I’ve been revising the glossary lately, see above. This required adjusting the post on Foundations of mechanics for time-space, among others. Here is an explanation:
Ordinary 3D space is measured by distances. Correspondingly, 3D time is measured by durations. That is, 3D time is a space of times. Call this time space.
Ordinary 1D time is the distime relative to a reference instant. Correspondingly, 1D space is the distance relative to a reference point, which may be called the station, a term from surveying in which a station is a point from which measurements are made. These scalars may be used as independent variables.
1D time is that which is measured by a clock. What is 1D space measured by? We need a measure of distance relative to a reference point. Since it is independent, it may continue indefinitely. A measuring wheel (surveyor’s wheel) would do that if it keeps going. Or the Voyager 1 spacecraft continuing into space, see here. Call this an odologe, from Greek odo(s), way/path + (horo)loge, clock.
Mechanics studies the motion of bodies in 3D space over 1D time. Correspondingly, mechanics can study the motion of time bodies in 3D time over 1D space. What is a time body? It’s a body but its dimensions are distimes, not lengths. That is, it is a body for motion, or a vehicle.
A body in dynamics is conceived as a collection of particles. What is a time body composed of? A time body is conceived as a collection of tempicles. A tempicle is a point vass with a destination, as a particle is a point mass.
Inertia is the resistance of a body to any change in its state of motion. Correspondingly, facilia is the nonresistance of a time body to a change in its state of motion. Inertial reference frames move at constant speed in a straight line. Facilial reference timeframes move at constant pace in a straight line. Because of the inverse relation between speed and pace, inertial and facilial frames are equivalent.