Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this mo...Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this model, equations of the special relativity can be extended more perfectly, thereby achieving a unity of the special relativity and quantum mechanics in deeper level. New equations can not only interpret issues explained by old equations but also solve several important pending problems. For example, a formula to strictly calculate the coefficient ξ of Lorentz invariance violation (LIV) is derived, to above 4 × 1019 eV UHECR protons the calculated |ξ| -30, although there is the LIV effect it is too weak to change the GZK cutoff, which is consistent with observations of HiRes and Auger;Also, a relation formula between the Hubble constant and several basic constants is derived, thus theoretically calculated H0 = 70.937 km·s-1·Mpc-1, which is well consistent with the final observation result of HST Key Project. In addition, an unusual effect predicted by new equations can be experimentally tested in the electron storage ring;a preliminary experiment result has hinted its signs of existence.展开更多
Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 k...Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.展开更多
The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in ...The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the generic solution cannot be expressed by means of the derivatives of a certain number of arbitrary potential-like functions, solving therefore negatively a 1000 $ challenge proposed by J. Wheeler in 1970. Accordingly, the mathematical foundations of electromagnetism and gravitation must be revisited within this formal framework, though striking it may look like. We insist on the fact that the arguments presented are of a purely mathematical nature and are thus unavoidable.展开更多
We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective ...We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by E1= mc2 /22 while the dark energy density of the vacuum is given by E2 = mc2 (21/22). The sum of both energies is equal to Einstein’s energy E = mc2. We conclude that E= mc2 makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.展开更多
The search for the generating compatibility conditions (CC) of a given operator is a very recent problem met in general relativity in order to study the Killing operator for various standard useful metrics. Accordingl...The search for the generating compatibility conditions (CC) of a given operator is a very recent problem met in general relativity in order to study the Killing operator for various standard useful metrics. Accordingly, this paper can be considered as a natural continuation of a previous paper recently published in JMP under the title Minkowski, Schwarschild and Kerr metrics revisited. In particular, we prove that the intrinsic link existing between the lack of formal exactness of an operator sequence on the jet level, the lack of formal exactness of its corresponding symbol sequence and the lack of formal integrability (FI) of the initial operator is of a purely homological nature as it is based on the long exact connecting sequence provided by the so-called snake lemma in homological algebra. It is therefore quite difficult to grasp it in general and even more difficult to use it on explicit examples. It does not seem that any one of the results presented in this paper is known as most of the other authors who studied the above problem of computing the total number of generating CC are confusing this number with the degree of generality introduced by A. Einstein in his 1930 letters to E. Cartan. One of the motivating examples that we provide is so striking that it is even difficult to imagine that such an example could exist. We hope this paper could be used as a source of testing examples for future applications of computer algebra in general relativity and, more generally, in mathematical physics.展开更多
This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calcula...This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.展开更多
In this paper we outline a non-perturbative quantum relativity theory. Subsequently an actual design of a nanotech energy reactor is based on spacetime vacuum fluctuation of the said quantum relativity theory. Using a...In this paper we outline a non-perturbative quantum relativity theory. Subsequently an actual design of a nanotech energy reactor is based on spacetime vacuum fluctuation of the said quantum relativity theory. Using a compact heap of Fullerene nano particle moduli of a nano matrix device we propose that by maximizing the Casimir forces between these particles as a desirable effect, we can achieve a gradual rather than a sudden implosion pressure. We expect that this will result in a mini holographic universe from which energy can be extracted in a way to constitute a nano energy reactor and function effectively on a hybrid principle somewhere between a Casimir effect and a cold fusion process based on the fusion algebra of a highly structured golden ring quantum field theory. The present theory depends upon many concepts and results, in particular J. Schwinger’s source theory as well as the modern theory of quantum sets, nonlinear dynamics, chaos and chaotic fractals.展开更多
Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean trian...Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc2. In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc2 is which agrees almost completely with the latest supernova and WMAP cosmological measurements. To put it succinctly what is really missing is a quantum mechanical factor equal 1/22 in Einstein’s purely relativistic equation. This factor on the other hand is derivable from the intrinsic hyperbolic Cantor set nature of quantum entanglement.展开更多
After discovery of the superluminal particle and consideration on development of contemporary physical theory research, also on the existing errors and omissions, the principle of constant light speed is found not a n...After discovery of the superluminal particle and consideration on development of contemporary physical theory research, also on the existing errors and omissions, the principle of constant light speed is found not a necessary condition in derivation of Lorentz Transformation;instead, this thesis proposes the velocity of graviton may feature superluminal, constant velocity in different directions, and independence of inertial reference frame speeds. This is an optional thought of correction. According serial hypothesis, an equation of graviton’s motion trace, i.e., the central curve of nebula density, is established for spiral galaxy. Thus we gain the method to measure velocity of graviton. If to totally avoid problem of limit speed, we have to search for independent of inertia frames, and relevant to space-time properties. Regarding current difficulties of singular points in the Theory of Limited Universe, this thesis points out that the document [1] is the best solution to these difficulties.展开更多
Up to now, cosmology metrics have been based on Einstein relativity, established in 1905. Hubble has discovered the correlation between redshift and distance. Cosmology interprets the redshift as an expansion effect a...Up to now, cosmology metrics have been based on Einstein relativity, established in 1905. Hubble has discovered the correlation between redshift and distance. Cosmology interprets the redshift as an expansion effect a(t) through the ΛCDM model. We have proposed a new theory to explain Hubble law. The theory has been validated against observation data. It proposes a new approach of time which introduces the cosmic time tc. Cosmic time is an absolute reference to universe. It is zero at the edge with tc = 0, tc = T at the observer position and tc = s for any source between the edge and the observer, with T > s > 0. This theory acts like the relativity of space-time. The redshift is interpreted as a perspective parameter p(tc) = tc/T. Using gravitation, it is the Einstein effect applied to the uni-verse. This paper comments and interprets further consequences of this new theory. We emphasize the difference between duration (as usually used in classical cosmologic metrics) and the cosmic time tc as a notion of date. It induces two related effects: relativity of speed of light and time stretching. We explain why the cosmological standard model is not well suited to describe the Hubble law, to describe the universe. We also explain why gravitation and temperature increase when going from the center to the edge of the universe, when going from present to birth. The model has no use of black energy. As a consequence, the universe is seen as a black hole created by the cosmic time shock wave when tc = 0.展开更多
In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in phys...In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in physics. In mathematics, since second order partial differential equations can be classified into hyperbolic, elliptic or parabolic type, therefore we show that it is also possible to classify relativity accordingly into hyperbolic, elliptic or parabolic type by establishing coordinate transformations that preserve the forms of these second order partial differential equations. The coordinate transformation that preserves the form of the hyperbolic equation is the Lorentz transformation and the associated space is the hyperbolic, or pseudo-Euclidean, relativistic spacetime. Typical equations in physics that comply with hyperbolic relativity are Maxwell and Dirac equations. The coordinate transformation that preserves the form of the elliptic equation is the modified Lorentz transformation that we have formulated in our work on Euclidean relativity and the associated space is the elliptic, or Euclidean, relativistic spacetime. As we will show in this work, equations that comply with elliptic relativity are the equations that describe the subfields of Maxwell and Dirac field. And the coordinate transformation that preserves the form of the parabolic equation is the Euclidean transformation consisting of the translation and rotation in the spatial space and the associated space is the parabolic relativistic spacetime, which is a Euclidean space with a universal time. Typical equations in physics that comply with parabolic relativity are the diffusion equation, the Schrödinger equation and in particular the diffusion equations that are derived from the four-current defined in terms of the differentiable structures of the spacetime manifold, and the Ricci flow.展开更多
