[drbaskin]

I haven't read Smolin's paper, so I'm not sure exactly what this article is getting at. Is he suggesting that there should be a different connection (i.e., not the Levi-Civita one) on the cotangent bundle of spacetime or is it something more pedestrian? Is he just doing microlocal analysis on spacetime? If the latter is the case, this article doesn't describe what is (mathematically) new about it.

On a second read of this article, it seems clear that my interpretation above is incorrect. It might still be that they are coming up with physical interpretations of microlocal analysis on curved spacetimes. (Though how you fix a quantization, I'm not sure.)

I'm not a physicist and have not read the original source, so please take anything I say with a large dose of salt.

[bermanoid]

As confused as this article seems, it does at least reference one Actual Paper: http://arxiv.org/PS_cache/arxiv/pdf/1101/1101.0931v2.pdf

I haven't had a chance to look through it yet, but here's the abstract:

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them.

This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.