and the E-Infinity Topology of Heterotic Superstrings. Chaos, Solitons & Fractals, 12, 1047-1055. http://dx.doi.org/10.1016/S0960-0779(00)00130-2
[42]	El Naschie, M.S. (2007) Ji-Huan He’s Ten Dimensional Polytope and High Energy Particle Physics. International Journal of Nonlinear Sciences & Numerical Simulation, 8, 475-476. http://dx.doi.org/10.1515/IJNSNS.2007.8.4.475
[43]	El Naschie, M.S. (1999) Hyperdimensional Geometry and the Nature of Physical Spacetime. Chaos, Solitons & Fractals, 10, 155-158. http://dx.doi.org/10.1016/S0960-0779(98)00235-5
[44]	Finkelstein, D. (1982) Quantum Sets and Clifford Algebras. International Journal of Theoretical Physics, 21, 489-503. http://dx.doi.org/10.1007/BF02650180
[45]	El Naschie, M.S. (2002) Derivation of the Threshold and Absolute Temperature Tc = 273.16 K from the Topology of Quantum Spacetime. Chaos, Solitons & Fractals, 14, 1117-1120. http://dx.doi.org/10.1016/S0960-0779(02)00053-X
[46]	El Naschie, M.S. (2008) Quarks Confinement via Kaluza-Klein Theory as a Topological Property of Quantum Classical Spacetime Phase Transition. Chaos, Solitons & Fractals, 35, 825-829. http://dx.doi.org/10.1016/j.chaos.2007.08.057
[47]	El Naschie, M.S. (2002) On a Class of General Theories for High Energy Particle Physics. Chaos, Solitons & Fractals, 14, 649-668. http://dx.doi.org/10.1016/S0960-0779(02)00033-4
[48]	He, J.H. (2009) Hilbert Cube Model for Fractal Spacetime. Chaos, Solitons & Fractals, 42, 2754-2759. http://dx.doi.org/10.1016/j.chaos.2009.03.182
[49]	Lomas, R. (1999) The Man Who Invented the Twentieth Century: Nicola Tesla, Forgotten Genius of Electricity. Headline Books, London.
[50]	Helal, M., Marek-Crnjac, L. and He, J.H. (2013) The Three 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, 141-145. http://dx.doi.org/10.4236/ojm.2013.34020
[51]	El Naschie, M.S. (2004) A Review of E-Infinity Theory 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
[52]	El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646. http://dx.doi.org/10.1016/j.chaos.2008.09.059
[53]	Marek-Crnjac, L. and He, J.H. (2013) An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. International Journal of Astronomy and Astrophysics, 3, 464-471. http://dx.doi.org/10.4236/ijaa.2013.34053
[54]	El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26. http://dx.doi.org/10.4236/jqis.2013.31006
[55]	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 & Astrophysics, 3, 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024
[56]	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
[57]	Peat, F.D. (1983) In Search of Nikola Tesla. Ashgrove Publications, London & Bath.
[58]	Susskind, L. and Lindesay, J. (2005) The Holographic Universe. World Scientific, Singapore.
[59]	Stiglitz, J. and Bilmes, L. (2008) The Three Trillion Dollar War: The True Cost of The Iraq Conflict. Allen-Lane, Penguin Books, London.
[60]	El Naschie, M.S. (2013) A Unified Newtonian-Relativistic Quantum Resolution of Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light. International Journal of Modern Nonlinear Theory & Application, 2, 43-54. http://dx.doi.org/10.4236/ijmnta.2013.21005
[61]	Malek, C. (2015) Abu Dhabi Crown Prince Details UAE Leaders’ Vision of Future without Oil. The National Newspaper, UAE, 10th February 2015. http://www.thenational.ae/uae/government/abu-dhabi-crown-prince-details-uae-leaders-vision-of-future-without-oil?utm_content='%20vision%20of%20future%20without%20oil
[62]	Zee, A. (2003) Quantum Field Theory in a Nutshell. Princeton University Press, Princeton.
[63]	Duplantier, B. and Rivasseau, V., Eds. (2003) Vacuum Energy-Renormalization. Birkhauser, Basel.
[64]	Milonni, P.W. (1994) The Quantum Vacuum. Academic Press, Boston.
