Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of (3 + 1)-dimensional quantum electrodynamics; the system endowed with a magnetic one-form symmetry. The conservation laws and constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for a thermodynamic functional enables us to obtain exact forms of constitutive relations. Applying the derivative expansion to exact formulas, we derive the first-order constitutive relations for nonlinear relativistic magnetohydrodynamics. Our results for the QED plasma preserving parity and charge-conjugation symmetries are equipped with two electrical resistivities and five (three bulk and two shear) viscosities. We also show that those transport coefficients satisfy the Onsager’s reciprocal relation and a set of inequalities, indicating semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.

A new Lorentz violating model with particle’s "maximum energy"

In this paper we re-investigated the relationship between the symmetry of inertial systems and the Lorentz transformation. We found that when we just follow the following three principles: (1)we can define the time in the whole space with a prescribed clock synchronization, (2)the time-space is uniform and the space is isotropic and (3)all the inertial systems are equivalent, then we can totally construct a general coordinate transformation to meet the symmetry of inertial systems, and with a special assumption on the speed of light, we can construct a non-Lorentz transformation between inertial systems to make the particle’s energy have a limited value, which is similar to the rainbow model.Similar to the usual Lorentz violating models, the non-Lorentz transformation in this paper lead to a new modified disperse relation. We applied the obtained disperse relation to analyze the photon’s arrival time lag effect in astronomy and found that the "maximum energy" derived in our model is somewhat related to the "maximum energy" assumed in the rainbow model.

A New Lorentz Violating Model with Particle’s "Maximum Energy"

In this paper we re-investigated the relationship between the symmetry of inertial systems and the Lorentz transformation. We found that when we just follow the following three principles: (1)we can define the time in the whole space with a prescribed clock synchronization, (2)the time-space is uniform and the space is isotropic and (3)all the inertial systems are equivalent, then we can totally construct a general coordinate transformation to meet the symmetry of inertial systems, and with a special assumption on the speed of light, we can construct a non-Lorentz transformation between inertial systems to make the particle’s energy have a limited value, which is similar to the rainbow model. Similar to the usual Lorentz violating models, the non-Lorentz transformation in this paper lead to a new modified disperse relation. We applied the obtained disperse relation to analyze the photon’s arrival time lag effect in astronomy and found that the "maximum energy" derived in our model is somewhat related to the "maximum energy" assumed in the rainbow model.

A New Lorentz Violating Model with Particle’s "Maximum Energy"

In Lorentz violating models, the rainbow model or theories of Quantum Gravity are usually discussed, and a common feature of these models is that they assume the particle’s energy have a limited value rather than be infinite derived from the Lorentz model. The introduction of "maximum energy" is considered to be necessary in the combination of Quantum theory and Gravity. However, this paper shows that if we just follow the next three principles: (1)we can define the time in the whole space with a prescribed clock synchronization, (2)the time-space is uniform and the space is isotropic and (3)all the inertial systems are equivalent, then we can totally construct a general coordinate transformation to meet the symmetry of inertial systems, and with a special assumption on the speed of light, we can also construct a non-Lorentz transformation between inertial systems to make the particle’s energy have a limited value. Similar to the usual Lorentz violating models, the non-Lorentz transformation in this paper lead to a new modified disperse relation. We applied the obtained disperse relation to analyze the photon’s arrival time lag effect and found that the "maximum energy" derived in our model is somewhat related to the "maximum energy" assumed in the rainbow model.

Can Lorentz transformations be determined by the null Michelson-Morley result?

The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of the Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.

Construction of energy–momentum tensor of gravitation

We construct the gravitational energy–momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy–momentum conservation is satisfied because one of the two indices of the energy–momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.

FOUR-VECTOR VERSUS FOUR-SCALAR REPRESENTATION OF THE DIRAC WAVE FUNCTION

In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincaré group. This is not an option in a curved spacetime. Therefore, in the equation proposed independently by Fock and Weyl, the four complex components of the Dirac wave function transform as scalars under a general coordinate transformation. Recent work has shown that a covariant complex four-vector representation is also possible. Using notions of vector bundle theory, we describe these two representations in a unified framework. We prove theorems that relate together the different representations and the different choices of connections within each representation. As a result, either of the two representations can account for a variety of inequivalent, linear, covariant Dirac equations in a curved spacetime that reduce to the original Dirac equation in a Minkowski spacetime. In particular, we show that the standard Dirac equation in a curved spacetime, with any choice of the tetrad field, is equivalent to a particular realization of the covariant Dirac equation for a complex four-vector wave function.

Study of Large Scale Measurement Method Based on Leapfrog Principle

At present，large scale and space coordinates measuring system with wide-range and high-precision has been widely used in modern manufacturing industry. In this paper, large scale measuring method based on leapfrog principle of flexible three coordinate measuring machine is described. The mathematical model of coordinate transformation is built and the general coordinate transformation formula after number of times leapfrogging is derived. The best positioning and each step of leapfrog are given.