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 ...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 .展开更多
The paper presents a detailed analysis of ordinary and dark energy density of the cosmos based on two different but complimentary theories. First, and starting from the concept of the speed of light being an average o...The paper presents a detailed analysis of ordinary and dark energy density of the cosmos based on two different but complimentary theories. First, and starting from the concept of the speed of light being an average over multi-fractals, we use Magueijo-Smolin’s ingenious revision of Einstein’s special relativity famous formula E = mc2 to a doubly special formula which includes the Planck energy as invariant to derive the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) wheremis the mass andcis the speed of light. Second we use the topological theory of pure gravity to reach the same result thus confirming the correctness of the theory of varying speed of light as well as the COBE, WMAP and Type 1a supernova cosmological measurements.展开更多
Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterica...Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterically small numbers to a manageably where P(H) is the famous Hardy’s probability for quantum entanglement which amounts to almost 9 percent and Based on these results, we conclude the equivalence of Einstein-Rosen “wormhole” bridges and Einstein’s Podolsky-Rosen’s spooky action at a distance. In turn these results are shown to be consistent with distinguishing two energy components which results in , namely the quantum zero set particle component which we can measure and the quantum empty set wave component which we cannot measure , i.e. the missing dark energy. Together the two components add to where E is the total energy, m is the mass and c is the speed of light. In other words, the present new derivation of the world’s most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physicomathematical meaning of the wave function and the nature of dark energy. In essence they are one and the same when looked upon from the view point of quantum-fractal geometry.展开更多
In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in ...In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in the cosmos according to Einstein’s prediction must be dark energy or not there at all. This percentage is in almost complete agreement with actual measurements.展开更多
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 dynam...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.展开更多
The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type....The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type. Subsequently this analogy is used to deduce the ordinary energy of the quantum particle and the dark energy of the quantum wave. The results agree completely with cosmological measurements. Even more surprisingly the sum of both energy expressions turned out to be exactly equal to Einstein’s iconic formula E = mc2. Consequently Einstein’s formula makes no distinction between ordinary and dark energy.展开更多
The Egyptian engineering scientist and theoretical physicist Mohamed El Naschie has found a definite resolution to the missing dark energy of the cosmos based on a revision of the theory of Relativity. Einstein’s equ...The Egyptian engineering scientist and theoretical physicist Mohamed El Naschie has found a definite resolution to the missing dark energy of the cosmos based on a revision of the theory of Relativity. Einstein’s equation of special relativity E = m0c2, where m0 is the controversial rest mass and c is the velocity of light developed in smooth 4D space-time was transferred by El Naschie to a rugged Calabi-Yau and K3 fuzzy Kahler manifold. The result is an accurate, effective quantum gravity energy-mass relation which correctly predicts that 95.4915028% of the energy in the cosmos is the missing hypothetical dark energy. The agreement with WMAP and supernova measurements is astounding. Different theories are used by El Naschie 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 and Nash’s Euclidean embedding all reinforce, without any reservation, the above mentioned theoretical result of El Naschie which in turn is in total agreement with the most sophisticated cosmological measurement. Incidentally these experimental measurements and analysis were awarded the 2011 Nobel Prize in Physics to Adam Riess, Brian Schmidt, and Saul Perlmutter.展开更多
This tutorial review is dedicated to the work of the outstanding Egyptian theoretical physicist and engineering scientist Prof. Mohamed El Naschie. Every physics student knows the well-known Einstein’s mass-energy eq...This tutorial review is dedicated to the work of the outstanding Egyptian theoretical physicist and engineering scientist Prof. Mohamed El Naschie. Every physics student knows the well-known Einstein’s mass-energy equation, E=mc2, but unfortunately for physics, few know El Naschie’s modification, E(O)=mc2/22, and El Naschie’s dark energy equation E(D)=mc2(21/22) although this new insight has truly far reaching implications. This paper gives a short tutorial review of El Naschie’s fractal-Cantorian space-time as well as dark energy. Emphasis is put on the fundamental concept of Cantor set, fractal dimensions, zero set, empty set, and Casimir effect.展开更多
The paper is a condensed but accurate account of El Naschie’s theory of Cantorian space-time which was used by him to clarify some major problems in theoretical physics and cosmology. In particular El Naschie’s revi...The paper is a condensed but accurate account of El Naschie’s theory of Cantorian space-time which was used by him to clarify some major problems in theoretical physics and cosmology. In particular El Naschie’s revision and completion of relativity theory and demystification of dark energy are destined to be two milestones in the history of theoretical physics.展开更多
Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-inte...Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-integer (Hausdorff) dimension for its geometry as well as infinite dimensional wild topology and non classical fuzzy logic. In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. This leads naturally to a new look at quantum gravity. In particular we will show that to understand and develop quantum gravity we have to bring various fields together, particularly fractals and nonlinear dynamics as well as sphere packing, fuzzy set theory, number theory and quantum entanglement and irrationally q-deformed algebra.展开更多
文摘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 .