The aim of this paper essentially lies in attributing a new meaning, coherent with phenomenological reality, to several phenomena usually classified as relativistic, such as the alleged increase of the mean lifetime o...The aim of this paper essentially lies in attributing a new meaning, coherent with phenomenological reality, to several phenomena usually classified as relativistic, such as the alleged increase of the mean lifetime of muons and the gravitational redshift. According to the model herein proposed, all the relativistic equations preserve their validity, albeit with a different connotation. We consider a Simple-Harmonically Oscillating Universe, characterized by a null curvature parameter, postulating the existence of a further spatial dimension, not directly perceivable. Time is considered as being absolute, although instruments and devices of whatever kind, commonly employed to measure it, may be significantly influenced by motion and gravity. The Planck Constant is regarded as a parameter, locally variable and subjected to a cyclic evolution. Time and space are treated as quantized physical quantities.展开更多
Inertia is one of the most mysterious forces of nature. Its physical nature is unknown. Accordingly, attempts are made to avoid this “dark force” in one way or another. In Newton’s mechanics and in the special rela...Inertia is one of the most mysterious forces of nature. Its physical nature is unknown. Accordingly, attempts are made to avoid this “dark force” in one way or another. In Newton’s mechanics and in the special relativity theory, this is done by postulating inertial reference frame, in the general relativity theory by postulating the equivalence principle. Postulates cannot change the laws of nature. One needs to know the latter. Given that the forces of inertia result in non-inertial reference frames only, a hypothesis of the induction nature of inertia has been made. According to this hypothesis, the forces of inertia result as the reaction of a body to external influence. A system of equations explaining the physical nature of inertia and its connection to gravity has been drafted. A group of coordinate conversion has been suggested, which without violating the general covariance of the laws of nature, enables to distinguish one reference frame associated with one body from another system associated with another body, to determine the privileged ones, and to take into consideration their influence on the readings of measurement instruments. A modified mechanics had been created. It takes into consideration the Mach’s principle and enables to cover all systems with the relativity principle. All of the relativistic effects arise from it. The reasons for emergence of new particles, dark matter, dark energy etc. are explained. New effects are predicted.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
In the socio-professional environment,the existence of values proves to be essential to the individual in order to live in harmony.It is by the search of oneself that you discover the world around you.Under this aspec...In the socio-professional environment,the existence of values proves to be essential to the individual in order to live in harmony.It is by the search of oneself that you discover the world around you.Under this aspect,the philosophy of education can contribute to the conveyance of a decisive reflection on the impact of the educator’s mission on the people who are taught.On the one hand,the relativity of values puts into question their universal dimension,since they diversify in place and time according to different eras but also to different customs of each country.In this case,what is the finality of education and learning in relation to cultural diversification with regard to innovation in teaching?On the other hand,the educator’s personality plays a considerable and effective role in motivating his/her target group to seek out the higher and universal values and disseminate the principles of citizenship.Lastly,with regard to vocational training,the introduction of diversified pedagogical approaches as well as the adoption of learning strategies will enable the Educator to act in full knowledge and awareness of his action while being preoccupied in the management of the pedagogical process.His/her effective intervention will offer the opportunity to the group members to create synergies,in order to develop their unexploited potential and achieve a high level of awareness through the development of their personality.展开更多
This paper briefly discusses existing problems with the theory of general relativity despite remarkable accuracy in most of its applications. The primary focus is on existing problems in the field of cosmology, partic...This paper briefly discusses existing problems with the theory of general relativity despite remarkable accuracy in most of its applications. The primary focus is on existing problems in the field of cosmology, particularly those pertaining to expectations of global cosmic space-time curvature in the absence of observational proof. The discussion centers on Krogdahl’s recent Lorentz-invariant flat space-time cosmology and its superiority to general relativity with respect to accounting for global cosmic space-time flatness and dark energy observations. The “cosmological constant problem” is briefly addressed as a problem for general relativity with respect to particle physics and quantum field theory. Finally, two very specific validation predictions in favor of Krogdahl’s flat space-time cosmology are made with respect to ongoing studies, including the dark energy survey (DES).展开更多
