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Journal Article•DOI•

A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

M. S. El Naschie
13 Mar 2013-International Journal of Modern Nonlinear Theory and Application (Scientific Research Publishing)-Vol. 2013, Iss: 01, pp 43-54
TL;DR: In this article, an effective quantum gravity energy-mass relation was found using Newtonian dynamics which correctly predicts that 95.4915028% of the energy in the cosmos is the hypothetical missing dark energy.
Abstract: Time dilation, space contraction and relativistic mass are combined in a novel fashion using Newtonian dynamics. In this way we can surprisingly retrieve an effective quantum gravity energy-mass equation which gives the accurate experimental value of vacuum density. Furthermore Einstein’s equation of special relativity E = mc2, where m is the mass and c is the velocity of light developed assuming smooth 4D space time is transferred to a rugged Calabi-Yau and K3 fuzzy Kahler manifolds and revised to become E=(mc2)/(22), where the division factor 22 maybe interpreted as the compactified bosonic dimensions of Veneziano-Nambu strings. The result is again an accurate effective quantum gravity energy-mass relation akin to the one found using Newtonian dynamics which correctly predicts that 95.4915028% of the energy in the cosmos is the hypothetical missing dark energy. The agreement with WMAP and supernova measurements is in that respect astounding. In addition different theories are used to check the calculations and all lead to the same quantitative result. Thus the theories of varying speed of light, scale relativity, E-infinity theory, M-theory, Heterotic super strings, quantum field in curved space time, Veneziano’s dual resonance model, Nash Euclidean embedding and super gravity all reinforce, without any reservation, the above mentioned theoretical result which in turn is in total agreement with the most sophisticated cosmological measurements which was deservingly awarded the 2011 Nobel Prize in Physics. Finally and more importantly from certain viewpoints, we reason that the speed of light is constant because it is a definite probabilistic expectation value of a variable velocity in a hierarchical fractal clopen, i.e. closed and open micro space time.

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Citations
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Journal Article•DOI•
A Tutorial Review on Fractal Spacetime and Fractional Calculus

[...]

Ji-Huan He1•
Soochow University (Suzhou)1
25 Jun 2014-International Journal of Theoretical Physics
TL;DR: In this paper, a tutorial review of fractal-Cantorian spacetime and fractional calculus is presented, starting with Leibniz's notation for derivative without limits which can be generalized to discontinous media like fractal derivative and q-derivative of quantum calculus.
Abstract: This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontin- uous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational itera- tion method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effec- tive analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional com- plex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

386 citations

Cites background from "A Unified Newtonian-Relativistic Qu..."

  • ...The fat Cantor set models the quantum wave but it also models quantum spacetime itself [4]....

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Journal Article•DOI•
The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology

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M. A. Helal, L. Marek-Crnjac, Ji-Huan He
21 Nov 2013
TL;DR: A short survey of the most important results obtained by El Naschie's E-infinity theory in the realm of quantum physics and cosmology is given in this article, where special attention is paid to his recent result on dark energy and revising Einstein's famous formula.
Abstract: In this short survey, we give a complete list of the most important results obtained by El Naschie’s E-infinity Cantorian space-time theory in the realm of quantum physics and cosmology. Special attention is paid to his recent result on dark energy and revising Einstein’s famous formula .

52 citations

Cites background or result from "A Unified Newtonian-Relativistic Qu..."

  • ...In a 2012 conference in the Bibliotheca Alexandrina [84] El Naschie announced the revision of Einstein’s special relativity energy-mass formula to 2 E mc  2 22 E mc  and showed that it is the sum of the energy of the quantum particle 2 1 22 E mc  and the energy of the quantum wave (21/22) [53-63]....

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  • ...It is mainly concerned with space, time and matter and gives an almost exhaustive list of the most important results obtained by El Naschie using his Cantorian-fractal theory of space-time [1-85]....

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  • ...In agreement with the work of Magueijo and Smolin [70], El Naschie showed that the speed of light is not constant but a constant expectation value [58]....

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  • ...It showed that dark energy is the negative energy of the quantum wave    2 2 21 22 E E D mc    which agrees completely with measurements [54-68]....

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Journal Article•DOI•
Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology

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L. Marek-Crnjac, M. S. El Naschie, Ji-Huan He1•
Soochow University (Suzhou)1
29 Mar 2013-International Journal of Modern Nonlinear Theory and Application
TL;DR: In this paper, a short survey of recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light is given.
Abstract: At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.

