Einstein’s General Relativity and Pure Gravity in a Cosserat and De Sitter-Witten Spacetime Setting as the Explanation of Dark Energy and Cosmic Accelerated Expansion

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.

Entanglement of E8E8 Exceptional Lie Symmetry Group Dark Energy, Einstein’s Maximal Total Energy and the Hartle-Hawking No Boundary Proposal as the Explanation for Dark Energy

The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.

Negative Norms in Quantized Strings as Dark Energy Density of the Cosmos

The present short paper is concerned with accurate explanation as well as quantification of the so called missing dark energy of the cosmos. It was always one of the main objectives of any successful general theory of high energy particle physics and quantum cosmology to keep non-physical negative norms, the so called ghosts completely out of that theory. The present work takes the completely contrary view by admitting these supposedly spurious states as part of the physical Hilbert space. It is further shown that rethinking the ghost free condition with the two critical spacetime dimensions D1 = 26 and D2 = 25 together with the corresponding intercept a1 = 1 and a2 ≤ 1 respectively and in addition imposing, as in Gross et al. heterotic superstrings, an overall 496 dimensional exceptional Lie symmetry group, then one will discover that there are two distinct types of energy. The first is positive norm ordinary energy connected to the zero set quantum particles which is very close to the measured ordinary energy density of the cosmos, namely E(O) = mc2/22. The second is negative norm (i.e. ghost) energy connected to the empty set quantum wave and is equal to the conjectured dark energy density of the cosmos E(D) = mc2 (21/22) presumed to be behind the observed accelerated cosmic expansion. That way we were able to not only explain the physics of dark energy without adding any new concepts or novel additional ingredients but also we were able to compute the dark energy density accurately and in full agreement with measurements and observations.

The Speed of the Passing of Time as Yet Another Facet of Cosmic Dark Energy

The topological speed of light which may be used to compute the density of ordinary energy and dark energy of the cosmos is replaced by dimensionless quantity taken from Special Relativity. The said quantity may be interpreted as akin to time dilation ergo a notion topologically equivalent to the speed of the passing of time or the difference of elapsed time between two events in Einstein’s Relativity Theory. This results via Newton’s kinetic energy into the well-known observationally confirmed and accurately measured 4.5 and 95.5 percent of ordinary and dark Cosmic Energy density respectively.

Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography

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.

Computing Dark Energy and Ordinary Energy of the Cosmos as a Double Eigenvalue Problem

We compute the dark energy and ordinary energy density of the cosmos as a double Eigenvalue problem. In addition, we validate the result using two different theories. The first theory is based on Witten’s 11 dimensional spacetime and the second is based on ‘tHooft’s fractal renormalization spacetime. In all cases, the robust result is E(O) = mc2/22 for ordinary energy and E(D) = mc2(21/22) for dark energy. Adding E(O) to E(D) we obtain Einstein’s famous equation which confirms special relativity, although it adds a quantum twist to its interpretation. This new interpretation is vital because it brings relativity theory in line with modern cosmological measurements and observations. In particular, we replace calculus by Weyl scaling in all computation which is essentially transfinite discrete.

Relativistic Derivations of de Broglie and Planck-Einstein Equations

Special Relativity sets tight constraints on the form of the possible relations between the four-momentum of a particle and the wave four-vector. In fact, we demonstrate that there is just one way, according to Special Relativity, to relate the energy and the momentum of a corpuscle with the characteristics of a plane wave, frequency and wave vector, if the momentum has to flow in the same direction of the wave propagation: the laws must be of direct proportionality like de Broglie and Planck-Einstein equations.

A Combined Heterotic String and Kähler Manifold Elucidation of Ordinary Energy,Dark Matter,Olbers’s Paradox and Pure Dark Energy Density of the Cosmos

We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.

Deviation of light path in Born-Infeld type gravitational field

The discovery of ＂twin quasi-stellar objects＂ arose interests among astronomers and astrophysicists to study gravitational leasing problem. Deviation of light from straight path is caused by the presence of massive objects, i.e., the presence of gravitational field according to the general theory of relativity. It is shown that the low energy effective field theory on D-branes is of the Born-Infeld type. In this work a Born-Infeld type gravitational field is pasttflated. An explicit representation of the angular deviation of light path is derived based on the space time metric in the Born-Infeld theory.