文摘The paper presents a detailed analysis of ordinary and dark energy density of the cosmos based on two different but complimentary theories. First, and starting from the concept of the speed of light being an average over multi-fractals, we use Magueijo-Smolin’s ingenious revision of Einstein’s special relativity famous formula E = mc2 to a doubly special formula which includes the Planck energy as invariant to derive the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) wheremis the mass andcis the speed of light. Second we use the topological theory of pure gravity to reach the same result thus confirming the correctness of the theory of varying speed of light as well as the COBE, WMAP and Type 1a supernova cosmological measurements.
文摘Following an inspiring idea due to D. Gross, we arrive at a topological Planck energy Ep and a corresponding topological Planck length effectively scaling the Planck scale from esoterically large and equally esoterically small numbers to a manageably where P(H) is the famous Hardy’s probability for quantum entanglement which amounts to almost 9 percent and Based on these results, we conclude the equivalence of Einstein-Rosen “wormhole” bridges and Einstein’s Podolsky-Rosen’s spooky action at a distance. In turn these results are shown to be consistent with distinguishing two energy components which results in , namely the quantum zero set particle component which we can measure and the quantum empty set wave component which we cannot measure , i.e. the missing dark energy. Together the two components add to where E is the total energy, m is the mass and c is the speed of light. In other words, the present new derivation of the world’s most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physicomathematical meaning of the wave function and the nature of dark energy. In essence they are one and the same when looked upon from the view point of quantum-fractal geometry.
文摘In this paper Nottale’s acclaimed scale relativity theory is given a transfinite Occam’s razor leading to exact predictions of the missing dark energy [1,2] of the cosmos. It is found that 95.4915% of the energy in the cosmos according to Einstein’s prediction must be dark energy or not there at all. This percentage is in almost complete agreement with actual measurements.
文摘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.
文摘The formula for the quantum amplitude of the Veneziano dual resonance model is shown to be formally analogous to the dimensionality of a K-theoretical fractal quotient manifold of the non-commutative geometrical type. Subsequently this analogy is used to deduce the ordinary energy of the quantum particle and the dark energy of the quantum wave. The results agree completely with cosmological measurements. Even more surprisingly the sum of both energy expressions turned out to be exactly equal to Einstein’s iconic formula E = mc2. Consequently Einstein’s formula makes no distinction between ordinary and dark energy.
文摘The Egyptian engineering scientist and theoretical physicist Mohamed El Naschie has found a definite resolution to the missing dark energy of the cosmos based on a revision of the theory of Relativity. Einstein’s equation of special relativity E = m0c2, where m0 is the controversial rest mass and c is the velocity of light developed in smooth 4D space-time was transferred by El Naschie to a rugged Calabi-Yau and K3 fuzzy Kahler manifold. The result is an accurate, effective quantum gravity energy-mass relation which correctly predicts that 95.4915028% of the energy in the cosmos is the missing hypothetical dark energy. The agreement with WMAP and supernova measurements is astounding. Different theories are used by El Naschie 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 and Nash’s Euclidean embedding all reinforce, without any reservation, the above mentioned theoretical result of El Naschie which in turn is in total agreement with the most sophisticated cosmological measurement. Incidentally these experimental measurements and analysis were awarded the 2011 Nobel Prize in Physics to Adam Riess, Brian Schmidt, and Saul Perlmutter.
文摘This tutorial review is dedicated to the work of the outstanding Egyptian theoretical physicist and engineering scientist Prof. Mohamed El Naschie. Every physics student knows the well-known Einstein’s mass-energy equation, E=mc2, but unfortunately for physics, few know El Naschie’s modification, E(O)=mc2/22, and El Naschie’s dark energy equation E(D)=mc2(21/22) although this new insight has truly far reaching implications. This paper gives a short tutorial review of El Naschie’s fractal-Cantorian space-time as well as dark energy. Emphasis is put on the fundamental concept of Cantor set, fractal dimensions, zero set, empty set, and Casimir effect.
文摘The paper is a condensed but accurate account of El Naschie’s theory of Cantorian space-time which was used by him to clarify some major problems in theoretical physics and cosmology. In particular El Naschie’s revision and completion of relativity theory and demystification of dark energy are destined to be two milestones in the history of theoretical physics.
文摘Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-integer (Hausdorff) dimension for its geometry as well as infinite dimensional wild topology and non classical fuzzy logic. In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. This leads naturally to a new look at quantum gravity. In particular we will show that to understand and develop quantum gravity we have to bring various fields together, particularly fractals and nonlinear dynamics as well as sphere packing, fuzzy set theory, number theory and quantum entanglement and irrationally q-deformed algebra.
