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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 (updated 2018):

lenticity (len·tis′·i·ty) is the rate of change of dischronment with respect to length. Mean lenticity is Δws. Puncstancial lenticity is dw/ds = dw/|dr|. From Latin lentus, slow. Symbol ℓ or u. (cf. velocity)

fulmentum is the lenticity divided by the mass. Cf. momentum. Symbolized by q. [was prolentum, etc.]

modal rate is the maximum or minimum 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 extreme conditions of the mode in the region (either fastest or slowest).

(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).

release is the retardation 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.

retardation is the rate of change of lenticity with respect to the travel length. A negative retardation may be called de-retardation. Symbolized by b. [was expedience, relentation, prestination, modulation]

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 pace (SMP) is the arithmetic mean of paces with a common space interval.

space mean speed (SMS) is the harmonic mean of speeds with a common space interval.

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 pace (TMP) is the harmonic mean of paces with a common time interval.

time mean speed (TMS) is the arithmetic mean of speeds with a common time interval.

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 dual 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 dual 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.

etherance (from ether + ance) is the inverse of mass. Units of kg-1. Symbolized by n.

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