iSoul In the beginning is reality

3D time + 1D space, pace, and celerity

Although there are three dimensions of space and three dimensions of time, I have pointed out before that we measure movement as either 3D space + 1D time (3+1) or 1D space + 3D time (1+3) or 1D space + 1D time (1+1). The (1+3) perspective is the focus of this post.

The measurement of movement in which time is multidimensional but space is not requires that instead of speed and velocity, one must use pace and what I have called celerity. That is, movement is measured by the change in time (duration) per unit of movement in space (length or distance). Pace is the directionless version of this.

For example, instead of speed in meters per second, one would use pace in seconds per meter or the like. This is not exactly the inverse of speed because the dependent units are different. Speed normally means the space speed, that is, the distance traveled in a fixed period of time. The time speed is a fixed travel distance per the corresponding travel time (which is strange because the independent variable is in the numerator). The pace is the time speed inverted, which puts the independent variable back in the denominator.

Celerity is the directional version of pace. An inertial system is a frame of reference that is at rest (zero velocity) or moves with a constant linear velocity. This can be expanded to include a frame of reference that is at zero or constant linear celerity.

Zero celerity means there is no change in time (duration) per unit of distance moved. We easily understand no change in distance per unit of time but this is strange. We have to remember that here the independent unit of motion is distance, not duration. In this context the distance measures the flow of movement (misleadingly called the flow of time).

So zero celerity means there is no change in time (duration) while a unit of distance passes, as by a “distance clock” like the odometer of an automobile moving at a constant rate. I have written about this here.

In classical (3+1) physics, time has an absolute meaning, independent of an observer. For a classical version of (1+3) physics space has an absolute meaning, independent of the observer. That is, either time or space continue indefinitely, and always serve as an independent variable, never as a dependent variable.

So there is always available information about an independent, inertial movement that provides a standard reference to measure any other movement. For absolute time this is called a clock or watch. For absolute space it could be called a distance clock (discussed here, here, and here). Then movement could always be measured by reference to this independent, standard movement.

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