47 citations

Journal Article•DOI•
Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography

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Mohamed S. El Naschie, Atef Helal
23 Aug 2013-International Journal of Astronomy and Astrophysics
TL;DR: In this article, a modified version of Einstein's energy mass relation E = mc2 was used to calculate the missing dark energy density of the cosmos by scaling the Planck scale and using the relatively novel discipline of cosmic crystallography and the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation.
Abstract: The aim of the present paper is to explain and accurately calculate the missing dark energy density of the cosmos by scaling the Planck scale and using the methodology of the relatively novel discipline of cosmic crystallography and Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation. Following this road we arrive at a modified version of Einstein’s energy mass relation E = mc2 which predicts a cosmological energy density in astonishing accord with the WMAP and supernova measurements and analysis. We develop non-constructively what may be termed super symmetric Penrose fractal tiling and find that the isomorphic length of this tiling is equal to the self affinity radius of a universe which resembles an 11 dimensional Hilbert cube or a fractal M-theory with a Hausdorff dimension where. It then turns out that the correct maximal quantum relativity energy-mass equation for intergalactic scales is a simple relativistic scaling, in the sense of Weyl-Nottale, of Einstein’s classical equation, namely EQR = (1/2)(1/) moc2 = 0.0450849 mc2 and that this energy is the ordinary measurable energy density of the quantum particle. This means that almost 95.5% of the energy of the cosmos is dark energy which by quantum particle-wave duality is the absolute value of the energy of the quantum wave and is proportional to the square of the curvature of the curled dimension of spacetime namely where and is Hardy’s probability of quantum entanglement. Because of the quantum wave collapse on measurement this energy cannot be measured using our current technologies. The same result is obtained by involving all the 17 Stein spaces corresponding to 17 types of the wallpaper groups as well as the 230-11=219 three dimensional crystallographic group which gives the number of the first level of massless particle-like states in Heterotic string theory. All these diverse subjects find here a unified view point leading to the same result regarding the missing dark energy of the universe, which turned out to by synonymous with the absolute value of the energy of the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equation while ordinary energy is the energy of the quantum particle into which the Hawking-Hartle wave collapse at cosmic energy measurement. In other words it is in the very act of measurement which causes our inability to measure the “Dark energy of the quantum wave” in any direct way. The only hope if any to detect dark energy and utilize it in nuclear reactors is future development of sophisticated quantum wave non-demolition measurement instruments.

40 citations

Cites background or methods from "A Unified Newtonian-Relativistic Qu..."

  • ...To put in a nutshell, dark energy is the energy of the quantum wave as modeled by the empty set in D = 5 while ordinary energy is the energy if the quantum particle modeled by the zero set in D = 5 Kaluza-Klein spacetime [26,27,38,39]....

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  • ...(A) The set theoretical particle-wave duality [38,41]:...

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  • ...Dark energy is the energy of the wave modeled by the empty set in five dimensional Kaluza-Klein spacetime [38,39,43]....

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  • ...where zero is the topological dimension and  is the Hausdorff dimension [38-41]....

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  • ...Even more profound than the above discussed result is the realization that dark energy is nothing but the energy of the quantum wave of the universe while ordinary energy is the energy of the quantum particle [35-39] (for elucidation see Figures 1, 2)....

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Journal Article•DOI•
Dark Energy from Kaluza-Klein Spacetime and Noether's Theorem via Lagrangian Multiplier Method

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Mohamed S. El Naschie
13 Jun 2013-Journal of Modern Physics
TL;DR: In this paper, it was shown that the Lagrangian multiplier is equal to the dark energy of the cosmos and is given by where E is energy, m is mass, c is the speed of light, and λ is the multiplier.
Abstract: The supposedly missing dark energy of the cosmos is found quantitatively in a direct analysis without involving ordinary energy. The analysis relies on five dimensional Kaluza-Klein spacetime and a Lagrangian constrained by an auxiliary condition. Employing the Lagrangian multiplier method, it is found that this multiplier is equal to the dark energy of the cosmos and is given by where E is energy, m is mass, c is the speed of light, and λ is the Lagrangian multiplier. The result is in full agreement with cosmic measurements which were awarded the 2011 Nobel Prize in Physics as well as with the interpretation that dark energy is the energy of the quantum wave while ordinary energy is the energy of the quantum particle. Consequently dark energy could not be found directly using our current measurement methods because measurement leads to wave collapse leaving only the quantum particle and its ordinary energy intact.

34 citations

References
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Book•
Quantum Gravity

[...]

Claus Kiefer
05 Aug 2004

3,583 citations

Posted Content•
What is string theory

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Joseph Polchinski
04 Nov 1994-arXiv: High Energy Physics - Theory
TL;DR: The first part is an introduction to conformal field theory and string perturbation theory and the second part deals with the search for a deeper answer to the question posed in the title as discussed by the authors.
Abstract: The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: 1. Conformal Field Theory 2. String Theory 3. Vacua and Dualities 4. String Field Theory or Not String Field Theory 5. Matrix Models

3,106 citations

Journal Article•DOI•
String theory

[...]

