Extremely sensitive readout of a stable "etalon of length" is achieved with laser frequency-locking techniques. Rotation of the entire electro-optical system maps any cosmic directional anisotropy of space into a corresponding frequency variation. We found a fractional length change $\frac{\ensuremath{\Delta}l}{l}=(1.5\ifmmode\pm\else\textpm\fi{}2.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, with the expected ${P}_{2}(cos\ensuremath{\theta})$ signature. This null result represents a 4000-fold improvement on the best previous measurement of Jaseja et al.

Improved laser test of the isotropy of space

In this paper, we consider higher order correction of the entropy and study the thermodynamical properties of recently proposed Schwarzschild-Beltrami-de Sitter black hole, which is indeed an exact solution of Einstein equation with a positive cosmological constant. By using the corrected entropy and Hawking temperature we extract some thermodynamical quantities like Gibbs and Helmholtz free energies and heat capacity. We also investigate the first and second laws of thermodynamics. We find that presence of higher order corrections, which come from thermal fluctuations, may remove some instabilities of the black hole. Also unstable to stable phase transition is possible in presence of the first and second order corrections.

Thermodynamics of Higher Order Entropy Corrected Schwarzschild-Beltrami-de Sitter Black Hole

In this paper, we consider higher-order correction of the entropy and study the thermodynamical properties of recently proposed Schwarzschild–Beltrami–de Sitter black hole, which is indeed an exact...

Based on the relativistic principle and the postulate of universal invariant constants (c, l), all kinematic symmetries can be set up as the subsets of the Umov-Weyl-Fock-Hua transformations for the inertial motions. These symmetries are connected to each other via combinations rather than via contractions and deformations.

The principle of relativity, kinematics and algebraic relations

Like Euclid, Riemann and Lobachevski geometries are on an almost equal footing, based on the principle of relativity of maximum symmetry proposed by Professor Lu Qikeng and the postulate on invariant universal constants c and R, the de Sitter/anti-de Sitter (dS/AdS) special relativity on dS/AdS-space with radius R can be set up on an almost equal footing with Einstein’s special relativity on the Minkowski-space in the case of R→∞. Thus the dS-space is coin-like: a law of inertia in Beltrami atlas with Beltrami time simultaneity for the principle of relativity on one side, and the proper-time simultaneity and a Robertson-Walker-like dS-space with entropy and an accelerated expanding S
 3 fitting the cosmological principle on another side. If our universe is asymptotic to the Robertson-Walker-like dS-space of R ≃ (3/Λ)1/2, it should be slightly closed in O(Λ) with entropy bound S ≃ 3πc
 3
 k
 B
 /ΛGħ. Contrarily, via its asymptotic behavior, it can fix on Beltrami inertial frames without ‘an argument in a circle’ and acts as the origin of inertia. There is a triality of conformal extensions of three kinds of special relativity and their null physics on the projective boundary of a 5-d AdS-space, a null cone modulo projective equivalence [
 $$
\mathcal{N}
$$
 ] ≅ ∂
 P
 (AdS
 5). Thus there should be a dS-space on the boundary of S
 5 × AdS
 5 as a vacuum of supergravity. In the light of Einstein’s ‘Galilean regions’, gravity should be based on the localized principle of relativity of full maximum symmetry with a gauge-like dynamics. Thus, this may lead to the theory of gravity of corresponding local symmetry. A simple model of dS-gravity characterized by a dimensionless constant g ≃(ΛGħ/3c
 3)1/2 ∼ 10−61 shows the features on umbilical manifolds of local dS-invariance. Some gravitational effects out of general relativity may play a role as dark matter. The dark universe and its asymptotic behavior may already indicate that the dS special relativity and dS-gravity be the foundation of large scale physics.