[65]	Parsegian, V.A. (2006) van der Waals Forces. Cambridge University Press, Cambridge.
[66]	Huang, K. (2007) Fundamental Forces of Nature. World Scientific, Singapore. http://dx.doi.org/10.1142/6447
[67]	Wapner, L.M. (2005) The Pea and the Sun. A.K. Peters Ltd., Wellesley.
[68]	Auffray, J.P. (2015) E-Infinity, Zero Set, Absolute Space and the Photon Spin. Journal of Modern Physics, 6, 536-545. http://dx.doi.org/10.4236/jmp.2015.65058
[69]	Connes, A. (1994) Noncommutative Geometry. Academic Press, San Diego. (See in particular pages 88-93 and Fig. II.4)
[70]	Wald, R.M. (1984) General Relativity. The University of Chicago Press, Chicago and London. (See in particular page 319 and Fig. 12.6)
[71]	Sternberg, S. (2012) Curvature in Mathematics and Physics. Dover Publications, New York.
[72]	El Naschie, M.S. (2011) On Twistors in Cantorian E-Infinity Space. Chaos, Solitons & Fractals, 12, 741-746. http://dx.doi.org/10.1016/S0960-0779(00)00193-4
[73]	El Naschie, M.S. (2015) On a Casimir-Dark Energy Nano Reactor. American Journal of Nano Research and Application, 3, 12-16.
[74]	Ho, M.W., El Naschie, M. and Vitiello, G. (2015) Is Spacetime Fractal and Quantum Coherent in the Golden Mean. Global Journal of Science Frontier Research—A: Physics and Space Science, 15, 61-80.
[75]	El Naschie, M.S. (2015) From Kantian-Reinen Vernunft to the Real Dark Energy Density of the Cosmos via the Measure Concentration of Convex Geometry in Quasi Banach Spacetime. Open Journal of Philosophy, 5, 123-130. http://dx.doi.org/10.4236/ojpp.2015.51014
[76]	El Naschie, M.S. (2015) Dark Energy and Its Cosmic Density from Einstein’s Relativity and Gauge Field Renormalization Leading to the Possibility of a New ‘tHooft Quasi Particle. The Open Astronomy Journal, 8, 1-17. http://dx.doi.org/10.2174/1874381101508010001
[77]	Stauffer, D. and Stanley, H.E. (1996) From Newton to Mandelbrot. 2nd Edition, Springer, Berlin.
[78]	El Naschie, M.S. (1998) Branching Polymers and the Fractal Cantorian Spacetime. Chaos, Solitons & Fractals, 9, 135-141. http://dx.doi.org/10.1016/S0960-0779(97)00133-1
[79]	El Naschie, M.S. (1997) The Bethe Lattice and the Dimension of Micro Spacetime. Chaos, Solitons & Fractals, 8, 1887-1889. http://dx.doi.org/10.1016/S0960-0779(97)00130-6
[80]	Miltao, M.S.R. (2008) Casimir Energy for a Double Spherical Shell: A Global Mode Sum Approach. Physical Review D, 78, Article ID: 065023. http://dx.doi.org/10.1103/PhysRevD.78.065023
[81]	El Naschie, M.S. (2015) Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem. Journal of Modern Physics, 6, 348-395. http://dx.doi.org/10.4236/jmp.2015.64042
[82]	El Naschie, M.S. (2015) A Fractal Rindler-Regge Triangulation in the Hyperbolic Plane and Cosmic de Sitter Accelerated Expansion. Journal of Quantum Information Science, 5, 24-31. http://dx.doi.org/10.4236/jqis.2015.51004
[83]	El Naschie, M.S. (2015) The Casimir Topological Effect and a Proposal for a Casimir-Dark Energy Nano Reactor. World Journal of Nano Science and Engineering, 5, 26-33. http://dx.doi.org/10.4236/wjnse.2015.51004
[84]	El Naschie, M.S. (2014) From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos. Advances in Pure Mathematics, 4, 641-648. http://dx.doi.org/10.4236/apm.2014.412073
[85]	Binnig, G. (1990) Ausdem Nichits: über die Kreativitat von Natur und Mensch. Piper Verlag, Munich, Germany.
[86]	‘tHooft, G. (1997) In Search of the Ultimate Building Blocks. Cambridge University Press, Cambridge.
[87]	Susskind, L. (2010) An Introduction to the Holographic Universe—Black Holes, Information and the String Theory Revolution. World Scientific, Singapore.
[88]	McKeon, D.G. and Ord, G.N. (1992) Time Reversal in Stochastic Processes and Dirac Equation. Physics Review Letters, 69, 3-4. http://dx.doi.org/10.1103/PhysRevLett.69.3

