What I’ve called the *characteristic rate* (modal rate) of travel or motion may be any rate independent of the travel mode, such as the typical, minimum, or maximum rate. The best-known example is the speed of light in a vacuum, *c*, which is generally considered the maximum speed for physics.

A characteristic rate that is a minimum speed may be appropriate in some contexts. A simple example is on expressways or freeways in which a minimum speed is posted. Another example is racing, such as automobile racing, in which a car going too slowly is black-flagged or pulled from the race.

Some have suggested that there is a minimum speed for physics (for example, *here*). I take the same approach with a minimum speed as with superluminal particles: the concept makes sense in a larger context, whether or not it is confirmed in physical science. There may also be reasons why the concept is valid for physics.

If there is a minimum speed, it transforms like the superluminal transformation, which has been shown *here* before:

*r′* = *γ* (*r* − *c²* *t*/*v*), *t′* = *γ* (*t* − *r*/*v*) with *γ* = (1 − *c²*/*v²*)^{–1/2} for |*v*| > |*c*|.

The maximum speed, *c*, is a ratio of travel distance and travel time: *c* = *Δr*/*Δt*. This may also be expressed as a pace *Δt*/*Δr* = 1/*c*. In the case of *c*, it is the ratio of a large travel distance and a small travel time, say *r _{high}* and

*t*. Convert these into

_{low}*r*and

_{low}*t*with the conversion factor,

_{high}*c*. That is,

*r*= c

_{low}*t*and

_{low}*t*=

_{high}*r*/

_{high}*c*. Then the ratio of

*r*and

_{low}*t*must also be a constant independent of reference frame. That is:

_{high}*r _{low}* /

*t*= c

_{high}*t*/ (

_{low}*r*/

_{high}*c*) =

*c*(

*t*/

_{low}*r*)/

_{high}*c*=

*c*(1/

*c*)/

*c*= 1/

*c*,

which equals the minimum speed independent of reference frame.

But what about a speed of zero, the state of rest? That would be smaller than 1/*c*. It may well be that for most purposes, 1/*c* ≈ 0. But physical phenomena at nanoscopic scales may show a minimum speed of 1/*c*. It could be called the speed of matter. Its existence is an empirical question.