A couple of models? Like?

Davis' and DET are the ones that spring to mind. Sure, you don't hear those words bandied about, but the principles are at play.

Thanks. Keep in mind, I said self-taught "physicist", certainly not mathematician. On top of that, I'm not even in the process of learning string theory or anything of the sort, and I'm not sure if topology is used *that* often in GR and such (unless we're getting very deep?). I can handle hyperbolic geometry and the very basics of metrics (not any real tensor stuff), at least for the sake of SR, but you won't see me doing any mathematical proofs any time soon.

Again, I know a bit more physics, but a bit less math that will cover it. The typical undergrad/PhD path of a physicist, in my opinion, covers even *less* math than I do (at least in proportion). If we're discussing things like the topology of spacetime, well I'd love to be as informed as possible to contribute, but I didn't expect any FET or DET to delve that far. I guess I stand corrected.

Maths and physics are pretty unavoidably intertwined. As far as what FET goes into, you don't get too much depth in most of the models, but they touch on a lot of concepts in a non-rigorous fashion. There's one user that idly mentions a non-Euclidean flat Earth to explain topics such as distances, but if you want to get into a good explanation of that you end up with the likes of:

[jsTex]d(P_1,P_2) = \cos^{-1} \left( \sin \left(\tan^{-1} \left(\frac{x_1^2 + y_1^2 -1}{2x_1} \right) \right) \sin \left(\tan^{-1} \left(\frac{x_2^2 + y_2^2 -1}{2x_2} \right) \right) +\cos \left(\tan^{-1} \left(\frac{x_1^2 + y_1^2 -1}{2x_1} \right) \right) \cos \left(\tan^{-1} \left(\frac{x_2^2 + y_2^2 -1}{2x_2} \right) \right) \cos \left|\tan^{-1} \left( \frac{y_1}{x_1} \right) - \tan^{-1} \left( \frac{y_2}{x_2} \right) \right| \right)[/jsTex]

You mentioned "Actually, I'd like to contribute some mathematically rigorous and testable arguments for FET that could hold water in a scientific light," which sounded like you were planning to go farther than FEers do. FET gets into complicated stuff fast, for better or for worse, so to test it you have to do likewise. DET relies entirely on altering the notion of space we have, Davis' non-Euclidean model leads to the above... If you want to avoid the topological, Scepti's denpressure model basically relies on reshaping the basic structure of molecules from the ground-up, postulating essentially an expanding ball-like object as the most fundamental particle and drawing conclusions from how they would vibrate, exert pressure...

There's a lot of pretty complicated stuff, basically. Physics isn't the biggest help because most of that gets rewritten.

So what's you take on Bolyai-Lobachevskian geometry Jane. Do you agree with the Bolyai dude when he stated that its just not possible to decide through mathematical reasoning that the geometry of our physical universe is Euclidean or non-Euclidean.....

But you do have to take what those Magyars say with a pinch of NaCl. Don't you think?

You could just say hyperbolic geometry. You can't deduce anything about the physical universe by mathematical reasoning alone, you have to go out and take measurements and run tests. When you do, well, it depends. In some geometries you'll find contradictions, in others you won't. However, we have found rather persuasive evidence that the geometry of our physical universe is best modeled by Minkowski space rather than Euclidean, so I'd have to say it is possible.

I mean, it's pretty clear you're just trolling, but there's your answer anyway.