PHOTONS IN THE GRAVITATIONAL FIELD

1966 ◽  
Vol 44 (7) ◽  
pp. 1639-1648 ◽  
Author(s):  
J. C. W. Scott
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Group Velocity ◽  
Gravitational Potential ◽  
Rest Mass ◽  
Red Shift ◽  
Field Equations ◽  
Proper Mass ◽  
Photon Frequency ◽  
Theory Of Gravitation

In a previous paper, "The Gravitokinetic Field and the Orbit of Mercury," a new theory of gravitation was introduced, according to which space–time is always flat and the gravitational field is described by equations of Maxwellian form. In this paper it is shown that the theory correctly predicts the gravitational red shift and the gravitational deflection of a light ray. The interaction of photons with a gravitational field follows from the basic premises of quantum theory, that photon frequency is proportional to its energy and that photon wavelength is inversely proportional to its momentum. The photon velocity and proper mass depend on the gravitational potential, and the deflection of a light ray is due to gravitational refraction. The validity of the antisymmetric field equations for sources of variable rest mass is due to the divergence of the group velocity from the dynamical velocity.

Red shift of photon frequency in the gravitational field

2021 ◽  
Author(s):  
Jin Tong Wang ◽  
Jiangdi Fan ◽  
Aaron X. Kan
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Schrodinger Equation ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Redshift ◽  
General Relativity Theory ◽  
Photon Frequency

It has been well known that there is a redshift of photon frequency due to the gravitational potential. Scott et al. [Can. J. Phys. 44 (1966) 1639, https://doi.org/10.1139/p66-137 ] pointed out that general relativity theory predicts the gravitational redshift. However, using the quantum mechanics theory related to the photon Hamiltonian and photon Schrodinger equation, we calculate the redshift due to the gravitational potential. The result is exactly the same as that from the general relativity theory.

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.

scholarly journals New mechanism for the cosmological red-shift explaining: non-observation of dark energy, large-number- coincidence and the cosmic coincidence

2015 ◽  
Vol 3 (1) ◽  
pp. 24
Author(s):  
Hasmukh K. Tank
Keyword(s):  
Gravitational Field ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Red Shift ◽  
Relativity Theory ◽  
Gravitational Potential Energy ◽  
Potential Well ◽  
Speed Of Light ◽  
Equivalent Mass ◽  
The Universe

<p>Accepting Einstein’s General Relativity Theory, that the changes in the gravitational field can propagate at the speed of light, it is proposed here that: before an electron in an atom emits a photon, the energy (<em>h f<sub>0</sub></em>) of the photon was a part of total energy of the atom; contributing to establish the gravitational-field around the atom. As soon as an electron in that atom emits a photon of energy <em>h f<sub>0</sub></em>, and the photon starts moving away from the atom, the gravitational-field around the atom partly reduces, proportional to the photon’s energy <em>h f<sub>0</sub></em>, and this wave of ‘reduced gravitational field’ propagates radially-outwards at the speed of light. And a part of energy of the photon gets spent in “filling” the ‘gravitational potential-well’ produced by its energy, when it was a part of energy of the atom. From the derivation presented here we find that the energy spent by the photon to “fill” the ‘gravitational potential-well’, during its inter-galactic journey manifests as the ‘cosmological red-shift’. And the so called ‘total-mass-of-the-universe'’ and ‘radius-of-the-universe'’ are just mathematically-equivalent mass and distance arising while converting electrostatic potential-energy into gravitational potential-energy. This is the reason why we find the large-number-coincidence (LNC). And since there is no expansion of the universe, there is no ‘cosmic coincidence’, that why only in this epoch we find the ‘large-number-coincidence’!</p>

scholarly journals Geometrodynamik

1976 ◽  
Vol 31 (10) ◽  
pp. 1155-1159 ◽  
Author(s):  
F. Vollendorf
Keyword(s):  
Gravitational Field ◽  
Maxwell Field ◽  
Field Equations ◽  
Theory Of Gravitation ◽  
Special Case

Abstract This article is based upon the idea to solve the problem of combining the electromagnetic and the gravitational field by starting from Maxwell's theory. It is shown that the theory of the Maxwell field can be generalized in such a way that Einstein's theory of gravitation becomes a special case of it. Finally we find field equations which refer only to geometric quantities.

The Annotated Manuscript

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Gravitational Field ◽  
General Theory ◽  
Equations Of Motion ◽  
Special Theory ◽  
Material Point ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Field Equations ◽  
Theory Of Gravitation

This section presents annotations of the manuscript of Albert Einstein's canonical 1916 paper on the general theory of relativity. It begins with a discussion of the foundation of the general theory of relativity, taking into account Einstein's fundamental considerations on the postulate of relativity, and more specifically why he went beyond the special theory of relativity. It then considers the spacetime continuum, explaining the role of coordinates in the new theory of gravitation. It also describes tensors of the second and higher ranks, multiplication of tensors, the equation of the geodetic line, the formation of tensors by differentiation, equations of motion of a material point in the gravitational field, the general form of the field equations of gravitation, and the laws of conservation in the general case. Finally, the behavior of rods and clocks in the static gravitational field is examined.

