Classical equation of motion of a spinning non-Abelian test body in general relativity

1982 ◽  
Vol 26 (2) ◽  
pp. 523-526 ◽  
Author(s):  
H. J. Wospakrik
Keyword(s):  
General Relativity ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Test Body

scholarly journals Kerr–Sen–Taub–NUT spacetime and circular geodesics

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Haryanto M. Siahaan
Keyword(s):  
String Theory ◽  
Equatorial Plane ◽  
Jacobi Equation ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Test Body ◽  
Low Energy ◽  
Energy Limit ◽  
Heterotic String Theory ◽  
Hamilton Jacobi Equation

AbstractWe present a solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed, and the separability of Hamilton–Jacobi equation for a test body in the spacetime is also investigated. Some numerical results related to the circular motions on equatorial plane are presented, but there is none that supports the existence of such geodesics.

Coherent states, Schrödinger equation, and the Hamilton–Jacobi equation

1995 ◽  
Vol 73 (7-8) ◽  
pp. 478-483
Author(s):  
Rachad M. Shoucri
Keyword(s):  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hidden Variables ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Phase Variable ◽  
Independent Variable ◽  
Hamilton Jacobi Equation

The self-adjoint form of the classical equation of motion of the harmonic oscillator is used to derive a Hamiltonian-like equation and the Schrödinger equation in quantum mechanics. A phase variable ϕ(t) instead of time t is used as an independent variable. It is shown that the Hamilton–Jacobi solution in this case is identical with the solution obtained from the Schrödinger equation without the need to introduce the idea of hidden variables or quantum potential.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

A Covariant Semi-Classical Theory of the Radiating Electron

1977 ◽  
Vol 32 (1) ◽  
pp. 101-102
Author(s):  
M. Sorg
Keyword(s):  
Classical Theory ◽  
Characteristic Length ◽  
Order Approximation ◽  
Classical Equation ◽  
Radiation Reaction ◽  
Equation Of Motion ◽  
Compton Wavelength ◽  
Classical Electron ◽  
Electron Radius ◽  
Classical Electron Radius

Abstract A new semi-classical equation of motion is suggested for the radiating electron. The characteristic length of the new theory is the Compton wavelength λc(= ħ/2 m c) instead of the classical electron radius which is used in all purely classical theories of the radiating electron. However, the lowest order approximation of the radiation reaction contains only the classical radius rc.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

Entwicklung einer physikalischen Geometrie der Raum-Zeit zum Zwecke der Interpretation der allgemeinen Relativitätstheorie

1964 ◽  
Vol 19 (6) ◽  
pp. 665-675 ◽  
Author(s):  
Ernst Schmutzer
Keyword(s):  
General Relativity ◽  
Physical Meaning ◽  
Physical Space ◽  
Equation Of Motion ◽  
Gravitational Acceleration ◽  
3 Dimensional ◽  
Einstein's Equation ◽  
Physical Geometry ◽  
Fixed System ◽  
Physical Components

Up to date the interpretation of the theory of general relativity is discussed. One cause for this situation is the use of mathematical coordinates without physical meaning. In continuation of thoughts of MØLLER and CATTANEO here physical coordinates are used and on this basis a 4-dimensional physical geometry of space-time is developed by projection the mathematical tensor components into physical components. For studying the curvature of the 3-dimensional physical space and for other purposes new socalled projective partial and projective covariant derivations are introduced. On this foundation EINSTEIN’S equation of motion is investigated. Definitions for the CORIOLIS acceleration and the centrifugal-gravitational acceleration for a fixed system of reference are given. The problem of energy conservation is analysed.

scholarly journals A TOPOLOGICAL EXTENSION OF GENERAL RELATIVITY TO EXPLORE THE NATURE OF QUANTUM SPACETIME, DARK ENERGY AND INFLATION

2013 ◽  
Vol 22 (10) ◽  
pp. 1330022
Author(s):  
M. SPAANS
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Discrete Time ◽  
Thought Experiment ◽  
Planck Scale ◽  
Equation Of Motion ◽  
Effective Equation ◽  
Dark Energy Density ◽  
Topological Quantum ◽  
Quantum Spacetime

General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BHs)/wormholes. Paths are fundamental and prime three-manifolds like T3, S1 × S2 and S3 are used to construct quantum spacetime. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum spacetime. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic BHs in the universe and is time-dependent in a manner consistent with current astrophysical observations, having an effective equation of state w ≈ -1.1 for redshifts smaller than unity. Inflation driven by mini BHs proceeds over n ≈ 55 e-foldings, without strong inhomogeneity. A discrete time effect visible in the cosmic microwave background is suggested.

QUANTUM BOUNCE OF A UNIFORM DUST STAR IN NEWTON GRAVITY

1991 ◽  
Vol 06 (10) ◽  
pp. 855-859 ◽  
Author(s):  
H. ISHIHARA ◽  
S. MORITA ◽  
H. SATO
Keyword(s):  
Wave Packet ◽  
Numerical Method ◽  
Quantum Dynamics ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Quantum Systems ◽  
Newtonian Limit ◽  
Newtonian Gravity

We investigate the quantum dynamics of a dust sphere collapsing uniformly in Newtonian gravity, in which the concept of time is obvious. The quantum bounce of the wave packet is observed by a numerical method. Our Newton Lagrangian is different from the Newtonian limit of the Einstein Lagrangian. They give the same classical equation of motion but derive the different quantum systems.

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