model selection math

This is an area of key integrative importance in this age of electronic ideastreams.

technical definition

Proper acceleration is the physical acceleration experienced by an object relative to a locally co-moving free-float frame. This may be quite different than the coordinate-acceleration seen in a separate reference frame (inertial or not) of co-moving yardsticks and synchronized clocks.

The proper-acceleration 3-vector, combined with a null time-component, yields the object's four-acceleration (as measured by the object itself) which makes proper-acceleration's magnitude Lorentz-invariant. Thus proper-acceleration comes in handy: (i) with accelerated coordinate systems, (ii) at relativistic speeds, and (iii) in curved spacetime.

Proper-acceleration reduces to coordinate-acceleration in an inertial coordinate system in flat spacetime (i.e. in the absence of gravity), provided the magnitude of the object's proper-velocity (momentum per unit mass) is much less than the speed of light c. Here we focus on situations where proper-acceleration and coordinate-acceleration are not always the same.