scholarly journals A note on ‘Einstein's special relativity beyond the speed of light by James M. Hill and Barry J. Cox’

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120672 ◽  
Author(s):  
Hajnal Andréka ◽  
Judit X. Madarász ◽  
István Németi ◽  
Gergely Székely
Keyword(s):  
Special Relativity ◽  
Space Time ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Principle Of Relativity ◽  
Faster Than Light

We show that the transformations Hill and Cox introduce, between inertial observers moving faster than light with respect to each other, are consistent with Einstein's principle of relativity only if the space–time is two dimensional.

scholarly journals Symmetry and Special Relativity

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1235 ◽  
Author(s):  
Yaakov Friedman ◽  
Tzvi Scarr
Keyword(s):  
Charged Particle ◽  
Special Relativity ◽  
Symmetric Domain ◽  
Analytic Solutions ◽  
Bounded Symmetric Domain ◽  
Speed Of Light ◽  
Conformal Maps ◽  
Principle Of Relativity ◽  
Electric And Magnetic Fields ◽  
Inertial Frames

We explore the role of symmetry in the theory of Special Relativity. Using the symmetry of the principle of relativity and eliminating the Galilean transformations, we obtain a universally preserved speed and an invariant metric, without assuming the constancy of the speed of light. We also obtain the spacetime transformations between inertial frames depending on this speed. From experimental evidence, this universally preserved speed is c, the speed of light, and the transformations are the usual Lorentz transformations. The ball of relativistically admissible velocities is a bounded symmetric domain with respect to the group of affine automorphisms. The generators of velocity addition lead to a relativistic dynamics equation. To obtain explicit solutions for the important case of the motion of a charged particle in constant, uniform, and perpendicular electric and magnetic fields, one can take advantage of an additional symmetry—the symmetric velocities. The corresponding bounded domain is symmetric with respect to the conformal maps. This leads to explicit analytic solutions for the motion of the charged particle.

scholarly journals One Observer Universe: A Geometric Interpretation of Speed of Light and Mass

2020 ◽  
Author(s):  
Ahmed Farag Ali
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Geometric Interpretation ◽  
Space Time ◽  
Red Shift ◽  
General Covariance ◽  
Speed Of Light ◽  
The Universe

In this paper, we investigate how Rindler observer measures the universe in the ADM formalism. We compute his measurements in each slice of the space-time in terms of gravitational red-shift which is a property of general covariance. In this way, we found special relativity preferred frames to match with the general relativity Rindler frame in ADM formalism. This may resolve the widely known incompatibility between special relativity and general relativity on how each theory sees the red-shift. We found a geometric interpretation of the speed of light and mass.

scholarly journals Special relativity: Interpretation and implications for space-time geometry

2005 ◽  
Vol 219 (2) ◽  
pp. 133-146 ◽  
Author(s):  
H Rahnejat
Keyword(s):  
Special Relativity ◽  
Light Cone ◽  
Small Variation ◽  
Special Theory ◽  
Space Time ◽  
Matter Field ◽  
Theory Of Relativity ◽  
Speed Of Light ◽  
Calculus Of Variation ◽  
Definition Of

The paper commemorates the centenary of the special theory of relativity, which effectively sets the limit for the structure of space-time to that of the stationary system. The long lasting debate for definition of concepts of instantaneity and simultaneity was thus resolved by the declaration of constancy of speed of light in vacuo as a law of physics. All motions were thus bounded by the light cone and described by the properties of differential geometry, firmly anchored in the calculus of variations. The key contribution underpinning the theory was the resolution of the contradiction imposed by the Galilean transformation through physical explanation and the adoption of the Lorentzian transformation. This highlighted the relative nature of both space and time and the linkage of these to preserve the sanctity of the light cone. The resulting space-time geometry was then founded on the traditional calculus of variation with the addition of this transformation. This retains the time as an independent coordinate and its linkage to space in an explicit form. One implication of this approach has been the retention of the concept of infinitum for some physical quantities as a drawback for use of the Lorentzian transformation. The paper shows that this singular behaviour need not arise if the explicit linkage in space-time is abandoned in favour of the implicit inclusion of time as a link between the curved structure of space and the speed of light, thus restating the calculus of variation in line with special relativity. This points to a closed loop space-matter field, which may belie the fabric of the continuum. One implication of this interpretation is that a small variation in speed of light within the field would be required to dispense with the aforementioned singular nature of the Lorentzian boost, while still remaining within the spirit of special relativity.