A Casimir-Dark Energy Nano Reactor Design—Phase One

A Casimir-Dark Energy Nano Reactor Design—Phase One

A Casimir-Dark Energy Nano Reactor Design—Phase One

 Download as PDF (Size:684KB)  HTML   XML  PP. 287-298  

DOI: 10.4236/ns.2015.76032  

Author(s)    Leave a comment

Mohamed S. El Naschie

Affiliation(s)

Department of Physics, University of Alexandria, Alexandria, Egypt.

ABSTRACT

A phase one design of a new free energy nano reactor is presented. The design is based on a basically topological interpretation of the Casimir effect as a natural intrinsic property of the geometrical topological structure of the quantum-Cantorian micro spacetime. In particular we view dark energy, Hawking negative energy, Unruh temperature and zero point vacuum energy as being different sides of the same multi-dimensional coin. This new interpretation compliments the earlier conventional interpretation as vacuum fluctuation or as a Schwinger source and links the Casimir energy to the so-called missing dark energy density of the cosmos. We start with a general outline of the theoretical principle and basic design concepts of a proposed Casimir dark energy nano reactor. In a nutshell the theory and consequently the actual design depend crucially upon the equivalence between the dark energy density of the cosmos and the faint local Casimir effect produced by two sides boundary condition quantum waves. This Casimir effect is then colossally amplified as a one internal quantum wave representing a Hartle-Hawking state vector of the universe pushing from the inside against the boundary of the universe with nothing balancing it from the non-existent outside. This strange situation becomes completely natural and logical when we remember that the boundary of the universe is a one sided Möbius like manifold. In view of the present theory, this is essentially what leads to the observed accelerated expansion of the cosmos. As in any reactor, the basic principle in the present design is to produce a gradient so that the excess energy on one side flows to the other side. Thus in principle we will restructure the local topology of space using material nanoscience technology to create an artificial local high dimensionality with a Dvoretzky theorem like 96 percent volume measure concentration. Without going into the intricate nonlinear dynamics and technological detail, it is fair to say that this would lead us to pure, clean, free energy obtained directly from the topology of spacetime via an artificial singularity. Needless to say, the entire design is based completely on the theory of quantum wave dark energy proposed by the present author for the first time in 2011 in a conference held in the Bibliotheca Alexandrina, Egypt and a little later in Shanghai, Republic of China. The quintessence of the present theory is easily explained as the Φ³ intrinsic Casimir topological energy where Φ= (√5-1)/2 is produced from the zero set Φ of the quantum particle when we extract the empty set quantum wave Φ² from it and find Φ-Φ²=Φ³ by restructuring space via conducting but uncharged plates similar to that of the classical Casimir experiments. Our proposed preliminary design of this Casimir-spacetime artificial singularity reactor follows in a natural way from the above.

