Summary

Within the scope of special relativity, space and time appear as follows.

Time

Two observers moving relative to each other may judge the simultaneity of the same pair of events differently.

Between two encounters of the observers, their clocks typically measure different durations. In the special case when one of them stays at rest in an inertial frame, the other's clock will always show less time elapsed when they again meet.

From the perspective of an observer moving at velocity v ≠ 0 relative to an inertial frame K, the time needed to cover a distance d in K is Δt' = Δt · √1 – v2   / c2   , where Δt = d / v is the time elapsed in terms of the coordinate time of K. That is, Δt' < Δt.

Basically, every result of special relativity is the consequence of the previous paragraph.

Space

Two observers moving relative to each other may judge the spatial distance between the same pair of events differently.

In an inertial frame K, the faster an object is moving, the more its length contracts relative to K along the direction of movement. On the other hand, there is no change in size along perpendicular directions (and planes).

From the perspective of an observer moving at velocity v ≠ 0 relative to an inertial frame K, every distance d in K along v becomes d' = d · √1 – v2   / c2   . This follows from what was told about time, since d = v · Δt and d' = v · Δt'. That is, d' < d.

Scope

Non-inertial reference frames are out of scope in special relativity.

The perspective of a non-uniformly moving observer is calculated by decomposing their motion into sections si during which they can be regarded as comoving with a respective inertial frame Ki.

The co-located clock of Ki then becomes, temporarily along section si, the observer's "own clock".

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