Further useful ideas

2021 ◽  
pp. 133-143
Author(s):  
Andrew M. Steane
Keyword(s):  
Inertial Frame ◽  
Antisymmetric Tensor ◽  
Divergence Theorem ◽  
Local Inertial Frame ◽  
Gauss Divergence Theorem ◽  
And Mathematics ◽  
Energy And Momentum ◽  
Covariant Version

The chapter discusses several further aspects of the physics and mathematics that prove very useful in practice. First we define 4-velocity, 4-momentum and 4-acceleration. Then we introduce the tetrad and show how it can be used to relate a given 4-momentum to the energy and momentum observed in a LIF (local inertial frame). Then we define covariant version of the vector operators div, grad, curl, and obtain simplified expressions for the divergence of a vector and an antisymmetric tensor. The generalized Gauss divergence theorem is then presented.

Terminology and notation

2021 ◽  
pp. 1-8
Author(s):  
Andrew M. Steane
Keyword(s):  
Inertial Frame ◽  
Normal Coordinates ◽  
Local Inertial Frame ◽  
Index Notation

Notation and sign conventions adopted for the rest of the book are explained. The book employs index notation, but not abstract index notation. The metric signature for GR is taken as (-1,1,1,1). Terminology such as “local inertial frame” and “Rieman normal coordinates” is explained.

scholarly journals Relativistic Reference Frames in Astrometry

1986 ◽  
Vol 7 ◽  
pp. 101-102
Author(s):  
C A Murray
Keyword(s):  
Coordinate System ◽  
Reference Frames ◽  
Inertial Frame ◽  
Space Time ◽  
Clock Time ◽  
Local Inertial Frame ◽  
Incoming Photon ◽  
Inertial Frames ◽  
Spatial Coordinates

Astrometry can be defined as the measurement of space-time coordinates of photon events. For example, in principle, in classical optical astrometry, we measure the components of velocity, and hence the direction, of an incoming photon with respect to an instrumental coordinate system, and the clock time, at the instant of detection. The observer’s coordinate system at any instant can be identified with a local inertial frame. In the case of interferometric observations, the measurements are of clock times of arrival of a wavefront at two detectors whose spatial coordinates are specified with respect to instantaneous inertial frames.

Mach’s principle and the creation of matter

1963 ◽  
Vol 273 (1352) ◽  
pp. 1-11 ◽  
Keyword(s):  
Inertial Frame ◽  
Relativity Theory ◽  
Mach's Principle ◽  
Mach’S Principle ◽  
Local Inertial Frame ◽  
Continuous Creation ◽  
Remarkable Degree ◽  
The One ◽  
Creation Of Matter ◽  
The Universe

Accurate experiments have shown that the local inertial frame is the one with respect to which the distant parts of the universe are non-rotating. This coincidence, first noticed by Newton, later led to the formulation of Mach’s principle. It is known that relativity theory by itself cannot explain this coincidence. The introduction of a scalar ‘creation field’ into the theory is likely to improve the situation. Calculation shows that the continuous creation of matter has the effect of smoothing out any irregularities in the universe as it expands, while rotation, if present, becomes less and less. This explains the observed remarkable degree of homogeneity and isotropy in the universe.

GEOMETRODYNAMIC STEERING PRINCIPLE REVEALS THE DETERMINERS OF INERTIA

1988 ◽  
Vol 03 (10) ◽  
pp. 2207-2247 ◽  
Author(s):  
JOHN ARCHIBALD WHEELER
Keyword(s):  
Inertial Frame ◽  
Newtonian Potential ◽  
Mass Energy ◽  
Simple Sentence ◽  
Initial Value ◽  
Physical Content ◽  
The Earth ◽  
Distance Vector ◽  
Lageos Satellite ◽  
And Mathematics

What shall we need to grasp the essence of quantum gravity? One requirement, at least, is essential: to understand the steering principle of classical geometrodynamics. We outline here the physical content of that steering principle—heart of the so-called initial value problem—in its J.W. York, Jr. formulation. The central idea epitomizes itself in a single simple sentence: Mass-energy there determines inertia here. We spell out this steering principle both in its precise form and in its poor man’s version. At both levels of analysis considerations of physics and mathematics alike require that the effective mass-energy of gravity waves must make itself felt on the space-time geometry—and therefore on the gyro-defined local inertial frame of reference—on the same level as matter itself. Additional to the (mass)/(distance) Newtonian potential so familiar as measure of the effect of a nearby mass on the local frame is the Thirring and Lense gravitomagnetic potential, proportional to (angular momentum)×(distance vector)/(distance)3. The recent proposal of Ciufolini for a dual laser-ranged LAGEOS satellite to detect the thus-predicted gravitomagnetism of the earth is briefly described.

scholarly journals Realization of the Local Inertial Geocentric Frame in Relativity

1990 ◽  
Vol 141 ◽  
pp. 430-430
Author(s):  
He Miao-Fu ◽  
Huang Cheng
Keyword(s):  
Solar System ◽  
Inertial Frame ◽  
The Sun ◽  
Gravitational Effects ◽  
Local Inertial Frame ◽  
Relativistic Corrections ◽  
Tidal Forces ◽  
The Earth

There are two kinds of geocentric frames: local inertial and non-inertial geocentric frames. Ashby et al successfully constructed a local inertial geocentric frame in the neighborhood of the gravitating Earth. In the frame with origin at the Earth's center, the gravitational effects of the sun and of planets other than the Earth are basically reduced to their tidal forces, with very small relativistic corrections.However, the spatial base vectors of the local inertial frame essentially experience the geodesic (or deSitter) precession with respect to the solar system barycentric frame. Hence the realization of the local inertial frame requires that the general precession should exclude the geodesic precession. This requirement is inconsistent with the convention that the amount of geodesic precession is included in that of the general precession given by Lieske et al.

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