A famous phrase from the Theory of Relativity.

The physical content of the theory of Special Relativity is Fitzgerald-Lorentz contraction, in which a moving object's length shrinks in the direction of travel, and the slowing of moving clocks.

Relative to resting clocks a moving clock ticks more slowly. If the relative velocity is 'c' - the velocity of light in a vacuum - the length of a tick/tock becomes infinite. For an inertial clock, a clock moving at constant velocity, the formula for slowing is:

t' = t*sqrt(1 - v2/c2)

(Where t' is the figure shown on the face of the moving clock, t ditto resting clocks - for simplicity, the moving clock showed zero when the resting clocks showed zero - and v is the velocity of the moving clock.)

One Way of Looking At It

Two mirrors facing each other have a lump of light bouncing back and forth between them. If the two are a distance c apart the time between bounces is one second - the clock "ticks" once a second. Orientate the clock vertically, so that one mirror is directly above the other, and give it a sideways velocity of v.

An observer moving with the clock measures the distance the lump of light travels between ticks to be c. The time between ticks being 1 second therefore. A resting observer measures the distance, x, to be sqrt(c2 + v2t2), by Pythagoras' theorem - the moving clock moves, between two ticks, a distance vt, where t is the time between the clock's ticks as measured by the resting clocks.

Since vanything = c (where vanything is the velocity of anything) is form invariant (and see Special Relativity) the time between ticks is t = x/c seconds, as measured by the resting observer. This simplifies to:

t = 1/sqrt(1 - v2/c2)

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