The Curvature Of A World Line Viewed Through Systemic Functional Linguistics

Penrose (2004: 389):

We can also consider world lines that are not geodesics. In ordinary spatial terms, these represent particle motions that accelerate. The actual magnitude of this acceleration is measured, in spacetime terms, as a curvature of the world-line. According to Newton’s second law, this acceleration is equal to the total force on the particle, divided by its mass. (This is Newton’s f = ma, in the form a = f ÷ m, where a is the particle’s acceleration, m is its mass, and f is the total force acting upon it.) Thus, the curvature of a world line, for a particle of given mass, provides a direct measure of the total force acting on that particle.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the curvature of a world line is not the curvature of spacetime, but the curvature of a process (motion) in spacetime. This confusion of process with circumstance accounts for the misconstrual of the curvature of trajectories (geodesics) as the curvature of spacetime, in the General Theory of Relativity.