The Curvature of Space-Time Through Systemic Functional Linguistics

Davies & Gribbin (1992: 84-5):

In a sense, the curvature of starbeams passing near the Sun can be regarded as a direct probe of the curvature of space. But it is important to appreciate that the curvature involves spacetime, not just space. The Earth follows a closed, elliptical orbit around the Sun, and on first acquaintance with general relativity it is natural to guess that this means the planet is following a path through curved space dictated by the gravitational field of the Sun. …

Viewed in spacetime, the Earth's orbit is not a closed ellipse, but a shape like a coiled spring, or helix. After each orbit of the Sun, the Earth returns to the same place, but to a different time, advancing one year along the time 'axis' for each orbit around the Sun. …

So the correct image of the Earth's orbit in terms of curved spacetime is a very shallow curve, weaving around the line that represents the path of the Sun through spacetime.

Blogger Comments:

From the perspective of Systemic Functional Linguistic Theory, the General Theory of Relativity models gravity as the relative contraction of space intervals and the relative expansion of time intervals with increasing proximity to a centre of mass. Because of this contraction, the shortest distance between two points — the geodesic — near a centre of mass will be towards that centre of mass, which means that the trajectory of a body in the vicinity, unless acted upon by another force, will be curved towards that centre of mass. 

Accordingly, the curvature of starbeams passing near the Sun is indicative of contracted space intervals, not curved space, and it is the trajectory of the Earth around the Sun that is curved, not space.

By the same token, the helix in Figure 17 is not the curvature of space-time, but the curved trajectory of the Earth through space plotted against time. The non-curvature of space-time is represented by the non-curvature of the space and time axes in Figure 17.