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Terminology for time-space

It has been thought best to introduce new terms for the physics of time-space since although in some respects the concepts are similar to standard terms of physics, in other respects they mean the opposite to those of space-time physics. Here is a compilation:

celentum is the allegrity divided by the mass. Cf. momentum. Symbolized by q. [was prolentum]

allegrity (al∙leg′∙ri∙ty) is the space rate of change of temporal position of a body; it is a vector quantity having temporal direction as well as magnitude. By space rate of change is meant the rate of change in time per unit of trajectory length. It is equivalent to a specification of the pace and direction of motion (e.g., 60 s/km toward magnetic north). Cf. velocity. Symbolized by ℓ. [was celerity, progressity]

modal rate is the pace or speed which is characteristic of a mode of movement or travel in a region or universally. A modal rate has the following properties:

(1) The rate is relative to a mode of movement or travel in a region.

(2) The rate reflects the normal conditions of the mode in the region.

(3) The rate serves as a general conversion between space and time for some region or universally.

Speeds less (paces greater) than the modal speed are submodal (cf. subluminal). Speeds greater (paces less) than the modal speed are supermodal (cf. superluminal).

surge is the modulation divided by the mass. Cf. force. Symbolized by M.

pace is the space rate of change of temporal position of a body without regard to temporal direction. By space rate of change is meant the rate of change per unit of travel distance (trajectory length). Pace comes from Latin passus, a step or stride, which relates to the unit of length in the denominator, as when walking or running. Units of s/m, min/mi, etc. Cf. speed.

modulation (mod∙u∙la′∙tion) is the rate of change of allegrity with respect to the magnitude of displacement. A negative modulation may be called demodulation. A small positive modulation leads to faster movement. Symbolized by b. [was retardation, relentation, prestination]

space is the length of a trajectory asynchronously compared with a reference trajectory. Units of metres, etc. Symbolized by r (with or without subscripts) or by x, y, and z.

space mean speed is the arithmetic average speed of objects over a common trajectory during a specified period of time, i.e., the average travel time divided by the specified length. If speeds are constant, it equals the harmonic average of objects passing a point in space during a period of time (spot speeds).

space-time is a four-dimensional continuum with three dimensions of space and one dimension of time.

time is the duration of a trajectory synchronously compared with a reference trajectory. Units of seconds, etc. Symbolized by t (with or without subscripts).

time mean speed is the arithmetic average speed of objects passing a point in space during a specified period of time (spot speeds). Time-mean speeds are commonly used in reference to a single point along a common trajectory, averaged over a time period.

time-space is a four-dimensional continuum with three dimensions of time and one dimension of space.

Galilean time-space means the measurement of space is the same for all observers, which is called absolute space, whereas the measurement of time is relative to the motion of each observer. The Galilean time-space transformation (also called the co-Galilean transformation) is as follows:
speed: = t – r/v,
pace: = t – ur,
and for all other coordinates the primed and unprimed values are equal. The reason the other coordinates are equal may be either because there is no motion in their direction or other directions are not known to exist.

Lorentz time-space is the Galilean time-space plus the principle of relativity, so that the Lorentz time-space transformation (also called the co-Lorentz transformation) includes a factor, γ, in the equation for the direction of motion, along with the modal rate, c:
speed: t′ = γ (tr/v) with γ = (1 − /)–1/2,
pace: t′ = γ (tur) with γ = (1 – /)–1/2,
and equal values for the other corresponding primed and unprimed coordinates. It applies only if |v| > |c| or |u| < |b|.

trajectory is the path that a body follows through space and time.

vass (from vast) is the inverse of mass. Units of kg-1. Symbolized by ℓ or L.

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