Space-time theories {Kaluza-Klein theory} can use four space dimensions and one time dimension. Fourth space dimension is only several Planck lengths long, has curvature so high that it makes a circle, and is unobservable. A small fourth space dimension allows the vacuum to have higher energy density than three space dimensions have.
Time relativistic theories {kinematic relativity theory} describe finite expanding universes.
Gravitation theories can use metrics {metric theory} or be non-metric. A ten-parameter general metric theory {parametrized post-Newtonian formalism} can model all metric gravitation theories, which then differ only in parameter values.
parameters
The ten parameters model: How mass causes space curvature. How gravity-field superposition is non-linear. If space has preferred reference frame, or all spatial directions are equivalent. If all four space-time components have momentum conservation. If distant galaxies affect local interactions. If general metric theory does or does not include gravitational-radiation effects or other gravity-strength changes.
types
Metric theories include general theory of relativity, scalar-tensor theories, vector-tensor theories, tensor-tensor theories, conformally flat theories, stratified theories, and quasi-linear theories.
non-metric
Non-metric gravitation theories violate completeness, consistency, relativity, and/or Newtonian limit.
Abstract spaces {superspace} can have approximate three-dimensional space by tetrahedron skeletons and have tetrahedral edge lengths. They can have space dynamics, change over time, and represent different geometries.
Riemann surfaces are Riemann sphere, torus, and pretzel-shaped surface. Their angles are the same as in Euclidean space. Riemann surfaces can define field theories {conformal field theory} that pair with string theory.
General-relativity dynamics {geometrodynamics}| is three-dimensional Riemann-space dynamics, using a method {ADM formalism} {canonical quantization} developed by Paul Dirac and later Richard Arnowitt, Stanley Deser, and Charles Misner.
Geometric optics {geometric optics}| models plane waves in flat space-time. Geometric optics applies if wave-packet wavelengths are much less than wave-front space-time curvature radius. Wave photons have same momentum and polarization. Photon number determines ray amplitude. Like adiabatic flow, photon number conserves. Light rays are null geodesics. Polarization vector is perpendicular to rays and propagates along rays.
Quantum general-relativity gravitation theories {relational quantum theory} have different observers whose calculations are the same at corresponding space-time points.
In one renormalization, electric field is relativistically invariant, so all force-induced fields, including reaction forces, form other particles using photon exchanges and go to zero {perfect absorption}. Perfect absorption has only retarded solutions, because advanced solutions are improbable by thermodynamic laws. In expanding universes, absorption happens at low frequency for retarded solutions and at high frequency for advanced solutions. However, this theory is not correct.
In a renormalization theory {Wheeler-Feynman theory}, universe particles absorb moving-charge electric field, so field at large distances is zero, and system has no advanced solutions and no infinities. However, this theory is not correct.
If general relativity has canonical quantization, Wheeler-DeWitt equation has no time coordinate {frozen time problem} {problem of frozen time} {problem of time} {time problem}.
In empty space, space-time can have many equivalent reference frames {covariance, relationalism} {covariance, relativity} {general covariance, relationalism}.
In relativity theories {relationalism}, mass-energy determines space-time curvature and shape, and space and time are not absolute or real but differ for different observers.
Perhaps, space and time are real and absolute {substantivalism, relativity}, and mass-energy alone does not determine space-time curvature and shape.
Vectors can equal another vector plus a scalar term {gauge, relativity}|. Scalar gauges can change with position. For example, space-time curvature can change with position, and gauges can represent linear curvature changes with position.
Using linear transformations {gauge transformation}, gauges can relate vectors expressed in different coordinate systems. Gravitation, electromagnetism, and chromodynamics use gauge transformations to model infinitesimal, finite, scalar-coordinate transformations. For local space-time regions, general relativity is invariant under finite coordinate transformations, and a generalized gauge transformation represents general relativity. Using gauge scalars can simplify differential equations.
Because derivatives of scalars equal zero, gauge changes do not affect physical measurements, motion differential equations do not change, and gauge transformations preserve invariants.
In gravitational fields so weak that space-time has negligible curvature, gravity does not move gravitational-field-source masses and does no work on them, so masses have no self-energy. For this case, theories {linearized theory of gravity} represent space-time-coordinate changes as infinitesimal gauge changes, which change space-time-metric coefficients.
5-Physics-Relativity-General Relativity
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Date Modified: 2022.0225