iSoul In the beginning is reality

Uniform motion

Uniform linear motion is the motion of a body at a constant linear rate. Uniform circular motion is the motion of a body at a constant angular rate. In both of these cases the spatial extent of motion and the temporal extent of motion are in a constant proportion.

Because of this constant proportion, from knowledge of the proportion and either the spatial extent or the temporal extent, one can determine the other. Moreover, one may specify a spatial extent by specifying a temporal extent or vice versa, given the constant proportion. Space and time are basically the same for uniform motion.

Since the speed of light is constant, it allows a standard conversion between space and time, as previously noted here. This does not change the nature of measurements of spatial and temporal extent.

What I’d like to point out here is that conversion between space and time can be done for circular motion, too, by using a standard uniform circular motion. The most obvious circular motion to use is the uniform circular motion of a circular clock with hands.

A standard uniform circular motion allows spatial angles and temporal angles to be basically the same. The protractor measure of the position of a uniform circular motion and the circular clock measure of the time of the same uniform circular motion are equivalent.

Because of this, spatial and temporal angles have not been distinguished. But just as linear motion has both a length (distance) and a time (duration), so angular motion has both a spatial angle and a temporal angle. The existence of uniform motion does not change that in either case.

One may specify a distance by specifying a time at a constant rate of linear motion. Inversely, one may specify a time by specifying a distance at a constant rate of linear motion. Similarly, one may specify a spatial angle by specifying a time at a constant rate of circular motion. Inversely, one may specify a temporal angle by specifying a spatial angle at a constant rate of circular motion.

Circular motion involves multiple dimensions of time or space. Whether the time or the space have multiple dimensions depends on which one is considered the dependent variable. That in turn depends on whether a length (distance) or a time (duration) are taken as the independent variable.

For non-uniform motion the time and space measures are not proportional, and their difference should be obvious. That is known for linear measures; it is true for angular measures as well.

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