The phrase 'matter in motion', requires us to define matter and motion. Presently, motion is considered the trajectory of an object through Space-Time.

General Relativity is based on the same symmetries as Special Relativity, however it makes Space-Time reflexive to external things, such as matter, and energy (which are then in turn affected by curved space-time).

The second step was taken by Einstein, who included time as a dimension, to give us a four dimensional symmetrical picture of nature, though this symmetry is not entirely perfect.

Physical space is often defined as having three linear dimensions, though within Physics, it is considered with Time, to be part of a four dimensional continuum, known as Space-Time.