The Curvature Of Space-Time Reconstrued Through Systemic Functional Linguistics

Davies & Gribbin (1992: 84):

Einstein realised that tidal forces cannot be transformed away by changing the reference frame — they represent a genuine effect of the gravitational field at work. He reasoned that if the effect of these forces is to stretch or distort the distances between freely falling objects, then the most satisfactory description of tidal gravitation is as a distortion or stretching of spacetime itself. That is, rather than regard gravity as a force, Einstein proposed that we regard it as a curvature or warping of spacetime.

Blogger Comments:

To be clear, gravity is the relative contraction (not stretching) of space intervals due to the presence of matter. The tidal bulges on the Earth and the Moon are manifestations of the fact that the space intervals between the two bodies are relatively contracted. On the other hand, gravity is the relative expansion of time intervals — the time interval between each tick of a clock is expanded — such that processes unfold relatively more slowly.

So while it is true that gravity is, in this sense, a warping of spacetime, it is neither the stretching of space, nor the curvature of spacetime. What gravity curves is the geodesic trajectory of a body through space, not the three spatial dimensions through which it moves, nor the dimension of time along which the process unfolds.