All Physics as Curvature?

William Kingdon Clifford (1845-1879) was an Nineteenth Century mathematician and geometer commemorated by modern mathematicians by having Clifford algebra named after him. He was also a fellow of the Royal Society and The Metaphysical Society, wrote a children's book, and made the occasional cutting remark about the inadvisability of trusting the opinions of groups of experts (unless one knew for a fact that at least one of the group had personal first-hand knowledge of the thing that they were talking about).

Amongst relativists, Clifford is remembered as having been one of the first people to come out unambiguously in favour of the idea that physics could (and should) be modelled as a problem involving curved space.

In 1870, Clifford addressed the Cambridge Philosophical Society ("On the Space-theory of Matter" *), declaring:

"...
I hold in fact,

1. That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them.
2. That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave.
3. That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial.
4. That in the physical world nothing else takes place but this variation subject (possibly) to the law of continuity.
   

... "

In other words, according to Clifford, matter was simply a persistent local curvature in space. While some other well-known theorists of the time (such as Oliver Lodge) were were interested in the idea of describing matter as a sort of condensation of a presumed aetherial medium, and using ideas from fluid dynamics as a shorthand for the properties of space, Clifford considered the mathematical curvature-based descriptions as more than just a means of expressing the variation in field-effect properties associated with density-variations and distortions of an underlying medium: for Clifford, the physics was simply the geometrical curvature itself.

Clifford was one of a number of C19th mathematicians working on geometrical descriptions of physics considered as a curved-space problem, a loose association of broadly similar-minded researchers whose presentations were sometimes propagated in lectures rather than in published journal papers (and who were memorably referred to by James Clerk Maxwell as the "space-crumplers".

Clifford's view was influential, but his vision arguably wasn't quite implemented by Einstein's general theory of relativity – although GR1915 implemented curvature-based descriptions of gravitation, rotation and acceleration effects, it still fell back on an underlying flat-spacetime layer when it came to describing inertial mechanics (that layer being special relativity).

This seems to be fixable, but we're not there yet.

* "William Kingdon Clifford, Mathematical Papers", (1882) pp.21-22