Einstein general theory of relativity (GTR) accounted well for the precession of the perihelion of planets and binary pulsars. While the ordinary Newton law of gravitation failed, a generalized version yields similar ...Einstein general theory of relativity (GTR) accounted well for the precession of the perihelion of planets and binary pulsars. While the ordinary Newton law of gravitation failed, a generalized version yields similar results. We have shown here that these effects can be accounted for as due to the existence of gravitomagnetism only, and not necessarily due to the curvature of space time. Or alternatively, gravitomagnetism is equivalent to a curved space-time. The precession of the perihelion of planets and binary pulsars may be interpreted as due to the spin of the orbiting planet (m) about the Sun (M). The spin (S) of planets is found to be related to their orbital angular momentum (L) by a simple formula, viz., S (m/M)L.展开更多
The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with line...The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with linear Algebra and Vector Analysis without the need for concept of space-time. This is important for the unification of general relativity with quantum mechanics, gravity with electromagnetic, and a better understanding of the universe, gravity, black holes. The most important is the separation between the space-time and the big bang theory, which prove the existence of space-time before that, which leads to the existence of the creator of the universe.展开更多
In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differentia...In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.展开更多
Deriving an acceptable quantum field theory of gravitation from general relativity has eluded some of the best scientific thinkers. It is gradually becoming more apparent that general relativity’s classical assumptio...Deriving an acceptable quantum field theory of gravitation from general relativity has eluded some of the best scientific thinkers. It is gradually becoming more apparent that general relativity’s classical assumptions are simply incompatible with quantum mechanics. For instance, simultaneous certainty of the location and momentum of any moving body, regardless of size, is a fundamental feature of general relativity. And yet, special relativity and quantum mechanics (thru Heisenberg’s uncertainty) reject the very notion of simultaneity. Since special relativity is already fully integrated into quantum field theory concerning the other forces of nature, were it possible to remove the confounding smoothly curved space-time fabric of general relativity and replace it in the form of a new and improved Lorentz-invariant (flat space-time) gravitational theory, final unification might well be achievable. This brief review paper further informs the reader as to why Krogdahl’s recent Lorentz-invariant relativity model of gravitation improves on general relativity, thus providing a deeper understanding of black holes, the cosmological flatness problem and dark energy. Most importantly, since the smoothly curved space-time of general relativity may well have been the road block to unification, Krogdahl’s flat space-time model is predicted to lead to an acceptable quantum theory of gravitation (i.e., “quantum gravity”) and unification (i.e., a so-called “theory of everything”).展开更多
文摘Based on the space spherical symmetry of 3-dimensional and the translational symmetry of time and the uncertainty principle, a 4-dimensional space-time cylinder model of quarks and leptons is established. With this model, equations of the special relativity can be extended more perfectly, thereby achieving a unity of the special relativity and quantum mechanics in deeper level. New equations can not only interpret issues explained by old equations but also solve several important pending problems. For example, a formula to strictly calculate the coefficient ξ of Lorentz invariance violation (LIV) is derived, to above 4 × 1019 eV UHECR protons the calculated |ξ| -30, although there is the LIV effect it is too weak to change the GZK cutoff, which is consistent with observations of HiRes and Auger;Also, a relation formula between the Hubble constant and several basic constants is derived, thus theoretically calculated H0 = 70.937 km·s-1·Mpc-1, which is well consistent with the final observation result of HST Key Project. In addition, an unusual effect predicted by new equations can be experimentally tested in the electron storage ring;a preliminary experiment result has hinted its signs of existence.
文摘Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.
文摘The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the generic solution cannot be expressed by means of the derivatives of a certain number of arbitrary potential-like functions, solving therefore negatively a 1000 $ challenge proposed by J. Wheeler in 1970. Accordingly, the mathematical foundations of electromagnetism and gravitation must be revisited within this formal framework, though striking it may look like. We insist on the fact that the arguments presented are of a purely mathematical nature and are thus unavoidable.
文摘We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by E1= mc2 /22 while the dark energy density of the vacuum is given by E2 = mc2 (21/22). The sum of both energies is equal to Einstein’s energy E = mc2. We conclude that E= mc2 makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.
