Universe has three continuous space dimensions and one continuous time dimension, and they unite symmetrically in four-dimensional space-time {space-time, relativity}|. Time and space are not separate and independent physical properties.
events
All particles and objects move through space-time at light speed. Observers and objects move through time as well as space.
Space-time has events, not independent times and spatial positions. Observers and objects move through space-time events. Objects travel through space-time along four-dimensional-vector paths {world line}, along geodesics.
units
Space-time coordinates have the same units for time and space. Because distance equals time times velocity, distance unit can be time unit times light speed: c*t. Because time equals distance divided by velocity, time unit can be distance unit divided by light speed: x/c. Time unit can use one oscillation over one distance unit: 1 / cm = cm^-1.
relativity
Though relatively moving observers calculate different lengths and times, because lengths and times shorten in same proportion, space-time separation between two space-time events is constant for all uniformly moving observers.
regions
Different space-time regions behave differently. Regions can be inside gravity or electromagnetic sources. Vacuum regions can be near sources. Regions, such as flat space-time, can have weak fields. Regions can have weak fields but have radiation.
time coordinate as imaginary numbers
Relatively moving observers have different reference frames and relative space-times. Relative space-times differ by relative velocity (boost), which causes three-dimensional rotations into time. The complex plane and space-time coordinate system have the same properties, so time coordinate is like imaginary-number coordinate.
Simultaneity requires an observer and two space-time events. By direct observation, two space-time events are simultaneous {simultaneity, relativity}| if light signals from both events reach observer at same time. See Figure 1. To another observer at a different space-time event, the two events are not simultaneous. (If an observer sees that two events happen at the same spatial location, relatively moving observers do not calculate that they coincide.)
synchronized clocks
Two space-time events can be simultaneous for an observer if they occur at the same time on observer's synchronized clocks. Because this simultaneity occurs at distant space-time events, observer can only measure and calculate this simultaneity.
Observer reference-frame space coordinates show all space locations, with clocks synchronized to same time. Events that happen on a space-time space coordinate are all at the same time. For example, at space-time origin, time is 0, and space coordinate shows all space locations, whose events have time 0.
space coordinates
Space coordinates for relatively moving observers are different. Compared to stationary observers, uniformly moving observers move toward stationary-observer synchronized clocks, and receive light rays sooner than stationary observers. Because they come sooner, relatively moving observers calculate that those light rays came from later-time events. See Figure 1.
examples
At s1, observer has time 0 and position 0. s2 and s3 happen at same time on time axis, and information about them reaches s4 at same time.
Information from s1 reaches s2 and s3 at same time on time axis, so they are simultaneous. s2 and s3 are two different observers.
Because signals travel at light speed, information from s1 can reach s6.
Information from s1 cannot reach s4, s5 or s7.
Information from s3 reaches s6 later.
At s4, observer is at time 2 and position 0. Information from s4 reaches s7.
s4, s5, and s6 happen at same time on time axis.
No information about s1, s2, s3, s4, and s6 reaches s5.
Information about s3 reaches s6.
Information about s5 comes to observer at position 0 sooner than information from s6, because s5 is closer in space.
s7 happens later than s4, s5, and s6 on time axis.
space-time separation
Observers and objects move through space-time events. Space-time events have space-time separations. In space-time, neither time separation nor space separation exists independently.
Simultaneous events for observer have same space-time separation from observer. Observers cannot detect events from space-time points outside their light cone. See Figure 2. s2 and s3 are simultaneous for observer at space-time position s4. s4 and s6 are simultaneous for observer at space-time position s7. s4, s5, and s6 are not simultaneous for any observer.
event order
Relatively moving observers do not agree on event locations or times, and can calculate that the same space-time events happen in different orders.
absolute time
Because relatively moving observers calculate different times, spatial positions, and event orders for the same space-time events, observers cannot detect absolute time (or absolute location).
Local space-time coordinate systems can transform by first-power functions into all other local space-time coordinate systems {Lorentz transformation} {linear transformation}.
Distinct space-time points have different pasts and futures {space-time point set}. Because maximum speed is light speed, space-time points have possible past points {past-set} and possible future points {future-set}. Point past-sets and future-sets are unique {indecomposable}. Indecomposable past-sets can affect the space-time point. The space-time point can affect indecomposable future-sets.
Geometries can have points at infinity (ideal point). Space-time should not have ideal points or singularities.
All space-time points {event} have past-set and future-set, so space-time has possible causes and effects {causal structure}. Space-time events change causal structure over time and space.
Space-time points have a space-time region {global causal structure} that light can reach in the future. A space-time point can only affect those events. A space-time point has a space-time region whose events can affect it.
Space paths cannot reverse time, so no event can happen at two times. Between past point and future point reachable from past point, all space-time points are reachable {hyperbolic space-time, global}, so space-time has no singularities.
All light rays from a space-time point make a space-time cone {light cone}|. All light rays to a space-time point make a light cone.
If light rays from a space-time point later converge {converging light cone}, convergence point is a singularity.
In zero gravity, object translations, rotations, vibrations, scale changes, and inversions in space do not change object geometric shape. Zero-gravity four-dimensional space-time has symmetry {conformal symmetry} {conformal symmetry group} that preserves geometric shape, because metric-scale changes {Weyl transformation} leave proper time and proper length unchanged. Mathematically, the Poincaré group, scale invariance (dilation or dilatation), and inversion-translation-inversion (special conformal transformation) have conformal symmetry and preserve geometric shape.
5-Physics-Relativity-Space-Time
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Date Modified: 2022.0225