On Compatibility of Covariance to the Equivalence Principle and Space‐Time Coordinate Systems

1998 ◽  
Vol 11 (2) ◽  
pp. 264-272 ◽  
Author(s):  
C. Y. Lo
Keyword(s):  
Equivalence Principle ◽  
Space Time ◽  
Coordinate Systems ◽  
Time Coordinate

Electrodynamics in arbitrary space-time coordinate systems

1974 ◽  
Vol 17 (12) ◽  
pp. 1656-1660
Author(s):  
Ts. I. Gutsunaev ◽  
V. D. Kazachkov ◽  
Ya. P. Terletskli
Keyword(s):  
Space Time ◽  
Coordinate Systems ◽  
Time Coordinate ◽  
Arbitrary Space

The Equivalence Principle

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Time Dilation ◽  
Gravitational Redshift ◽  
Coordinate Systems ◽  
Spacetime Metric

The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

Sectional Curvature and Chaos in Dynamical Problems: Toward the Invariant Measure of Chaos in Hamiltonian Systems

1993 ◽  
Vol 46 (7) ◽  
pp. 427-437 ◽  
Author(s):  
Marek Szydłowski ◽  
Adam Krawiec
Keyword(s):  
General Relativity ◽  
Invariant Measure ◽  
Coordinate System ◽  
Sectional Curvature ◽  
Hamiltonian Systems ◽  
Invariant Theory ◽  
Space Time ◽  
Gauge Invariant ◽  
Time Coordinate ◽  
Physical Description

Chaotic phenomena in general relativity are investigated. In relativistic astrophysical problems no space-time coordinate system is privileged in any way as far as the physical description of phenomena is concerned. Effects which depend on the choice of the particular coordinate system should be treated as an artifact of the incorrect methods. To avoid such difficulties the gauge invariant theory of chaos is proposed.

Numerical construction of space-time

1979 ◽  
Vol 368 (1732) ◽  
pp. 15-16 ◽  
Keyword(s):  
Scalar Function ◽  
Space Time ◽  
Point Of View ◽  
Hamiltonian Approach ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Time Coordinate ◽  
Natural Approach ◽  
Spatial Coordinates ◽  
Practical Algorithm

Traditional analytic methods have not been powerful enough to solve for strongfield time-dependent solutions of the nonlinear Einstein field equations. For this reason, numerical solution of the equations seemed to be a natural approach. Building on the earlier work inspired by DeWitt & Misner, my colleagues and I have developed a practical algorithm for constructing space-times. The point of view is that space-time is decomposed into spacelike time slices and a congruence of curves threading these slices. The time coordinate is that scalar function which is constant on each time slice, while spatial coordinates are constant along the members of the congruence. The systematic 3+1 Hamiltonian approach was exhaustively studied by Arnowitt et al . (1962); the application to solution of the field equations was recently stressed by Smarr & York (1978 a, b ).

scholarly journals A fundamental special-relativistic theory valid for all real-valued speeds

1984 ◽  
Vol 7 (3) ◽  
pp. 565-589
Author(s):  
Vedprakash Sewjathan
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relativistic Theory ◽  
Equivalence Principle ◽  
Rest Mass ◽  
Space Time ◽  
Twin Paradox ◽  
Relativistic Factor ◽  
Time Frames ◽  
Time Transformations

This paper constitutes a fundamental rederivation of special relativity based on thec-invariance postulate but independent of the assumptionds′2=±ds2(Einstein [1], Kittel et al [2], Recami [3]), the equivalence principle, homogeneity of space-time, isotropy of space, group properties and linearity of space-time transformations or the coincidence of the origins of inertial space-time frames. The mathematical formalism is simpler than Einstein's [4] and Recami's [3]. Whilst Einstein's subluminal and Recami's superluminal theories are rederived in this paper by further assuming the equivalence principle and “mathematical inverses” [4,3], this paper derives (independent of these assumptions) with physico-mathematical motivation an alternate singularity-free special-relativistic theory which replaces Einstein's factor[1/(1−V2/c2)]12and Recami's extended-relativistic factor[1/(V2/c2−1)]12by[(1−(V2/c2)n)/(1−V2/c2)]12, wherenequals the value of(m(V)/m0)2as|V|→c. In this theory both Newton's and Einstein's subluminal theories are experimentally valid on account of negligible terms. This theory implies that non-zero rest mass luxons will not be detected as ordinary non-zero rest mass bradyons because of spatial collapse, and non-zero rest mass tachyons are undetectable because they exist in another cosmos, resulting in a supercosmos of matter, with the possibility of infinitely many such supercosmoses, all moving forward in time. Furthermore this theory is not based on any assumption giving rise to the twin paradox controversy. The paper concludes with a discussion of the implications of this theory for general relativity.

scholarly journals EXTENSION OF THE SHIRAFUJI MODEL FOR MASSIVE PARTICLES WITH SPIN

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4137-4160 ◽  
Author(s):  
SERGEY FEDORUK ◽  
ANDRZEJ FRYDRYSZAK ◽  
JERZY LUKIERSKI ◽  
CÈSAR MIQUEL-ESPANYA
Keyword(s):  
Electric Charge ◽  
Degrees Of Freedom ◽  
Twistor Space ◽  
Space Time ◽  
Particle Model ◽  
Intermediate Step ◽  
Time Coordinate ◽  
Massive Particles ◽  
Relativistic Particles ◽  
Primary Space

We extend the Shirafuji model for massless particles with primary space–time coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the space–time four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both space–time and four-momenta vectors are composite, and the standard particle model, where both space–time and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wave functions describing relativistic particles with mass, spin and electric charge. The space–time coordinates in the model are not commutative; this leads to a wave function that depends only on one covariant projection of the space–time four-vector (covariantized time coordinate) defining plane wave solutions.

scholarly journals Electrodynamics in Euclidean Space Time Geometries

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 731-742
Author(s):  
Jörn Schliewe
Keyword(s):  
Wave Propagation ◽  
Energy Transport ◽  
Poynting Vector ◽  
Empty Space ◽  
Space Time ◽  
Field Energy ◽  
Field Equations ◽  
Time Coordinate ◽  
Cartesian Space ◽  
Field Energy Density

Abstract In this article it is proven that Maxwell’s field equations are invariant for a real orthogonal Cartesian space time coordinate transformation if polarization and magnetization are assumed to be possible in empty space. Furthermore, it is shown that this approach allows wave propagation with finite field energy transport. To consider the presence of polarization and magnetization an alternative Poynting vector has been defined for which the divergence gives the correct change in field energy density.

A SUPERSPACE OF (1, 1/2)+(1/2, 1) FERMIONIC COORDINATES

1990 ◽  
Vol 05 (19) ◽  
pp. 3801-3809
Author(s):  
CHRISTOPHER PILOT ◽  
SUBHASH RAJPOOT
Keyword(s):  
Minkowski Space ◽  
Lorentz Group ◽  
Space Time ◽  
Time Coordinate ◽  
Covariant Derivatives ◽  
Minkowski Space Time

A superspace is constructed in which the elements of the superspace consist of the four Minkowski space-time coordinates and a set of vector-spinor coordinates that belong to the irreducible (1, 1/2)+(1/2, 1) representation of the Lorentz group. It is shown that a translation in the vector-spinor coordinates leads to a vector-spinor coordinate dependent translation in the space-time coordinate xμ. The super covariant derivatives are also constructed.

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