文摘The search for the generating compatibility conditions (CC) of a given operator is a very recent problem met in general relativity in order to study the Killing operator for various standard useful metrics. Accordingly, this paper can be considered as a natural continuation of a previous paper recently published in JMP under the title Minkowski, Schwarschild and Kerr metrics revisited. In particular, we prove that the intrinsic link existing between the lack of formal exactness of an operator sequence on the jet level, the lack of formal exactness of its corresponding symbol sequence and the lack of formal integrability (FI) of the initial operator is of a purely homological nature as it is based on the long exact connecting sequence provided by the so-called snake lemma in homological algebra. It is therefore quite difficult to grasp it in general and even more difficult to use it on explicit examples. It does not seem that any one of the results presented in this paper is known as most of the other authors who studied the above problem of computing the total number of generating CC are confusing this number with the degree of generality introduced by A. Einstein in his 1930 letters to E. Cartan. One of the motivating examples that we provide is so striking that it is even difficult to imagine that such an example could exist. We hope this paper could be used as a source of testing examples for future applications of computer algebra in general relativity and, more generally, in mathematical physics.
基金Supported in part by National Natural Science Foundation of China under Grant No.11375169
文摘This is a follow of previous work entitled "One Electron Atom in Special Relativity with de Sitter SpaceTime Symmetry" [Commun. Theor. Phys. 57(2012) 930]. In this paper, we consider the higher order calculations and contributions in the previous framework to solve one electron atoms in de Sitter invariant relativistic quantum mechanics. The next-to-leading-order calculations in 1/R2-expansions show that the fine-structure constant α is variant with cosmologic time going by in the de Sitter invariant special relativistic quantum mechanics with standard FRW cosmologic model.
文摘In this paper we outline a non-perturbative quantum relativity theory. Subsequently an actual design of a nanotech energy reactor is based on spacetime vacuum fluctuation of the said quantum relativity theory. Using a compact heap of Fullerene nano particle moduli of a nano matrix device we propose that by maximizing the Casimir forces between these particles as a desirable effect, we can achieve a gradual rather than a sudden implosion pressure. We expect that this will result in a mini holographic universe from which energy can be extracted in a way to constitute a nano energy reactor and function effectively on a hybrid principle somewhere between a Casimir effect and a cold fusion process based on the fusion algebra of a highly structured golden ring quantum field theory. The present theory depends upon many concepts and results, in particular J. Schwinger’s source theory as well as the modern theory of quantum sets, nonlinear dynamics, chaos and chaotic fractals.
文摘Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc2. In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc2 is which agrees almost completely with the latest supernova and WMAP cosmological measurements. To put it succinctly what is really missing is a quantum mechanical factor equal 1/22 in Einstein’s purely relativistic equation. This factor on the other hand is derivable from the intrinsic hyperbolic Cantor set nature of quantum entanglement.
文摘After discovery of the superluminal particle and consideration on development of contemporary physical theory research, also on the existing errors and omissions, the principle of constant light speed is found not a necessary condition in derivation of Lorentz Transformation;instead, this thesis proposes the velocity of graviton may feature superluminal, constant velocity in different directions, and independence of inertial reference frame speeds. This is an optional thought of correction. According serial hypothesis, an equation of graviton’s motion trace, i.e., the central curve of nebula density, is established for spiral galaxy. Thus we gain the method to measure velocity of graviton. If to totally avoid problem of limit speed, we have to search for independent of inertia frames, and relevant to space-time properties. Regarding current difficulties of singular points in the Theory of Limited Universe, this thesis points out that the document [1] is the best solution to these difficulties.
