Space-time curvature describes motions of accelerating objects and objects in gravitational fields {general relativity}| (geometrodynamics).
space-time
Three spatial dimensions and one time dimension unify into space-time. Space-time has no preferred time direction, no preferred spatial direction, and no handedness.
local space-time
Physical laws are about what happens at space-time points. With small gravity and/or acceleration, space-time-point reference frames locally approximate uniform-velocity reference frames, which have linear coordinate transformations. Their space and time coordinates are straight lines.
Distant galaxies have negligible gravitational effects on local space-time, so empty space has no gravitational fields and no space-time curvature.
Observers traveling with relative uniform velocity to objects calculate that objects shorten time and contract length, whose amount corresponds to angle between time coordinate and motion-direction space coordinate. Angle varies directly with relative velocity.
space-time curvature
Objects accelerate by mechanical force or by gravitation. Observers accelerating with respect to objects increase relative velocity, so length contraction and time dilation change. When they change, reference-frame space-time coordinates change angle between time coordinate and motion-direction space coordinate. This coordinate angle change is space-time curvature. Space curvature alone and time curvature alone cannot happen, because curvature is the angle change between space and time coordinates.
Therefore, models using circle curvature (1/r), sphere curvature (1/r^2), or 4-sphere curvature (1/r^3) do not show the essence of the story. Neither do models showing a flat surface with curvature in the middle, for example, a trampoline with a weight on it.
In space-time, all objects move at light speed. Objects at rest move through time only. Objects moving at light speed move equally through time and space. (Objects cannot move only through space, because motion requires time by definition. Objects cannot move through space more than time, because experiment shows that light speed is maximum speed.)
Space-time plots for motions through flat space-time have object trajectories that are straight lines. Coordinates show equally spaced units of space and time. Coordinate positions are number of space units (meters) and number of time units (seconds or light-seconds).
If coordinates show equally spaced units of space and time, space-time plots for motions through curved space-time have object trajectories that are curved lines, because the relation between space and time is always changing. Note: Using log-log plots, with ln (y) and ln (x), makes power law functions, y = a * x^b, become straight lines. Using semi-log plots, with ln (y) and x, makes exponential functions, y = a * e^(b*x), become straight lines. However, the relation between space and time coordinates is not a power law or exponential function.
Space-time curvature is not about changes to coordinate units. Time dilation and length contraction are about simultaneity relations between objects and observers in different coordinate systems (reference frames). Space-time curvature is about intrinsic properties of space, and how motion partitions between time and space. In curved space-time, motion cannot be purely through time, because the time and space coordinates are not orthogonal, so motion must have both time and space components. Objects originally at rest in a gravitational field must move through space, since all objects move through space-time at light speed. The more space-time curves, the more the space component increases compared to the time component, so objects move faster through space the closer they get to a (larger) mass. A ball thrown upward slows down as space-time curvature decreases, until it is at rest at the top of its trajectory, where upward and downward motions are equal.
global
Non-locally, time coordinate and motion-direction space coordinate angle changes make global reference frames non-linear.
non-linearity
Objects with mass have gravitational fields and curve space-time. Because the objects pass through this curved space-time, their own gravitational field affects their motions. In general relativity, mass acts on itself through its gravitational field. In general relativity, therefore, total force is not the vector sum of forces. Non-local motions are non-linear. Non-local curved space-time is non-linear.
absolute effects
Objects start with no acceleration and in negligible gravitational fields. After objects mechanically accelerate and/or pass through gravitational fields, they return to no acceleration and negligible gravitational fields. Stationary observers calculate that objects have permanently shorter times, so passing through curved space-time has absolute physical effects for stationary observers.
energy-momentum tensor
Energy conservation is due to space-time time symmetry. Momentum conservation is due to space-time spatial symmetry. Angular-momentum conservation is due to space-time right-left symmetry. Because space-time unifies distance and time, space-time unifies energy, momentum, and angular momentum into an energy-momentum tensor.
relativity tests
Relativity tests have all proved that general relativity is correct, and other metric and non-metric theories are not correct. Measurements agree with general-relativity theory to within 10^-12 percent.
For example, the sun bends light rays that come from stars behind Sun at calculated rate.
Uniform-velocity observers calculate that accelerated and then decelerated clocks have lost time and aged less at calculated rate.
Mercury's perihelion precesses around Sun at calculated rate.
Earth and Moon change separation distance periodically at calculated rate.
Distant-star spectral lines red-shift at calculated rate.
Spectral lines red-shift as they pass through Earth gravity at calculated rate.
Accelerating masses, and objects changing mass, make gravity waves. Gravity-wave emission causes binary pulsars to have smaller orbits and shorter orbital periods at calculated rate.
other physics theories
Besides gravity and accelerations, general relativity applies to thermodynamics, hydrodynamics, electrodynamics, and geometric optics.
Physical Sciences>Physics>Relativity>General Relativity
5-Physics-Relativity-General Relativity
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Date Modified: 2022.0224