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:
"...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.
I hold in fact,
- 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.
- 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.
- 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.
- That in the physical world nothing else takes place but this variation subject (possibly) to the law of continuity.
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