Actual and possible motion

This post continues the topic posted here.

The action motion of a particle or rigid body may be measured by the scalar (or 1D) rate of motion, expressed as a speed or a pace. The numerator of a speed is the measured length or travel distance, and the denominator is the unit of time or the measured travel time. The pace is the inverse.

The possible motion of a particle or rigid body is limited to three dimensions of motion. This may be represented as a rate of motion in a Euclidean space of three-dimensions. The rate of motion is the speed or pace. With the direction of motion this is the velocity or lenticity.

If time (travel time) is held constant, this becomes a spatial 3D Euclidean geometry, commonly called “space”. If length (travel distance) is held constant, this becomes a temporal 3D Euclidean geometry, which may be called “time-world”.

The combination of space and time-world is a 6D Euclidean geometry of possible representations. This is not the extent of motion but the extent of the representation of motion, the next level of abstraction.