KEYWORDS

Casimir Effect, Dark Energy, E-Infinity, Cantorian Spacetime, Nano Reactor Avant Projet, Free Energy, Zero Point Vacuum Energy, Hartle-Hawking Quantum Wave of the Cosmos

Cite this paper

El Naschie, M. (2015) A Casimir-Dark Energy Nano Reactor Design—Phase One. Natural Science, 7, 287-298. doi:10.4236/ns.2015.76032.

References

[1]	El Naschie, M.S. (2015) Three Quantum Particles Hardy Entanglement from the tOpology of Cantorian-Fractal Spacetime and the Casimir Effect as Dark Energy—A Great Opportunity for Nanotechnology. American Journal of Nano Research and Applications, 3, 1-5.
[2]	El Naschie, M.S. (2014) Casimir-Like Energy as a Double Eigenvalue of Quantumly Entangled System Leading to the Missing Dark Energy Density of the Cosmos. International Journal of High Energy Physics, 1, 55-63. http://dx.doi.org/10.11648/j.ijhep.20140105.11
[3]	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
[4]	Slezak, M. (2015) Quantum Wave Function Gets Real. New Scientist, 14. http://dx.doi.org/10.1016/s0262-4079(15)60242-1
[5]	El Naschie, M.S. (2015) Dark Energy and Its Cosmic Density from Einstein’s Relativity and Gauge Fields Renormalization Leading to the Possibility of a New ‘tHooft Quasi Particle. The Open Astronomy Journal, 8, 1-17. http://dx.doi.org/10.2174/1874381101508010001
[6]	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
[7]	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 Entanglement Origin. Journal of Quantum Information Science, 4, 284-291. http://dx.doi.org/10.4236/jqis.2014.44023
[8]	El Naschie, M.S. (2014) The Hidden Quantum Entanglement Roots of E = mc2 and Its Genesis to E = mc2/22 plus mc2(21/22) Confirming Einstein’s Mass-Energy Formula. American Journal of Electromagnetics and Applications, 2, 39-44. http://dx.doi.org/10.11648/j.ajea.20140205.11
[9]	El Naschie, M.S. (1999) From Implosion to Fractal Spheres. A Brief Account of the Historical Development of Scientific Ideas Leading to the Trinity Test and Beyond. Chaos, Solitons & Fractals, 10, 1955-1965. http://dx.doi.org/10.1016/S0960-0779(99)00030-2
[10]	El Naschie, M.S. and Al Athel, S. (2000) Estimating the Eigenvalue of Fast Reactors and Cantorian Space. Chaos, Solitons & Fractals, 11, 1957-1961. http://dx.doi.org/10.1016/S0960-0779(99)00069-7
[11]	El Naschie, M.S. (2000) On Nishina’s Estimate of the Critical Mass for Fussion and Early Nuclear Research in Japan. Chaos, Solitons & Fractals, 11, 1809-1818. http://dx.doi.org/10.1016/S0960-0779(99)00172-1
[12]	El Naschie, M.S. (2000) Remarks on Heisenberg’s Farm-Hall Lecture on the Critical Mass of Fast Neutron Fission. Chaos, Solitons & Fractals, 11, 1327-1333. http://dx.doi.org/10.1016/S0960-0779(99)00136-8
[13]	El Naschie, M.S. and Hussein, A. (2000) On the Eigenvalue of Nuclear Reaction and Self-Weight Buckling. Chaos, Solitons & Fractals, 11, 815-818. http://dx.doi.org/10.1016/s0960-0779(99)00106-x
[14]	El Naschie, M.S. (2000) Elastic Buckling Loads and Fission Critical Mass as an Eigenvalue of a Symmetry Breaking Bifurcation. Chaos, Solitons & Fractals, 11, 631-639. http://dx.doi.org/10.1016/S0960-0779(99)00063-6
