scholarly journals Finite Rest Masses of Wave Quanta in Material Media

1971 ◽  
Vol 24 (4) ◽  
pp. 871 ◽  
Author(s):  
KD Cole
Keyword(s):  
Gravitational Field ◽  
Doppler Effect ◽  
Plasma Frequency ◽  
Rest Mass ◽  
Gravitational Redshift ◽  
Mass Energy ◽  
Dynamical Equations ◽  
Dispersion Relationship ◽  
New Form ◽  
The Doppler Effect

The equivalence of a dispersion relationship and Einstein's mass--energy relationship leads to the specification of a particle in a vacuurrt which is equivalent to a "photon" in a medium. The invariance of the rest mass of this particle leads to a formula for the Doppler effect which is good for all forms of waves whose quanta can be described by E = nw and p = nk. Applying dynamical equations to the equivalent particle in the case of a radiofrequency photon in a plasma around a star, a new gravitational redshift formula is deduced which reduces to the well-known expression in the appropriate limit. A new form of bending of photon trajectories in a gravitational field is also described. At frequencies near the plasma frequency Vp the bending is vp/4(v-vp} times that for light in a vacuum.

THE SOLAR AND EXTRAGALACTIC RED SHIFTS

1965 ◽  
Vol 43 (1) ◽  
pp. 57-73 ◽  
Author(s):  
A. H. Gillieson
Keyword(s):  
Gravitational Field ◽  
Doppler Effect ◽  
Red Shift ◽  
The Doppler Effect ◽  
Peculiar Nature

A photon model is postulated whereby the peculiar nature of the observed solar red shift is explained, and by which the extragalactic red shifts are interpreted as caused not by the Doppler effect, but by interaction and consequent loss of energy of the photon in passing through the inhomogeneities of the gravitational field in space.

scholarly journals Gravitational Fields and Gravitational Waves

2021 ◽  
Author(s):  
Tony Yuan
Keyword(s):  
Gravitational Field ◽  
Gravitational Waves ◽  
Doppler Effect ◽  
Relative Velocity ◽  
Gravitational Force ◽  
Speed Of Light ◽  
Finite Velocity ◽  
Gravitational Fields ◽  
Light Waves ◽  
The Doppler Effect

Abstract For any object with finite velocity, the relative velocity between them will affect the effect between them. This effect can be called the chasing effect (general Doppler effect). LIGO discovered gravitational waves and measured the speed of gravitational waves equal to the speed of light c. Gravitational waves are generated due to the disturbance of the gravitational field, and the gravitational waves will affect the gravitational force on the object. We know that light waves have the Doppler effect, and gravitational waves also have this characteristic. The article studies the following questions around gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of the gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field on the object)? What is the speed of the gravitational field? Will gravitational waves caused by the revolution of the sun affect planetary precession?

THE CLOCK MISSION OPTIS

2007 ◽  
Vol 16 (12b) ◽  
pp. 2499-2510 ◽  
Author(s):  
HANSJÖRG DITTUS ◽  
CLAUS LÄMMERZAHL
Keyword(s):  
Gravitational Potential ◽  
Doppler Effect ◽  
Light Propagation ◽  
Gravitational Redshift ◽  
Speed Of Light ◽  
Fundamental Physics ◽  
Fundamental Structure ◽  
Perihelion Advance ◽  
The Doppler Effect ◽  
Matter Sector

Clocks are an almost universal tool for exploring the fundamental structure of theories related to relativity. For future clock experiments, it is important for them to be performed in space. One mission which has the capability to perform and improve all relativity tests based on clocks by several orders of magnitude is OPTIS. These tests consist of (i) tests of the isotropy of light propagation (from which information about the matter sector which the optical resonators are made of can also be drawn), (ii) tests of the constancy of the speed of light, (iii) tests of the universality of the gravitational redshift by comparing clocks based on light propagation, like light clocks and various atomic clocks, (iv) time dilation based on the Doppler effect, (v) measuring the absolute gravitational redshift, (vi) measuring the perihelion advance of the satellite's orbit by using very precise tracking techniques, (vii) measuring the Lense–Thirring effect, and (viii) testing Newton's gravitational potential law on the scale of Earth-bound satellites. The corresponding tests are not only important for fundamental physics but also indispensable for practical purposes like navigation, Earth sciences, metrology, etc.

scholarly journals Gravitational Fields and Gravitational Waves

2021 ◽  
Author(s):  
Tony Yuan
Keyword(s):  
Gravitational Field ◽  
Gravitational Waves ◽  
Doppler Effect ◽  
Relative Velocity ◽  
Gravitational Force ◽  
Gravitational Equation ◽  
Speed Of Light ◽  
Gravitational Fields ◽  
Light Waves ◽  
The Doppler Effect

