Terms for motion again

Previous posts deal with terms for motion, such as here. Further thoughts are below.

When someone asks about the length of a trip, they are not asking for the distance between the origin and destination of the trip – that is the magnitude of the displacement. They are asking about the length of the route taken. Mathematically, travel length is the arc length of the curve of the route.

The length of a trip in time, or travel time, is the duration of a trip. Time is a kind of length, not a distance; an arc length, not a straight-line distance.

The magnitude of a displacement is the distance between two points. Call the magnitude of a dischronment between two points in time the distime. This is the shortest-length travel time between them, which depends on the mode of travel.

We have the expression “as the crow flies” to distinguish the straight-line distance between two points from the travel length. Physicists would say “as light travels” to indicate the straight-line (geodesic) distance or time between two events.

While physicists may convert time and space dimensions (by multiplying time by the speed of light, or dividing length by the speed of light), this does not change the character of the dimensions. Only if the time and space dimensions are switched does their character change.