Sunday, 15 March 2009

Special Relativity is not Compulsory

Katsushika Hokusai: The Great Wave off Kanagawa
One of the foundations of Twentieth Century relativity theory was the idea that Einstein's early "special-case" theory of relativity ("Special Relativity", or "SR") had to appear as a complete subset of any larger and more sophisticated models.

At first glance, this seemed unavoidable.

Einstein's later and more sophisticated general theory was at its heart a geometrical theory of curved spacetime... it described gravitational fields in terms of how they warp lightbeam geometry, and then used the principle of equivalence to argue that the effects associated with accelerations and rotations must also follow the same set of rules. We could then model all three classes of effect as an exercise in curved-spacetime geometry, and go on to extend the model to include more sophisticated gravitomagnetic effects.

But Einstein's general theory didn't attempt to apply these new curvature principles to simpler problems involving basic relative motion, because his earlier special theory had already dealt with those cases by assuming flat spacetime. Instead of going over the same ground a second time, Einstein simply said that, just as classically-curved surfaces reduced over sufficiently small regions to apparent flatness, so the geometry and physics of general relativity, if we zoomed in sufficiently far, ought to reduce to flat spacetime and the "flat-spacetime" version of physics described by the special theory.

There were good pragmatic reasons for Einstein's adoption of special relativity as a foundation for GR, but geometrical necessity wasn't one of them. Here's why:
... It's true that if we zoom in on a GR-type model sufficiently far, we end up with effectively-flat spacetime, but this doesn't automatically mean that we then have flat-spacetime physics. It might instead mean that we've zoomed in so far that there's no longer any meaningful classical physics to be had. We have to accept at least the logical possibility that real physical particles (and their interactions) might be unavoidably associated with spacetime curvature, and in that scenario, we can't derive their relationships by presuming absolutely flat spacetime, because that condition would only be met if our particles didn't physically exist.

Allow any form of velocity-dependent curvature at all around moving particles, and SR's flat-spacetime derivations fracture and fail. This is especially unfortunate since the experimental evidence suggests that moving particles do seem to disturb the surrounding lightbeam geometry, just as we'd expect if curvature effects were a fundamental part of physics, and if the flat-spacetime basis of special relativity was wrong.


This suggestion that "all physics is curvature" was put forward at the end of the Nineteenth Century by a mathematician called William Kingdon Clifford, who's usually remembered for having his name on Clifford Algebra. The critical thing about a "Cliffordian" model in this context is that when we implement the principle of relativity within it, we find that the resulting physics doesn't reduce to special relativity and the relationships of Minkowski spacetime. Instead of a Minkowski metric, it reduces in the presence of moving particles to something that looks more like a relativistic acoustic metric, and which appears to be much more compatible with quantum mechanics than our current classical models.

So the perfect, unbreakable geometrical proofs of SR's inevitability as physics aren't complete. In order to complete them, we have to be able to show that Cliffordian models can't work ... and that seems to be difficult, because the results of taking a Cliffordian approach seem to be pretty damned good.

To date, nobody seems to have been able to come up with a convincing disproof of this class of curvature-based solution, and until that happens we have to accept the possibility that special relativity might not be a part of our final system of physics.

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