Electrodynamics in curved space-time: Free-space longitudinal wave propagation

2019 ◽  
Vol 32 (3) ◽  
pp. 282-291 ◽  
Author(s):  
Ole Keller ◽  
Lee M. Hively
Keyword(s):  
Scalar Field ◽  
Longitudinal Wave ◽  
Free Space ◽  
Quantum Electrodynamics ◽  
Wave Theory ◽  
Space Time ◽  
Metric Tensor ◽  
Curved Space ◽  
Magnetization Density ◽  
General Relativistic

Jiménez and Maroto [Phys. Rev. D 83, 023514 (2011)] predicted free-space, longitudinal electrodynamic waves in curved space-time, if the Lorenz condition is relaxed. A general-relativistic extension of Woodside’s electrodynamics [Am. J. Phys. 77, 438 (2009)] includes a dynamical, scalar field in both the potential- and electric/magnetic-field formulations without mixing the two. We formulate a longitudinal-wave theory, eliminating curvature polarization, magnetization density, and scalar field in favor of the electric/magnetic fields and the metric tensor. We obtain a wave equation for the longitudinal electric field for a spatially flat, expanding universe with a scale factor. This work is important, because: (i) the scalar- and longitudinal-fields do not cancel, as in classical quantum electrodynamics; and (ii) this new approach provides a first-principles path to an extended quantum theory that includes acceleration and gravity.

scholarly journals A slow Galileon scalar field in curved space-time

2012 ◽  
Vol 85 (10) ◽  
Author(s):  
Cristiano Germani ◽  
Luca Martucci ◽  
Parvin Moyassari
Keyword(s):  
Scalar Field ◽  
Space Time ◽  
Curved Space

scholarly journals Covariant information theory and emergent gravity

2018 ◽  
Vol 33 (34) ◽  
pp. 1845019 ◽  
Author(s):  
Vitaly Vanchurin
Keyword(s):  
Information Theory ◽  
Scalar Field ◽  
Entropy Production ◽  
Thermodynamic Description ◽  
Local Equilibrium ◽  
Information Matrix ◽  
Space Time ◽  
Wave Functions ◽  
Complex Scalar ◽  
Metric Tensor

Informational dependence between statistical or quantum subsystems can be described with Fisher information matrix or Fubini-Study metric obtained from variations/shifts of the sample/configuration space coordinates. Using these (noncovariant) objects as macroscopic constraints, we consider statistical ensembles over the space of classical probability distributions (i.e. in statistical space) or quantum wave functions (i.e. in Hilbert space). The ensembles are covariantized using dual field theories with either complex scalar field (identified with complex wave functions) or real scalar field (identified with square roots of probabilities). We construct space–time ensembles for which an approximate Schrodinger dynamics is satisfied by the dual field (which we call infoton due to its informational origin) and argue that a full space–time covariance on the field theory side is dual to local computations on the information theory side. We define a fully covariant information-computation tensor and show that it must satisfy certain conservation equations. Then we switch to a thermodynamic description of the quantum/statistical systems and argue that the (inverse of) space–time metric tensor is a conjugate thermodynamic variable to the ensemble-averaged information-computation tensor. In (local) equilibrium, the entropy production vanishes, and the metric is not dynamical, but away from the equilibrium the entropy production gives rise to an emergent dynamics of the metric. This dynamics can be described approximately by expanding the entropy production into products of generalized forces (derivatives of metric) and conjugate fluxes. Near equilibrium, these fluxes are given by an Onsager tensor contracted with generalized forces and on the grounds of time-reversal symmetry, the Onsager tensor is expected to be symmetric. We show that a particularly simple and highly symmetric form of the Onsager tensor gives rise to the Einstein–Hilbert term. This proves that general relativity is equivalent to a theory of nonequilibrium (thermo)dynamics of the metric, but the theory is expected to break down far away from equilibrium where the symmetries of the Onsager tensor are to be broken.

Dimensional renormalization of scalar field theory in curved space-time

1980 ◽  
Vol 130 (1) ◽  
pp. 215-248 ◽  
Author(s):  
Lowell S Brown ◽  
John C Collins
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Space Time ◽  
Scalar Field Theory ◽  
Curved Space

scholarly journals Schwinger’s approach to Einstein’s gravity and beyond

2014 ◽  
Vol 92 (9) ◽  
pp. 964-967 ◽  
Author(s):  
K.A. Milton
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
20Th Century ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Space Time ◽  
Gravity Theory ◽  
Curved Space ◽  
Theoretical Physicist ◽  
The Subject

J. Schwinger (1918–1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. Schwinger himself had no doubt of the validity of general relativity, although he preferred a particle physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved space–time. This article provides a brief summary of his contributions and attitudes toward the subject of gravity.