[15]	El Naschie, M.S. (2000) On the Zel’dovich-Khuriton Critical Mass for Fast Fission. Chaos, Solitons & Fractals, 11, 819-824. http://dx.doi.org/10.1016/S0960-0779(99)00113-7
[16]	El Naschie, M.S. (2000) On the Eigenvalue of Transport Reaction Involving Fast Neutrons. Chaos, Solitons & Fractals, 11, 929-934. http://dx.doi.org/10.1016/S0960-0779(99)00066-1
[17]	El Naschie, M.S. (2000) Heisenberg’s Critical Mass Calculations for an Explosive Nuclear Reaction. Chaos, Solitons & Fractals, 11, 987-997. http://dx.doi.org/10.1016/S0960-0779(99)00110-1
[18]	El Naschie, M.S. (1998) Chaos and Fractals in Nano and Quantum Technology. Chaos, Solitons & Fractals, 9, 1793- 1802.
[19]	El Naschie, M.S. (2006) Nanotechnology for the Developing World. Chaos, Solitons & Fractals, 30, 769-773. http://dx.doi.org/10.1016/j.chaos.2006.04.037
[20]	El Naschie, M.S. (2007) The Political Economy of Nanotechnology and the Developing World. International Journal of Electrospun Nanofibrers and Applications, 1, 41-50.
[21]	El Naschie, M.S. (1998) Some Tentative Proposals for the Experimental Verification of Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 9, 143-144. http://dx.doi.org/10.1016/S0960-0779(97)00175-6
[22]	Johnston, H. (2012) Physicists Solve Casimir Conundrum. Physicsworld.com, July 18, 2012.
[23]	Rencroft, S. and Swain, J. (1998) What Is the Casimir Effect? Scientific American, June 22, 1998.
[24]	Wongjun, P. (2015) Casimir Dark Energy, Stabilization and the Extra Dimensions and Gauss-Bonnet Term. The European Physical Journal C, 75, 6.
[25]	El Naschie, M.S. (2007) A Review of Application and Results of E-Infinity. International Journal of Nonlinear Science & Numerical Simulation, 8, 11-20. http://dx.doi.org/10.1515/IJNSNS.2007.8.1.11
[26]	Smolin, L. (2001) The Strong and the Weak Holographic Principles. Nuclear Physics B, 601, 209-247. http://dx.doi.org/10.1016/S0550-3213(01)00049-9
[27]	El Naschie, M.S. (2006) Holographic Dimensional Reduction Center Manifold Theorem and E-Infinity. Chaos, Solitons & Fractals, 29, 816-822. http://dx.doi.org/10.1016/j.chaos.2006.01.013
[28]	Misner, C., Thorne, K. and Wheeler, J.A. (1973) Gravitation. Freeman, New York.
[29]	El Naschie, M.S. (2003) Kleinian Groups in E-Infinity and Their Connection to Particle physics and Cosmology. Chaos, Solitons & Fractals, 16, 637-649. http://dx.doi.org/10.1016/S0960-0779(02)00489-7
[30]	El Naschie, M.S. (2005) A Guide to the Mathematics of E-Infinity Cantorian Spacetime Theory. Chaos, Solitons & Fractals, 25, 935-939. http://dx.doi.org/10.1016/j.chaos.2005.02.029
[31]	El Naschie, M.S. (2004) The Concepts of E-Infinity: An Elementary Introduction to the Cantorian-Fractal Theory of Quantum Physics. Chaos, Solitons & Fractals, 22, 495-511. http://dx.doi.org/10.1016/j.chaos.2004.02.028
[32]	El Naschie, M.S. (2003) Complex Vacuum Fluctuation as a Chaotic ‘Limit’ Set of Any Kleinian Group Transformation and the Mass Spectrum of High Energy Particle Physics via Spontaneous Self Organization. Chaos, Solitons & Fractals, 17, 631-638. http://dx.doi.org/10.1016/s0960-0779(02)00630-6
[33]	El Naschie, M.S. (2003) Modular Groups in Cantorian E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 16, 353-366. http://dx.doi.org/10.1016/S0960-0779(02)00440-X