Abstract For any object with finite velocity, the relative velocity between them will affect the effect between them. This effect can be called the chasing effect (general Doppler effect). LIGO discovered gravitational waves and measured the speed of gravitational waves equal to the speed of light c. Gravitational waves are generated due to the disturbance of the gravitational field, and the gravitational waves will affect the gravitational force on the object. We know that light waves have the Doppler effect, and gravitational waves also have this characteristic. The article studies the following questions around gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of the gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field on the object)? What is the speed of the gravitational field? Will gravitational waves caused by the revolution of the sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

scholarly journals Modelling the asymmetry of the halo cross-correlation function with relativistic effects at quasi-linear scales

2020 ◽  
Vol 498 (1) ◽  
pp. 981-1001
Author(s):  
Shohei Saga ◽  
Atsushi Taruya ◽  
Michel-Andrès Breton ◽  
Yann Rasera
Keyword(s):  
Correlation Function ◽  
Doppler Effect ◽  
Cross Correlation ◽  
Relativistic Effects ◽  
Cross Correlation Function ◽  
Gravitational Redshift ◽  
Wide Angle ◽  
Redshift Surveys ◽  
Angle Effect ◽  
The Doppler Effect

ABSTRACT The observed galaxy distribution via galaxy redshift surveys appears distorted due to redshift-space distortions (RSD). While one dominant contribution to RSD comes from the Doppler effect induced by the peculiar velocity of galaxies, the relativistic effects, including the gravitational redshift effect, are recently recognized to give small but important contributions. Such contributions lead to an asymmetric galaxy clustering along the line of sight, and produce non-vanishing odd multipoles when cross-correlating between different biased objects. However, non-zero odd multipoles are also generated by the Doppler effect beyond the distant-observer approximation, known as the wide-angle effect, and at quasi-linear scales, the interplay between wide-angle and relativistic effects becomes significant. In this paper, based on the formalism developed by Taruya et al., we present a quasi-linear model of the cross-correlation function taking a proper account of both the wide-angle and gravitational redshift effects, as one of the major relativistic effects. Our quasi-linear predictions of the dipole agree well with simulations even at the scales below $20\, h^{-1}\,$Mpc, where non-perturbative contributions from the halo potential play an important role, flipping the sign of the dipole amplitude. When increasing the bias difference and redshift, the scale where the sign flip happens is shifted to a larger scale. We derive a simple approximate formula to quantitatively account for the behaviours of the sign flip.

Dynamics of a test null string in the gravitational field of a null string domain that radially changes its size

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040011 ◽  
Author(s):  
A. P. Lelyakov
Keyword(s):  
Gravitational Field ◽  
Initial Conditions ◽  
Rest Mass ◽  
Symmetric Domain ◽  
Life Time ◽  
Mass Energy ◽  
Axially Symmetric ◽  
Number Of Layers ◽  
External Conditions ◽  
Null String

The motion of a test null string “inside” an axially symmetric domain of null strings which has a layered structure and radially changes its size has been investigated. It is shown that the action of the gravitational field of such a domain on a test null string for any initial conditions leads to oscillations of a test null string inside a region limited in space. The motion (drift) of the region inside which the test null string oscillates depends on the ratio of the initial parameters characterizing the test null string and the null string domain. These regions can be considered as particles localized in space with an effective nonzero rest mass. For these particles, you can enter the concept of “life time”, which depends on the number of layers in the multi-string system. It is also possible to introduce the concept of particle “mass” (energy), which is determined by the size of the region in which the null string oscillates and depends on the trajectory of the null string in this region. Under the influence of changing external conditions one kind of particles can pass into another.

Relativistic Doppler Effect and Group Velocity in Homogeneous Nonlinear and Inhomogeneous Plasmas

1971 ◽  
Vol 26 (9) ◽  
pp. 1531-1538
Author(s):  
John S. Nicolis ◽  
E. Athanassoula
Keyword(s):  
Differential Equation ◽  
Refractive Index ◽  
Plane Wave ◽  
Group Velocity ◽  
Doppler Effect ◽  
Order Differential Equation ◽  
Plasma Frequency ◽  
Isotropic Plasma ◽  
One Dimensional ◽  
The Doppler Effect

Abstract We study the variations of the received frequencies (Complex Doppler effect) from a source moving uniformly in a homogeneous isotropic plasma and emitting a uniform EM plane wave with amplitude E0, as a function of ωe/Eo where ωe is the plasma frequency. The ratio of the velocity U of the source over the group velocity Ugr of the transmitted wave is then calculated from the slope of the Doppler curves. When the plasma is inhomogeneous (one-dimensional stratification) the Doppler effect depends on the particular profile of the refractive index and its higher (even) derivatives with respect to the direction of stratification z. In this case the ratio U/Ugr=f(z) is given as the solution of a higher order differential equation with inhomogeneous part depending on the slope of the Doppler curve with respect to frequency. Typical cases involving symmetrical and transition profiles are examined. Harmonic generation in the plasma is not taken into account.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

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