# Principle of relativity

The relativity of uniform motion was stated by Galileo in the 17th century, though it was known to Buridan in the 14th century. Galileo’s statement of the principle of relativity is in terms of ships in uniform motion:

… so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still [Galileo Galilei, Dialogues Concerning the Two Chief World Systems (February 1632), Stillman Drake tr. (University of California Press, Berkeley, 1962, pp 186-8.]

This has been applied to constant speeds or zero accelerations, but it could just as well be applied to constant paces or zero relentations. In any case, if the speed is constant, so is its inverse, the pace. Let’s see how this operates.

The standard configuration for space-time is above, with frame L moving with velocity v relative to frame K. If a body moves with velocity u in frame K, what is its relative velocity in frame L (call it u’)? It is uv = u’ since frame L is also moving in the same direction. This is a form of the addition of velocities since u = v + u’.

Above is the standard temporo-spatial configuration, with frame L moving with lenticity q relative to frame K. If a body moves with lenticity p in frame K, what is its relative lenticity in frame L (call it p’)? It is pq = p’ since frame L is also moving in the same direction. This is a form of the addition of lenticities since p = q + p’.

In one dimensional motion, p = 1/u and q = 1/v, that is, pace and speed are inverses. Thus if the independent variable is distance, then the relative motion is pq = 1/u − 1/v. Recall that if the distance is pre-selected, then that is the independent variable, and the relative motion is temporo-spatial.