LIGO的O1/O2引力波事件对Einstein-aether理论限制能力探讨

广义相对论是继牛顿万有引力理论后,在强引力场、强动态时空区域更精准的引力理论,大量的天文观测验证了广义相对论的正确性。但广义相对论与量子理论在逻辑体系上不相容,广义相对论还存在时空奇点的理论问题,宇宙学中还存在暗物质和暗能量的引力本质问题等。在使用Yunes等人提出的Einstein-aether理论修改引力波模板的基础上,用Fisher Matrix的参数估计法,探讨了几个典型双星系统对修改引力模板的参数估计所能达到的参数估计精度,以及LIGO和VIRGO已经发现的11个双星并合事件应对修改引力的限制能力;最后,使用匹配因子的方法,探讨修改引力的参数对引力波模板的影响。如果Einstein-aether理论只是微小修正广义相对论引力波波形,11个双星引力波事件可以对Einstein-aether理论的3个参数给出限制;如果Einstein-aether理论波形与广义相对论引力波波形存在明显偏离,对Einstein-aether理论的检验需要更仔细的引力波波形研究和数据分析。

A Potentially Unifying Constant of Nature (Brief Note)

This brief note describes a method by which numerous empirically-determined quantum constants of nature can be substituted into Einstein’s field equation (EFE) for general relativity. This method involves treating the ratio G/ћ as an empirical constant of nature in its own right. This ratio is repre- sented by a new symbol, NT. It turns out that the value of NT (which is 6.32891937 × 1023 m⋅kg-2⋅s-1) is within 5% of Avogadro’s number NA, although the units are clearly different. Nevertheless, substitutions of NT or NA into the EFE, as shown, should yield an absolute value similar in magnitude to that calculated by the conventional EFE. The method described allows for quantum term EFE substitutions into Einstein’s gravitational constant κ. These terms include ћ, α, me, mp, R, kB, F, e, MU, and mU. More importantly, perhaps, one or more of the many new expressions given for κ may provide a more accurate result than κ incorporating G. If so, this may have important implications for additional forward progress towards unification. Whether any of these new expressions for Einstein’s field equation can move us closer to quantizing gravity remains to be determined.

Airy, Beltrami, Maxwell, Einstein and Lanczos Potentials Revisited

The purpose of this paper is to revisit the well known potentials, also called stress functions, needed in order to study the parametrizations of the stress equations, respectively provided by G.B. Airy (1863) for 2-dimensional elasticity, then by E. Beltrami (1892), J.C. Maxwell (1870) for 3-dimensional elasticity, finally by A. Einstein (1915) for 4-dimensional elasticity, both with a variational procedure introduced by C. Lanczos (1949, 1962) in order to relate potentials to Lagrange multipliers. Using the methods of Algebraic Analysis, namely mixing differential geometry with homological algebra and combining the double duality test involved with the Spencer cohomology, we shall be able to extend these results to an arbitrary situation with an arbitrary dimension n. We shall also explain why double duality is perfectly adapted to variational calculus with differential constraints as a way to eliminate the corresponding Lagrange multipliers. For example, the canonical parametrization of the stress equations is just described by the formal adjoint of the components of the linearized Riemann tensor considered as a linear second order differential operator but the minimum number of potentials needed is equal to for any minimal parametrization, the Einstein parametrization being “in between” with potentials. We provide all the above results without even using indices for writing down explicit formulas in the way it is done in any textbook today, but it could be strictly impossible to obtain them without using the above methods. We also revisit the possibility (Maxwell equations of electromagnetism) or the impossibility (Einstein equations of gravitation) to obtain canonical or minimal parametrizations for various equations of physics. It is nevertheless important to notice that, when n and the algorithms presented are known, most of the calculations can be achieved by using computers for the corresponding symbolic computations. Finally, though the paper is mathematically oriented as it aims providing new insights towards the mathematical foundations of general relativity, it is written in a rather self-contained way.

