Diachronic and synchronic physics

Diachronic, 1857, from Greek dia “throughout” + khronos “time” means something happening over time, particularly the historical development of something such as a language through time.

Synchronic, 1775, means “occurring at the same time,” from Late Latin synchronus “simultaneous,” means the analysis of something such as a language over a wide area at a point or period in time.

The terms diachronic and synchronic may be used to distinguish two approaches to the analysis of anything with spatial and temporal aspects. The diachronic approach stays with one place or people and focuses on the development through time. In transportation it is the perspective on a moving vehicle or data gathered from inside moving vehicles. The synchronic approach looks at a wide area or multiple places at a point in time or within a particular time period. In transportation it is the perspective from the side of the road, on the earth.

Diachronically, the pace of each vehicle is measured from as the ratio of its travel time over a road segment. The (arithmetic) average pace or harmonic average speed is the space mean traffic speed for the length of roadway.

Synchronically, vehicle speeds (spot speeds) are measured from sensors at a location on the road over a period of time. The (arithmetic) average is the time mean traffic speed for a given period of time.

Physics normally uses speeds, not paces, combined with the time displacement and so is synchronic. If the pace is used instead of the speed, combined with the length displacement, physics is diachronic. The laws of physics are the same in either case: space and time are symmetric. For example, the Lorentz transformation:

x’ = γ (x – vt), y’ = y, z’ = z, and t’ = γ (t – vx/c2)

may be interpreted as spatial coordinates x, y, and z, time displacement t, and speeds c and v; or as temporal coordinates x, y, and z, length displacement t, and paces c and v.