Minkowski applied Einstein's principle of relativity to moving media and developed electrodynamics of moving media. Like Einstein introduced the EM field-strength tensor $F^{μν}$ for electric field $\mathbf{E}$ and magnetic induction $\mathbf{B}$, Minkowski introduced another EM field-strength tensor $G^{μν}$ for the electric displacement $\mathbf{D}$ and magnetic field $\mathbf{H}$; thus leading to Minkowski tensor. Recently, Partanen and Tulkki criticize that Minkowski tensor contradicts special relativity, and proposed a mass-polariton stress-energy-momentum (MP SEM) tensor to replace Minkowski tensor. In this paper, based on a careful analysis of previous literature on this topic, (i) I reasonably argue that Minkowski tensor is a covariant combination of two EM field-strength tensors, and thus all the physical results obtained from Minkowski tensor are already embodied in the two EM field-strength tensors; (ii) I propose three rules for covariantly and self-consistently constructing the physical tensors in Einstein's special relativity, with Minkowski tensor following all the rules while both Abraham tensor and the MP SEM tensor not. Finally, by enumerating a specific example I show that the Lorentz covariance of a tensor provides no guarantee of the consistency of the tensor with the principle of relativity.
An unexpected Minkowskian solution of the equation of General Relativity (Einstein-1915) is trivial because it simply means that both members of the equation are equal to zero. However, if alternatively, one considers the complete equation with a non-zero (cosmological constant (Einstein-1917), a Minkowskian solution is no longer trivial because it amounts to impose a constraint on the right hand side of the equation (i.e. a non-null stress-energy tensor). If furthermore one identifies (as usual) this tensor to the one of a perfect fluid, one finds that this fluid has a positive energy density…
We are proving that the Lorentz boost entails the relative velocity to be ternary: ternary relative velocity is a velocity of a body with respect to an interior observer as seen by a preferred exterior-observer. The Lorentz boosts imply non-associative addition of ternary relative velocities. Within Einstein's special relativity theory, each preferred observer (fixed stars, aether, etc), determine the unique relative velocity among each pair of massive bodies. Therefore, the special relativity founded on Minkowski's axiom, that each pair of reference systems must be related by Lorentz isometry…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to convert a probabilistic theory to a geometric form to merge it with general theory of relativity. We explore the differential geometric formulation of Scalar Electrodynamics and Spinor Electrodynamics and its coupling to the gravitational field equation. Using Feynman-Gell-Mann equation (second order Dirac equation), the fermionic matter field is nicely inco…
We show that, in the framework of Deformed Special Relativity (DSR), namely a (four-dimensional) generalization of the (local) space-time struc- ture based on an energy-dependent "deformation" of the usual Minkowski geometry, two kinds of gauge symmetries arise, whose spaces either coin- cide with the deformed Minkowski space or are just internal spaces to it. This is why we named them "metric gauge theories". In the case of the internal gauge fields, they are a consequence of the deformed Minkowski space (DMS) possessing the structure of a generalized Lagrange space. Such a geometrical struct…
In this paper, a novel approach for resolution of the Abraham-Minkowski debate is proposed, in which the principle of relativity is used to uniquely determine the light momentum formulation for a plane wave in a moving non-dispersive lossless isotropic uniform medium. It is shown by analysis of the plane-wave solution that, (1) there may be a pseudo-power flow when a medium moves, and the Poynting vector does not necessarily denote the direction of real power flowing, (2) Minkowski's light momentum and energy constitute a Lorentz four-vector in a form of single photon or single EM-field cell, …
We investigate which are the independent equations of continuum electrodynamics and what is their number, beginning with the standard equations used in special and in general relativity. We check by using differential identities that there are as much independent equations as there are unknowns, for the case with given sources as well as for the general case where the motion of the charged medium producing the field is unknown. Then we study that problem in an alternative theory of gravity with a preferred reference frame, in order to constrain an additional, "interaction" energy tensor that h…
The transformation rules for the basic electrodynamical quantities are routinely derived from the hypothesis that the relativity principle (RP) applies for Maxwell's electrodynamics. These derivations leave open several questions: (1) Is the RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of electrodynamics in one single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of el…
The book is based largely on the author's researches presented at conferences in the period 1992 onwards. It is a historically based exposition and an extension of the hyperbolic version of special relativity first proposed by Varićak (1910 etc) and others not long after the appearance of the early papers of Einstein and Minkowski. The book's approach puts emphasis on the concept of hyperbolic velocity (scaled rapidity) and in this respect differs markedly from the gyro theory of Ungar. New formulations are given in optics relating hyperbolic velocity with logarithmic redshift and in dynamics …
Doubly special relativity(DSR) introduce a minimal length scale i.e. the Planck length scale, which is independent length scale in addition to the speed of light in the normal special theory of relativity(STR). Doubly special relativity leads to study the $κ$-Minkowski space-time. In this paper, we present the result of our investigation on the thermodynamics of photon gas in the $κ$-Minkowski space-time. For studying this, we start with the $κ$-deformed dispersion relation and keep terms upto first order in the deformation parameter $a$ and we study that how does $κ$-deformed dispersion relat…
Conventional relativistic electrodynamics is set on flat Minkowski spacetime, where all computable quantities are calculated from the flat metric $η_{μν}$. We can redefine the metric of spacetime from the Dirac algebra. In this paper, we study how an electrodynamic interaction can alter the normal gamma matrix to an effective one and result in a shift in the metric perturbatively. The curvature properties inferred from the curved metric are also investigated. We also study how the spin operator is changed under the interaction that contribute to an effective spin operator and how the spin of a…
I show that no force or torque is generated in cases involving a charge and a magnet with their relative velocity zero, in any inertial frame of reference. A recent suspicion of an anomalous torque and conflict with relativity in this case is rested. What is distilled as `Lorentz force' in standard electrodynamics, with relative velocity as the parameter, is an under-representation of two distinct physical phenomena, an effect due to Lorentz contraction and another due to the Ampere current-current interaction, rolled into one due to prejudice from special relativity applied only to linear mot…
We present a solution for the apparent paradox regarding an incompatibility between the Lorentz force law and special relativity presented by Mansuripur [Phys. Rev. Lett. 108, 193901 (2012)]. A connection between the apparent paradox and the Abraham-Minkowski debate about the momentum of electromagnetic waves in material media is also presented.
We show that Cosmological Constant (CC) is not optional in GR (General Relativity) because it is required by SR (Special Relativity). This completely unexpected result is obtained by introducing a minimal acceleration (Milgrom), square root of CC, in Einstein boost with Lorentz Transformation (LT). We prove that hyperbolic rotation (LT) is an hyperbolic motion with a centrifugal acceleration. In SR with CC (CSR or CR), the universe is not only in expansion (with the law of Hubble) but even in accelerated expansion (cosmological parameter is minus one). Given that the structure of space-time in…
