The fact that light travels at a constant speed has a distinct effect on time.

The Effect on Time

Imagine a clock that measured time by bouncing a photon (a particle of light) between two mirrors that are its walls. The photon must always travel at the speed of light (c). Even if the ship were moving (at velocity v_ship), the light would move at exactly the speed of light. This can be represented by a vector, whose magnitude is c and whose sideways magnitude were v_ship. The vectors c, vship, and the speed of the photon upward or downward form a right triangle and therefore, the speed at which the photon moves upward or downward (v_photon) could be figured using the Pythagorean Theory (a² + b² = c²):

Rearranged to:

To check, substituting 0 for v_ship makes:

v_photon = c (which makes sense)

If the length of the ship were h_ship and the ship were not moving, then based on the definition of speed:

t_stationary = h_ship / c

where t_stationary is the time interval measured by the stationary clock.

If the clock were moving, then the speed of the photon towards the opposite mirror (v_photon) is . Then, the time interval measured by the moving clock will be:

Since we don't want to deal with the length of the ship, but rather, the time interval, we rearrange the equation, t_stationary = h_ship / c to:

h_ship = t_stationary * c

We can substitute that into the equation above to get:

c can be factored out of the by factoring the c² out of the to get factor the c² out to get The cs in the numerator and the denominator cancel out to make

The reason that this is so definately correct is the fact that h_ship is the length of the ship in a dimension in which in is not moving, so the ship in that dimension cannot be affected. That means that because the ship is not moving in the direction of h_ship, h_ship is not changed by relativity.

Because all motion is relative, if ship A is moving relative to ship B, occupants of ship A see the time of occupants of ship B running slow and occupants of ship B see the time of occupants of ship A running slow. There is no experimental way of finding out which occupants are right, so they can both be said to be correct.