[34]	El Naschie, M.S. (1994) On Certain ‘Empty’ Cantor Sets and Their Dimensions. Chaos, Solitons & Fractals, 4, 293- 296. http://dx.doi.org/10.1016/0960-0779(94)90152-X
[35]	He, J.-H., Xu, L., Zhang, L.-N. and Wu, X.-H. (2007) Twenty Six Dimensional Polytope and High Energy Spacetime Physics. Chaos, Solitons & Fractals, 33, 5-13. http://dx.doi.org/10.1016/j.chaos.2006.10.048
[36]	El Naschie, M.S. (1994) Is Quantum Space a Random Cantor Set with a Golden Mean Dimension at the Core? Chaos, Solitons & Fractals, 4, 177-179. http://dx.doi.org/10.1016/0960-0779(94)90141-4
[37]	El Naschie, M.S. (2008) Mathematical Foundation of E-Infinity via Coxeter and Reflection Groups. Chaos, Solitons & Fractals, 37, 1267-1268. http://dx.doi.org/10.1016/j.chaos.2008.02.001
[38]	El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508. http://dx.doi.org/10.1016/0960-0779(95)00052-6
[39]	El Naschie, M.S. (1995) On the Initial Singularity and the Banach-Tarski Theorem. Chaos, Solitons & Fractals, 5, 1391-1392. http://dx.doi.org/10.1016/0960-0779(95)99645-2
[40]	El Naschie, M.S. (1998) COBE Satellite Measurement, Hyper Spheres, Superstrings and the Dimension of Spacetime. Chaos, Solitons & Fractals, 9, 1445-1471. http://dx.doi.org/10.1016/S0960-0779(98)00120-9
[41]	El Naschie, M.S. (2001) Infinite Dimensional Branes and the E-Infinity Toplogy of Heterotic Superstrings. Chaos, Solitons & Fractals, 12, 1047-1055. http://dx.doi.org/10.1016/S0960-0779(00)00130-2
[42]	El Naschie, M.S. (2007) Ji-Huan He’s Ten Dimensional Polytope and High Energy Particle Physics. International Journal of Nonlinear Science & Numerical Simulation, 8, 475-476. http://dx.doi.org/10.1515/ijnsns.2007.8.4.475
[43]	El Naschie, M.S. (1999) Hyper-Dimensional Geometry and the Nature of Physical Spacetime. Chaos, Solitons & Fractals, 10, 155-158. http://dx.doi.org/10.1016/S0960-0779(98)00235-5
[44]	Finkelstein, D. (1982) Quantum Sets and Clifford Algebras. International Journal of Theoretical Physics, 21, 489-503.
[45]	El Naschie, M.S. (2002) Derivation of the Threshold and Absolute Temperature Ei = 273.16k from the Topology of Quantum Spacetime. Chaos, Solitons & Fractals, 14, 1117-1120. http://dx.doi.org/10.1016/S0960-0779(02)00053-X
[46]	El Naschie, M.S. (2008) Quarks Confinement via Kaluza-Klein Theory as a Topological Property of Quantum-Classical Spacetime Phase Transition. Chaos, Solitons & Fractals, 35, 825-829. http://dx.doi.org/10.1016/j.chaos.2007.08.057
[47]	El Naschie, M.S. (2002) On a Class of General Theories for Higher Energy Particle Physics. Chaos, Solitons & Fractals, 14, 649-668. http://dx.doi.org/10.1016/S0960-0779(02)00033-4
[48]	He, J.-H. (2009) Hilbert Cube Model for Fractal Spacetime. Chaos, Solitons & Fractals, 42, 2754-2759. http://dx.doi.org/10.1016/j.chaos.2009.03.182
[49]	Lomas, R. (1999) The Man Who Invented the Twentieth Century, Nicola Tesla, Forgotten Genius of Electricity. Headline Books, London.
[50]	Helal, M., Marek-Crnjac, L. and He, J.-H. (2013) The Three Page Guide to the Most Important Results of M.S. El Naschie’s Research in E-Infinity Quantum Physics. Open Journal of Microphysics, 3, 141-145. http://dx.doi.org/10.4236/ojm.2013.34020