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

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
J. A. S. Lima ◽  
Fernando D. Sasse
Keyword(s):  
Special Relativity ◽  
Maxwell Equations ◽  
Relativity Theory ◽  
Lorentz Transformations ◽  
Speed Of Light ◽  
Principle Of Relativity ◽  
General Coordinate Transformation ◽  
Special Relativity Theory ◽  
Lorentzian Form ◽  
Morley Experiment

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.

Comment on “Generalization of Einstein’s synchronization for the case of anisotropic light speed”1Appears in Can. J. Phys. 87, 969.

2012 ◽  
Vol 90 (2) ◽  
pp. 207-210 ◽  
Author(s):  
Alon Drory
Keyword(s):  
Special Relativity ◽  
Recent Article ◽  
Speed Of Light ◽  
Light Speed ◽  
Principle Of Relativity ◽  
Frame Invariance ◽  
Anisotropic Light Speed

In a recent article, A. Sfarti attempted to derive the frame-invariance of the speed of light from the principle of relativity, thereby eliminating the second postulate from the foundations of special relativity (Can. J. Phys. 87, 969 (2009)). I analyse his derivation and conclude that it is incorrect.

Derivation of special relativity from Maxwell and Newton

2008 ◽  
Vol 366 (1871) ◽  
pp. 1861-1865 ◽  
Author(s):  
D.J Dunstan
Keyword(s):  
Special Relativity ◽  
Experimental Work ◽  
Displacement Current ◽  
Lorentz Transformations ◽  
Speed Of Light ◽  
Principle Of Relativity ◽  
Propagation Of Light ◽  
Newton’S Laws ◽  
Laws Of Motion

Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the − c −2 term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

Special relativity and the Lorentz sphere

2020 ◽  
Vol 33 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Stephen J. Crothers
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Spherical Wave ◽  
Special Theory ◽  
Inertial System ◽  
Rectilinear Motion ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Principle Of Relativity

The special theory of relativity demands, by Einstein's two postulates (i) the principle of relativity and (ii) the constancy of the speed of light in vacuum, that a spherical wave of light in one inertial system transforms, via the Lorentz transformation, into a spherical wave of light (the Lorentz sphere) in another inertial system when the systems are in constant relative rectilinear motion. However, the Lorentz transformation in fact transforms a spherical wave of light into a translated ellipsoidal wave of light even though the speed of light in vacuum is invariant. The special theory of relativity is logically inconsistent and therefore invalid.

scholarly journals Relationship Between Conical Perspective, Hyperbolic Curves, and Hyperbolic Medicine

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Jesús M. González-González
Keyword(s):  
Human Physiology ◽  
Three Dimensional ◽  
Space Time ◽  
Point Of View ◽  
Human Vision ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Parallel Lines ◽  
The One ◽  
Living Being

Perspective” is the art of representing objects in such a way that they are visualized from the observer’s point of view. Using this technique, a three-dimensional (3D) world is projected onto a two-dimensional (2D) Surface. “Conical perspective” is the one that interests us in hyperbolic medicine since it is the one that most closely approximates the reality we see. We call “hyperbolic medicine” (abbreviated “Medipérbola”) to the study of hyperbolic curves that occur in the physiology of a living being, especially in humans, about other hyperbolic curves that may be in nature, such as electromagnetic fields, expansion-contraction systems in motion, circadian rhythms, and space-time relativity. We think that when we observe an object, the conical perspective of that image is not parallel lines that converge at a point, but hyperbolic curves of space-time, and the hyperbolic curves that occur in human physiology would be related to them. The relationships between conic perspective, hyperbolic curves of space-time, and hyperbolic curves of human physiology have been studied. Conclusions: 1. Conic perspective represents images that travel at the speed of light to the eye of the observer, following hyperbolic curves of space-time. 2. Human vision is hyperbolic because the space in which we live is deformed by “hyperbolic curves”, which exist in any longitude and latitude of the earth’s geography. 3. Human physiology can be conditioned by these hyperbolic curves, to adapt to this hyperbolic deformation of the space in which we live.

scholarly journals BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

scholarly journals Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

2021 ◽  
Vol 11 (8) ◽  
pp. 3421
Author(s):  
Cheng-Yu Ku ◽  
Li-Dan Hong ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Wei-Po Huang
Keyword(s):  
Porous Media ◽  
Time Domain ◽  
Numerical Solutions ◽  
Space Time ◽  
Two Dimensional ◽  
Transient Flows ◽  
Layered Porous Media ◽  
Time Marching ◽  
Time Basis ◽  
Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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