文摘Up to now, cosmology metrics have been based on Einstein relativity, established in 1905. Hubble has discovered the correlation between redshift and distance. Cosmology interprets the redshift as an expansion effect a(t) through the ΛCDM model. We have proposed a new theory to explain Hubble law. The theory has been validated against observation data. It proposes a new approach of time which introduces the cosmic time tc. Cosmic time is an absolute reference to universe. It is zero at the edge with tc = 0, tc = T at the observer position and tc = s for any source between the edge and the observer, with T > s > 0. This theory acts like the relativity of space-time. The redshift is interpreted as a perspective parameter p(tc) = tc/T. Using gravitation, it is the Einstein effect applied to the uni-verse. This paper comments and interprets further consequences of this new theory. We emphasize the difference between duration (as usually used in classical cosmologic metrics) and the cosmic time tc as a notion of date. It induces two related effects: relativity of speed of light and time stretching. We explain why the cosmological standard model is not well suited to describe the Hubble law, to describe the universe. We also explain why gravitation and temperature increase when going from the center to the edge of the universe, when going from present to birth. The model has no use of black energy. As a consequence, the universe is seen as a black hole created by the cosmic time shock wave when tc = 0.
文摘In this work, we discuss the possibility to classify relativity in accordance with the classification of second order partial differential equations that have been applied into the formulation of physical laws in physics. In mathematics, since second order partial differential equations can be classified into hyperbolic, elliptic or parabolic type, therefore we show that it is also possible to classify relativity accordingly into hyperbolic, elliptic or parabolic type by establishing coordinate transformations that preserve the forms of these second order partial differential equations. The coordinate transformation that preserves the form of the hyperbolic equation is the Lorentz transformation and the associated space is the hyperbolic, or pseudo-Euclidean, relativistic spacetime. Typical equations in physics that comply with hyperbolic relativity are Maxwell and Dirac equations. The coordinate transformation that preserves the form of the elliptic equation is the modified Lorentz transformation that we have formulated in our work on Euclidean relativity and the associated space is the elliptic, or Euclidean, relativistic spacetime. As we will show in this work, equations that comply with elliptic relativity are the equations that describe the subfields of Maxwell and Dirac field. And the coordinate transformation that preserves the form of the parabolic equation is the Euclidean transformation consisting of the translation and rotation in the spatial space and the associated space is the parabolic relativistic spacetime, which is a Euclidean space with a universal time. Typical equations in physics that comply with parabolic relativity are the diffusion equation, the Schrödinger equation and in particular the diffusion equations that are derived from the four-current defined in terms of the differentiable structures of the spacetime manifold, and the Ricci flow.
文摘The aim of this paper essentially lies in attributing a new meaning, coherent with phenomenological reality, to several phenomena usually classified as relativistic, such as the alleged increase of the mean lifetime of muons and the gravitational redshift. According to the model herein proposed, all the relativistic equations preserve their validity, albeit with a different connotation. We consider a Simple-Harmonically Oscillating Universe, characterized by a null curvature parameter, postulating the existence of a further spatial dimension, not directly perceivable. Time is considered as being absolute, although instruments and devices of whatever kind, commonly employed to measure it, may be significantly influenced by motion and gravity. The Planck Constant is regarded as a parameter, locally variable and subjected to a cyclic evolution. Time and space are treated as quantized physical quantities.
文摘Inertia is one of the most mysterious forces of nature. Its physical nature is unknown. Accordingly, attempts are made to avoid this “dark force” in one way or another. In Newton’s mechanics and in the special relativity theory, this is done by postulating inertial reference frame, in the general relativity theory by postulating the equivalence principle. Postulates cannot change the laws of nature. One needs to know the latter. Given that the forces of inertia result in non-inertial reference frames only, a hypothesis of the induction nature of inertia has been made. According to this hypothesis, the forces of inertia result as the reaction of a body to external influence. A system of equations explaining the physical nature of inertia and its connection to gravity has been drafted. A group of coordinate conversion has been suggested, which without violating the general covariance of the laws of nature, enables to distinguish one reference frame associated with one body from another system associated with another body, to determine the privileged ones, and to take into consideration their influence on the readings of measurement instruments. A modified mechanics had been created. It takes into consideration the Mach’s principle and enables to cover all systems with the relativity principle. All of the relativistic effects arise from it. The reasons for emergence of new particles, dark matter, dark energy etc. are explained. New effects are predicted.