[51]	El Naschie, M.S. (2004) A Review of E-Infinity Theory and the Mass Spectrum of High Energy Physics. Chaos, Solitons & Fractals, 19, 209-236. http://dx.doi.org/10.1016/S0960-0779(03)00278-9
[52]	El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646. http://dx.doi.org/10.1016/j.chaos.2008.09.059
[53]	Marek-Crnjac, L. and He, J.-H. (2013) An Invitation to El Naschie’s Theory of Cantorian Spacetime and Dark Energy. International Journal of Astronomy and Astrophysics, 3, 464-471. http://dx.doi.org/10.4236/ijaa.2013.34053
[54]	El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26. http://dx.doi.org/10.4236/jqis.2013.31006
[55]	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 & Astrophysics, 3, 205-211. http://dx.doi.org/10.4236/ijaa.2013.33024
[56]	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
[57]	Peat, F.D. (1983) In Search of Nikola Tesla. Ashgrove Publications, London & Bath.
[58]	Susskind, L. and Lindesay, J. (2005) The Holographic Universe. World Scientific, Singapore.
[59]	Stiglitz, J. and Bilmes, L. (2008) The Three Trillion Dollar War: The True Cost of the Iraq Conflict. Allen-Lane, Penguin Books, London.
[60]	El Naschie, M.S. (2013) A Unified Newtonian-Relativistic Quantum Resolution of Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light. International Journal of Modern Nonlinear Theory & Application, 2, 43-54. http://dx.doi.org/10.4236/ijmnta.2013.21005
[61]	Malek, C. (2015) Abu Dhabi Crown Prince Details UAE Leaders’ Vision of Future without Oil. The National Newspaper. http://www.thenational.ae/uae/government/abu-dhabi-crown-prince-details-uae-leaders-vision-of-future-without-oil?utm_content='%20vision%20of%20future%20without%20oil
[62]	Zee, A. (2003) Quantum Field Theory in a Nutshell. Princeton University Press, Princeton.
[63]	Duplantier, B. and Rivasseau, V., Eds. (2003) Vacuum Energy-Renormalization. Birkhauser, Basel.
[64]	Milonni, P.W. (1994) The Quantum Vacuum. Academic Press, Boston.
[65]	Parsegian, V.A. (2006) Van der Waals Forces. Cambridge University Press, Cambridge.
[66]	Huang, K. (2007) Fundamental Forces of Nature. World Scientific, Singapore. http://dx.doi.org/10.1142/6447
[67]	Wapner, L.M. (2005) The Pea and the Sun. A.K. Peters Ltd., Wellesley.
[68]	El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Micro Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508. http://dx.doi.org/10.1016/0960-0779(95)00052-6
[69]	Agvis, P.Y. (2014) Decoding the Genome: A Modified View. Nucleic Acids Research, 32, 223-238.
[70]	Xiao, W.W. and Qian, C.N. (2014) Our Dream of Defeating Cancer. Chinese Journal of Cancer, 33, 125-132.
[71]	Stauffer, D. and Stanley, H.E. (1989) From Newton to Mandelbrot. Springer, Berlin.
[72]	Bunde, A. and Havlin, S., Eds. (1995) Fractals in Science. Springer, Berlin.
[73]	Froler, V. and Zelnikov, A. (2013) Introduction to Black Hole Physics. Oxford University Press, Oxford.
[74]	El Naschie, M.S. (2015) Kerr Black Hole Geometry Leading to Dark Matter and Dark Energy via E-Infinity Theory and the Possibility of a Nano Spacetime Singularities Reactor. Natural Science, 7, 210-225. http://dx.doi.org/10.4236/ns.2015.74024