Brian R. Greene, David R. Morrison, Joseph Polchinski
15 Sep 1998-Proceedings of the National Academy of Sciences of the United States of America
TL;DR: The standard model of particle physics is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm as discussed by the authors.
Abstract: Particle physicists have spent much of this century grappling with one basic question in various forms: what are the fundamental degrees of freedom needed to describe nature, and what are the laws that govern their dynamics? First molecules, then atoms, then “elementary particles” such as protons and neutrons all have been revealed to be composite objects whose constituents could be studied as more fundamental degrees of freedom. The current “standard model” of particle physics—which is nearly 25 years old, has much experimental evidence in its favor and is comprised of six quarks, six leptons, four forces, and the as yet unobserved Higgs boson—contains internal indications that it, too, may be just another step along the path toward uncovering the truly fundamental degrees of freedom. The standard model is valid to distances as small as 10−16 cm, and there is some evidence (such as that obtained by extrapolating the strengths of the four forces to determine the distance scale at which they might become indistinguishable) that the next level of structure will be detected only at a distance scale of roughly 10−32 cm, far beyond our abilities to measure in the laboratory. The study of motion and gravity also has undergone several revisions during this century. Reconciling the Newtonian theory of motion with the experimentally observed constancy of the speed of light required the introduction of special relativity, which quite remarkably insists that space and time are intimately related, much as different faces of the same …

2,812 citations

Book•
The Variational Principles of Mechanics

[...]

Cornelius Lanczos
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"A Unified Newtonian-Relativistic Qu..." refers background or methods in this paper

  • ...The result is essentially a Lagrangian [30,31] multiplier equal 1 22 which is used as a scaling (see Table 1 No....

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  • ...The fundamental similarity factor found here 1 22   is mathematically the Lagrangian multiplier of an Isoperimetric variational problem when setting 2 1 mc  [30,31] and physically is the effect of quantum entanglement of the Hardy type on relativity for a single particle 5 2  i....

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  • ...A realistic theory of nature however must have a Lagrangian with a minimum of 12 generalized coordinates representing 12 massless gauge Bosons being the number of messenger particles of the standard model of high energy physics [1,7,14]....

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  • ...The fundamental similarity factor found here 1 22 is mathematically the Lagrangian multiplier of an Isoperimetric variational problem when setting 2 1mc [30,31] and physically is the effect of quantum entanglement of the Hardy type on relativity for a single particle 5 2 i.e. where 5 1 11 for two particle entanglement [22]....

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  • ...15) Lagrangian multiplier method for isoparametric variational problems 2 21 2 V a mv G Where is the Lagrangian multiplier and consequently steady state is given by 11 0 0 12 1 11iG 2 0v which leads for to v c 21 11 0 2 mc or 2 22 mc ....

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Journal Article•DOI•
Lorentz invariance with an invariant energy scale.

[...]

João Magueijo1, Lee Smolin1, Lee Smolin2•
Imperial College London1, Perimeter Institute for Theoretical Physics2
26 Apr 2002-Physical Review Letters
TL;DR: A modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies is proposed.
Abstract: We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

1,194 citations

"A Unified Newtonian-Relativistic Qu..." refers background or methods in this paper

  • ...However this is all linked to quantum gravity [1-23] and we start here from special relativity and address the greatest puzzle of them all which we invariably took and rather wrongly as a given experiential fact of Nature which cannot be reduced or interrogated any further namely the constancy of the speed of light....

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  • ...That is why self similarity manifests itself here directly as simple scaling from Newton to Einstein and beyond all that, to quantum gravity [1,3,5,6, 12,15]....

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  • ...13) Varying speed of Light Theory of Magueijo and Smolin 2 2 1 P mcE mc E Transferring to unit the interval one finds 5HardyPE P SigalottiC v Kaluza-Klein dimension 5KKm m D...

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  • ...Speed of Light as a Probabilistic Expectation Value 1....

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  • ...On the other hand should the principle of scale relativity hold, then one would expect to retrieve Einstein’s familiar formula in a scaled form [3-5]....

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Trending Questions (1)
Who is the only person to win the Nobel Prize for physics twice once for inventing the transistor and the other time for the theory of superconductivity?

Thus the theories of varying speed of light, scale relativity, E-infinity theory, M-theory, Heterotic super strings, quantum field in curved space time, Veneziano’s dual resonance model, Nash Euclidean embedding and super gravity all reinforce, without any reservation, the above mentioned theoretical result which in turn is in total agreement with the most sophisticated cosmological measurements which was deservingly awarded the 2011 Nobel Prize in Physics.

See answers from 7 other papers