information:filtering
Time dilation

The time lapse between two events is not invariant from one observer to another, but is dependent on the relative speeds of the observers' reference frames.

Suppose a clock is at rest in the unprimed system S. The location of the clock on two different ticks is then characterized by Δ x = 0. To find the relation between the times between these ticks as measured in both systems, Equation 3 can be used to find:

This shows that the time (Δ t ′) between the two ticks as seen in the frame in which the clock is moving (S ′), is longer than the time (Δ t) between these ticks as measured in the rest frame of the clock (S). Time dilation explains a number of physical phenomena; for example, the lifetime of high speed muons created by the collision of cosmic rays with particles in the Earth's outer atmosphere and moving towards the surface is greater than the lifetime of slowly moving muons, created and decaying in a laboratory.

Whenever one hears a statement to the effect that "moving clocks run slow", one should envision an inertial reference frame thickly populated with identical, synchronized clocks. As a moving clock travels through this array, its reading at any particular point is compared with a stationary clock at the same point.

The measurements that we would get if we actually looked at a moving clock would, in general, not at all be the same thing, because the time that would see would be delayed by the finite speed of light, i.e. the times that we see would be distorted by the Doppler effect. Measurements of relativistic effects must always be understood as having been made after finite speed-of-light effects have been factored out.