scholarly journals GENERATING FUNCTIONAL FOR THE GRAVITATIONAL FIELD: IMPLEMENTATION OF AN EVOLUTIONARY QUANTUM DYNAMICS

2005 ◽  
Vol 14 (10) ◽  
pp. 1739-1760
Author(s):  
ERIKA CERASTI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Quantum Dynamics ◽  
Hamiltonian Formalism ◽  
Field Equations ◽  
Lagrangian Multipliers ◽  
Generating Functional ◽  
Mean Values ◽  
Classical Counterpart ◽  
Gravitational Field Equations

We provide a generating functional for the gravitational field that is associated with the relaxation of the primary constraints by extending to the quantum sector. This requirement of the theory relies on the assumption that a suitable time variable exists, when taking the T-products of the dynamical variables. More precisely, we start from the gravitational field equations written in the Hamiltonian formalism and expressed via Misner-like variables; hence we construct the equation to which the T-products of the dynamical variables obey and transform this paradigm in terms of the generating functional, as taken on the theory phase-space. We show how the relaxation of the primary constraints (which corresponds to the breakdown of the invariance of the quantum theory under the four-diffeomorphisms) is summarized by a free functional taken on the Lagrangian multipliers, accounting for such constraints in the classical theory. The issue of our analysis is equivalent to a Gupta–Bleuler approach on the quantum implementation of all the gravitational constraints; in fact, in the limit of small ℏ, the quantum dynamics is described by a Schrödinger equation as soon as the mean values of the momenta, associated to the lapse function and the shift vector, are not vanishing. Finally we show how, in the classical limit, the evolutionary quantum gravity reduces to General Relativity in the presence of an Eckart fluid, which corresponds to the classical counterpart of the physical clock, introduced in the quantum theory.

Gravitational Field Equations

1971 ◽  
Vol 49 (6) ◽  
pp. 678-684
Author(s):  
Peter Rastall
Keyword(s):  
Gravitational Field ◽  
Einstein Equations ◽  
Tensor Form ◽  
Field Equations ◽  
Scalar Theory ◽  
Gravitational Fields ◽  
Gravitational Field Equations ◽  
Theory Of Gravitation ◽  
Alternative Field

An earlier, scalar theory of gravitation is assumed to be valid for a class of static gravitational fields. The theory is written in tensor form, and generalized to the case of an arbitrary gravitational field. The interaction between the field and its sources is discussed, and the linearized form of the field equations is derived. Some possible alternative field equations are considered which are compatible with the linearized Einstein equations.

scholarly journals SOLUTIONS WITHOUT SINGULARITIES IN GAUGE THEORY OF GRAVITATION

2004 ◽  
Vol 15 (07) ◽  
pp. 1031-1038 ◽  
Author(s):  
G. ZET ◽  
C. D. OPRISAN ◽  
S. BABETI
Keyword(s):  
Gravitational Field ◽  
Gauge Theory ◽  
Mathematical Structure ◽  
Space Time ◽  
Relativity Theory ◽  
De Sitter ◽  
Field Equations ◽  
Underlying Space ◽  
Minkowski Space Time ◽  
Theory Of Gravitation

A de-Sitter gauge theory of the gravitational field is developed using a spherical symmetric Minkowski space–time as base manifold. The gravitational field is described by gauge potentials and the mathematical structure of the underlying space–time is not affected by physical events. The field equations are written and their solutions without singularities are obtained by imposing some constraints on the invariants of the model. An example of such a solution is given and its dependence on the cosmological constant is studied. A comparison with results obtained in General Relativity theory is also presented.

AN APPROACH TO A THEORY OF GRAVITATION

1960 ◽  
Vol 38 (8) ◽  
pp. 975-982 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
Space Time ◽  
Red Shift ◽  
Additive Constant ◽  
The Sun ◽  
Field Equations ◽  
Scalar Theory ◽  
Theory Of Gravitation ◽  
Bending Of Light

The form of the space–time metric in a scalar theory of gravitation follows from the assumption that the potential is arbitrary to the extent of an additive constant. No field equations are needed. Expressions are found for the gravitational red shift, the perihelion motion of a planet, and the bending of light by the sun. From the observed values of these quantities one can determine the metric and the potential due to a gravitating mass.

Approximate gravitational field equations

1980 ◽  
Vol 58 (11) ◽  
pp. 1599-1613
Author(s):  
Peter Rastall
Keyword(s):  
Gravitational Field ◽  
Gravitational Potential ◽  
Gravitational Radiation ◽  
Field Equations ◽  
Newtonian Theory ◽  
Gravitational Field Equations

Two useful ways of approximating the exact gravitational field equations are described. In the first, the gravitational potential ψ is arbitrary and the spatial components of the covector field n are small; in the second, ψ is small and the spatial components of n are arbitrary. A canonical stress-momentum is defined which is often easier to use than the symmetric stress-momentum of earlier papers. Applications of the formalism to gravitational radiation, the post-Newtonian theory, and cosmology are outlined.

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