Newtonian quantum gravity and the derivation of the gravitational constant G and its fluctuations

2020 ◽  
Vol 33 (4) ◽  
pp. 387-394
Author(s):  
Reiner Georg Ziefle
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Quantum Physics ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Wave Theory ◽  
Space Time ◽  
Gravitational Fields ◽  
General Relativistic ◽  
Theory Of Gravity

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

scholarly journals Points of general relativistic shock wave interaction are ‘regularity singularities’ where space–time is not locally flat

2012 ◽  
Vol 468 (2146) ◽  
pp. 2962-2980 ◽  
Author(s):  
Moritz Reintjes ◽  
Blake Temple
Keyword(s):  
Shock Wave ◽  
Wave Interaction ◽  
Delta Function ◽  
Space Time ◽  
Coordinate Transformations ◽  
Metric Tensor ◽  
Shock Wave Interaction ◽  
Perfect Fluids ◽  
Time Singularities ◽  
General Relativistic

We show that the regularity of the gravitational metric tensor in spherically symmetric space–times cannot be lifted from C 0,1 to C 1,1 within the class of C 1,1 coordinate transformations in a neighbourhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel's theorem, which states that such coordinate transformations always exist in a neighbourhood of a point on a smooth single shock surface. The results thus imply that points of shock wave interaction represent a new kind of regularity singularity for perfect fluids evolving in space–time, singularities that make perfectly good sense physically, that can form from the evolution of smooth initial data, but at which the space–time is not locally Minkowskian under any coordinate transformation. In particular, at regularity singularities, delta function sources in the second derivatives of the metric exist in all coordinate systems of the C 1,1 -atlas, but due to cancellation, the full Riemann curvature tensor remains supnorm bounded .

Quantum Electrodynamics in Curved Space-Time

1981 ◽  
Vol 29 (5) ◽  
pp. 187-218 ◽  
Author(s):  
I. L. Buchbinder ◽  
E. S. Fradkin ◽  
D. M. Gitman
Keyword(s):  
Quantum Electrodynamics ◽  
Space Time ◽  
Curved Space

Radiation coordinates in general relativity

1966 ◽  
Vol 292 (1428) ◽  
pp. 1-13 ◽  
Keyword(s):  
Gravitational Radiation ◽  
General System ◽  
Space Time ◽  
Timelike Curve ◽  
Null Cone ◽  
Metric Tensor ◽  
Curved Space ◽  
The World ◽  
The Future ◽  
World Function

This paper introduces a system of coordinates (called radiation coordinates ) which may be useful in discussing problems of gravitational radiation. Starting with a general system of coordinates x i in curved space-time, an assigned timelike curve C , and an orthonormal tetrad assigned along C , the radiation coordinates x a of any event P are defined by a formula involving the world function. In radiation coordinates the equation of any null cone, drawn from an event x a' on C into the future, has the Minkowskian form This paper introduces a system of coordinates (called radiation coordinates ) which may be useful in discussing problems of gravitational radiation. Starting with a general system of coordinates x i in curved space-time, an assigned timelike curve C , and an orthonormal tetrad assigned along C , the radiation coordinates x a of any event P are defined by a formula involving the world function. In radiation coordinates the equation of any null cone, drawn from an event x a' on C into the future, has the Minkowskian form ƞ ab (x a - x a' ) (x b - x b’ ) = 0, ƞ ab = diag (1, 1, 1, - 1 ) . The metric tensor satisfies the coordinate conditions g ab (x b - x b' ) = ƞ ab (x b - x b' ), where x b' are regarded as functions of x b viz. the coordinates of the point of intersection of C with the null cone drawn into the past from x b . Continuity on C of the Jacobian matrix of the transformation x → x^ ~ is ensured by demanding the constancy of the components on the tetrad of the unit tangent vector to C . Continuity of the second derivatives of the transformation cannot be obtained except in very special circumstances. If space-time is flat, C a geodesic, and the orthonormal tetrad transported parallelly along C with the fourth vector tangent to C , then radiation coordinates reduce to the usual Minkowskian coordinates having C for time axis.

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