Physical objects and events occur in unified space-time. Uniformly moving observers observe no forces and no accelerations and have space-time coordinates (reference frames) with no curvatures. All system parts and reference-frame points have the same motion.
Because uniformly moving reference frames can linearly transform into each other, and objects move through space-time at light speed, physical laws are the same {invariance, uniform motion} for all uniformly moving observers and objects. Locally, kinetics and dynamics equations, Maxwell's electromagnetism equations, and Newton's and Einstein's gravitation laws are invariant for all reference frames with uniform velocity.
conservation laws
Motion equations relate local momentum and energy exchanges between particles and fields. Energy and momentum conservation laws are examples of invariance. Energy conservation is about time symmetry. Momentum conservation is about space symmetries. Space-time unites space and time, so space-time has one energy-momentum conservation law.
cause
By relativity, stationary observers calculate shortened lengths and times for moving objects, in the same ratio. Therefore, velocity is constant, and system kinetics remain the same.
no absolute velocities
Because systems with different uniform velocities have the same physical laws, uniform velocity has no physical effects, and observers cannot determine their or object absolute uniform velocity through space-time. All velocities are relative to observers and reference frames.
no absolute lengths and times
Because systems with different uniform velocities have the same physical laws, observers cannot determine absolute lengths and times. All lengths and times are relative to observers and reference frames.
linear coordinate transformations
Uniform velocities relate reference-frame coordinates linearly. All uniform-velocity reference frames can transform to all other uniform-velocity reference frames by linear coordinate transformations. Therefore, physical laws are invariant for linear coordinate transformations. For example, linear coordinate transformations can derive Maxwell's equations from Coulomb's law.
events and physical laws
Because physical laws are invariant for all uniform-velocity reference frames and under linear coordinate transformations, physical space-time location can have no influence on physical laws, so physical laws are the same at all universe space-time points (events).
space-time separation
Space-time separation is invariant for linear coordinate transformations.
physical constants
Because physical laws are invariant for all uniform-velocity reference frames and under linear coordinate transformations, fundamental physical values are constant for all uniform-velocity reference frames and under linear coordinate transformations. For example, angular momentum and other quanta remain constant.
accelerating objects
In local space-time regions, and for small accelerations, reference frames can approximate uniform-motion reference frames, so physical laws are invariant over linear coordinate transformations. Large space-time regions and large accelerations break physical-law invariance.
Physical Sciences>Physics>Relativity
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Date Modified: 2022.0224