Special relativity and theory of gravity via maximum symmetry and localization

Lagrangian of the Einstein's special relativity with universal parameter $c$ ($\mathcal{SR}_c$) is invariant under Poincar\'e transformation which preserves Lorentz metric $\eta_{\mu\nu}$. The $\mathcal{SR}_c$ has been extended to be one which is invariant under de Sitter transformation that preserves so called Beltrami metric $B_{\mu\nu}$. There are two universal parameters $c$ and $R$ in this Special Relativity (denote it as $\mathcal{SR}_{cR}$). The Lagrangian-Hamiltonian formulism of $\mathcal{SR}_{cR}$ is formulated in this paper. The canonic energy, canonic momenta, and 10 Noether charges corresponding to the space-time's de Sitter symmetry are derived. The canonical quantization of the mechanics for $\mathcal{SR}_{cR}$-free particle is performed. The physics related to it is discussed.

Hamiltonian Formalism of the de-Sitter Invariant Special Relativity

We explore the recent OPERA experiment of superluminal neutrinos in the framework of special relativity with de Sitter spacetime symmetry (dS-SR). According to Einstein, a photon is treated as a massless particle in the framework of special relativity. In special relativity (SR) we have the universal parameter c, the photon velocity cphoton and the phase velocity of a light wave in vacuum cwave = λν. Due to the null experiments of Michelson–Morley we have c = cwave. The parameter cphoton is determined by the Noether charges corresponding to the spacetime symmetries of SR. In Einstein's special relativity (E-SR) we have c = cphoton. In dS-SR, i.e. the special relativity with SO(4, 1) de Sitter spacetime symmetry, we have cphoton > c. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPERA anomaly is in agreement with the prediction of dS-SR with R≃1.95×1012 l.y. Based on the p-E relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.

http://inspirehep.net/record/946838/files/arXiv:1111.4532.pdf

Superluminal neutrinos from special relativity with de sitter spacetime symmetry

Under consideration of coordinate conditions, we get the Schwarzschild–Beltrami–de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant Λ. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a Λ) is presented. The Beltrami metric Bμν provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild–de Sitter (S-dS) metric existed in literatures since 1918, we find that the existed S-dS metric describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" M in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric . In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.

Schwarzschild–de sitter metric and inertial beltrami coordinates

The recent OPERA experiment of superluminal neutrinos has deep consequences in cosmology. In cosmology a fundamental constant is the cosmological constant. From observations one can estimate the effective cosmological constant Λeff which is the sum of the quantum zero point energy Λdark energy and the geometric cosmological constant Λ. The OPERA experiment can be applied to determine the geometric cosmological constant Λ. It is the first study to distinguish the contributions of Λ and Λdark energy from each other by experiment. The determination is based on an explanation of the OPERA experiment in the framework of Special Relativity with de Sitter spacetime symmetry.

On determination of the geometric cosmological constant from the opera experiment of superluminal neutrinos

We explore the recent OPERA experiment of superluminal neutrinos in the framework of Special Relativity with de Sitter space-time symmetry (dS-SR). According to Einstein a photon is treated as a massless particle in the framework of Special Relativity. In Special Relativity (SR) we have the universal parameter $c$, the photon velocity $c_{photon}$ and the phase velocity of a light wave in vacuum $c_{wave}=\lambda\nu$. Due to the null experiments of Michelson-Morley we have $c=c_{wave}$. The parameter $c_{photon}$ is determined by the Noether charges corresponding to the space-time symmetries of SR. In Einstein's Special Relativity (E-SR) we have $c=c_{photon}$. In dS-SR, i.e. the Special Relativity with SO(4,1) de Sitter space-time symmetry, we have $c_{photon}>c$. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPREA anomaly is in agreement with the prediction of dS-SR with $R\simeq 1.95\times 10^{12}l.y.$ Based on the $p$-$E$ relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.

Wei Huang

Papers

Hamiltonian Formalism of the de-Sitter Invariant Special Relativity

Superluminal neutrinos from special relativity with de sitter spacetime symmetry

Schwarzschild–de sitter metric and inertial beltrami coordinates

On determination of the geometric cosmological constant from the opera experiment of superluminal neutrinos

Superluminal Neutrinos from Special Relativity with de Sitter Space-time Symmetry