Wave-Particle Duality in Einstein-de Broglie Programs

The standard model of particle physics forms a consistent system for universe description. After following quantum mechanics, it derives particles from relativistic quantum fields. Since it does not include gravitation, it describes only one aspect of the universe. In extension of general relativity, Einstein had proposed a symmetrical and complementary approach of physics. In his program, he privileged a relativist field based on representations for physical phenomena, before a precise mathematical description. It allows completing and unifying the universe description, like both eyes for relief vision, and both ears for stereophonic audition. We propose to show it with many simple examples.

从“间隔疏离”到“互动亲近”——基于相对剥夺理论的研究生教学模式优化研究

研究生的心理因素会直接影响师生关系和教育质量,通过引入相对剥夺感理论能够有效阐释教学过程中研究生不健康心理的产生与解决对策。基于此,本文首先分析了研究生相对剥夺感的产生过程和危害,提出了优化传统教学模式、构建新型师生教学关系的必要性;其次指出教师在研究生教育中应当以研究生为主体,实现教学思想和教学行为的转变,同时做到分配公正、关注公正和承认公正;最后提出推进教师意识、课程评价、教师评价和教师队伍等一系列改革措施,实现师生教学关系由“间隔疏离”变为“互动亲近”。

从狭义相对论看爱因斯坦的科学思想、研究方法及哲学思想

爱因斯坦创立的狭义相对论,宣告了现代时空观的到来。论文深入地发掘了狭义相对论体现的统一性科学思想、逻辑思辨与探索性演绎研究方法、唯物的辩证自然观哲学思想,揭示了产生这项带给人类科学创见、思想革命、精神解放的理智的自由发明的真正原因。借以领受人类智慧的洗礼,传承人类知性的火种,捍卫宇宙法则的尊严。

狭义相对论矛盾方程探讨

研究洛伦兹变换关系式与狭义相对论的关系,采用2种不同的方法分别揭示在狭义相对论中存在的矛盾方程.第1种方法是将坐标系S原点O和坐标系S′原点O′对应的参数值分别代入洛伦兹变换关系式x′=γ(x-vt)和x=γ(x′+vt′)中,得到矛盾方程;第2种方法是采用狭义相对论的结论"动钟变慢"的推导过程进一步重新推导,得到矛盾方程,从而证明狭义相对论在逻辑上是值得商榷的.

从引力波谈爱因斯坦的幸运

在引力波被直接探测之际,从独特的视角回顾了爱因斯坦创立广义相对论、预言引力波、引进宇宙学常数的历程,也介绍分析了他的若干论文的发表情况,从而将爱因斯坦的若干科学事件有机地融合起来。

爱因斯坦的科学美学思想探析

通过对爱因斯坦的“宇宙宗教观”、相对论体系和科学方法论中所蕴含的科学美学思想之探析 ,揭示爱因斯坦的这一往往被人们所忽视的思想 ,是一笔极其丰富的科学哲学遗产 ,应该予以继承和光大。

爱因斯坦相对论诞生之初的失误

近光速的宇宙航行需要遵循相对论力学。然而,作者发现爱因斯坦1905年创立相对论的第一篇论文有误:他的代数运算失误,他运用"光源-光线-反射镜"模型也有误。正确的运算和运用这个模型得到的应该是普适的同时性。

科学思维方式的一场革命——爱因斯坦狭义相对论思想解读

狭义相对论首次把观察者引进物理学,认为与人无关的、绝对不变的自然界是不存在的,科学研究的一切成果和结论都与观察者有关,观察者本身、观察角度、观察方法等都是理论结论不可缺少的重要因素,从而实现了科学思维方式上的一场革命。狭义相对论深刻揭示了物质及其运动与时间、空间之间的内在统一性,揭示了主体与客体之间的相互作用,从根本上否定了牛顿的绝对时空观,宣布了传统绝对主义和纯粹客观主义思维方式的终结,确立了绝对与相对相统一、主观与客观相统一的辩证思维观。