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In the socio-professional environment,the existence of values proves to be essential to the individual in order to live in harmony.It is by the search of oneself that you discover the world around you.Under this aspect,the philosophy of education can contribute to the conveyance of a decisive reflection on the impact of the educator’s mission on the people who are taught.On the one hand,the relativity of values puts into question their universal dimension,since they diversify in place and time according to different eras but also to different customs of each country.In this case,what is the finality of education and learning in relation to cultural diversification with regard to innovation in teaching?On the other hand,the educator’s personality plays a considerable and effective role in motivating his/her target group to seek out the higher and universal values and disseminate the principles of citizenship.Lastly,with regard to vocational training,the introduction of diversified pedagogical approaches as well as the adoption of learning strategies will enable the Educator to act in full knowledge and awareness of his action while being preoccupied in the management of the pedagogical process.His/her effective intervention will offer the opportunity to the group members to create synergies,in order to develop their unexploited potential and achieve a high level of awareness through the development of their personality.
文摘This paper briefly discusses existing problems with the theory of general relativity despite remarkable accuracy in most of its applications. The primary focus is on existing problems in the field of cosmology, particularly those pertaining to expectations of global cosmic space-time curvature in the absence of observational proof. The discussion centers on Krogdahl’s recent Lorentz-invariant flat space-time cosmology and its superiority to general relativity with respect to accounting for global cosmic space-time flatness and dark energy observations. The “cosmological constant problem” is briefly addressed as a problem for general relativity with respect to particle physics and quantum field theory. Finally, two very specific validation predictions in favor of Krogdahl’s flat space-time cosmology are made with respect to ongoing studies, including the dark energy survey (DES).
文摘Einstein general theory of relativity (GTR) accounted well for the precession of the perihelion of planets and binary pulsars. While the ordinary Newton law of gravitation failed, a generalized version yields similar results. We have shown here that these effects can be accounted for as due to the existence of gravitomagnetism only, and not necessarily due to the curvature of space time. Or alternatively, gravitomagnetism is equivalent to a curved space-time. The precession of the perihelion of planets and binary pulsars may be interpreted as due to the spin of the orbiting planet (m) about the Sun (M). The spin (S) of planets is found to be related to their orbital angular momentum (L) by a simple formula, viz., S (m/M)L.
文摘The theory of general relativity is related to the concept of curvature of space- time induced by the presence of the massive objects. We will see through this paper that the general relativity can be linked with linear Algebra and Vector Analysis without the need for concept of space-time. This is important for the unification of general relativity with quantum mechanics, gravity with electromagnetic, and a better understanding of the universe, gravity, black holes. The most important is the separation between the space-time and the big bang theory, which prove the existence of space-time before that, which leads to the existence of the creator of the universe.
文摘In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.
文摘Deriving an acceptable quantum field theory of gravitation from general relativity has eluded some of the best scientific thinkers. It is gradually becoming more apparent that general relativity’s classical assumptions are simply incompatible with quantum mechanics. For instance, simultaneous certainty of the location and momentum of any moving body, regardless of size, is a fundamental feature of general relativity. And yet, special relativity and quantum mechanics (thru Heisenberg’s uncertainty) reject the very notion of simultaneity. Since special relativity is already fully integrated into quantum field theory concerning the other forces of nature, were it possible to remove the confounding smoothly curved space-time fabric of general relativity and replace it in the form of a new and improved Lorentz-invariant (flat space-time) gravitational theory, final unification might well be achievable. This brief review paper further informs the reader as to why Krogdahl’s recent Lorentz-invariant relativity model of gravitation improves on general relativity, thus providing a deeper understanding of black holes, the cosmological flatness problem and dark energy. Most importantly, since the smoothly curved space-time of general relativity may well have been the road block to unification, Krogdahl’s flat space-time model is predicted to lead to an acceptable quantum theory of gravitation (i.e., “quantum gravity”) and unification (i.e., a so-called “theory of everything”).
