Yeah, but I want to differentiate between things that we know HOW to test, but CAN'T until we achieve some new technological milestone (like a more powerful supercollider, or probes that are light-years away), vs. those things for which we can't even devise a good gedanken experiment to validate/invalidate.
I sympathize with that point of view. But I've recently been reading the history of the Dirac equation. That equation, which predicts the existence of anti-electrons (positrons), was developed by Dirac from just fooling around with trying to put special relativity together with the new quantum mechanics of Heisenberg and Schrödinger. Dirac played around until he got something interesting, then was able to predict some spectral deviations that non-relativistic QM couldn't predict...and he also got the prediction of anti-matter, too, which was a neat plus (er, minus?). Anyway, the Dirac equation turns out not to be right, but it was right for its time, and now it has been re-interpreted in Relativistic Quantum Field Theory as an operator equation, and all is well (within its range of applicability).
The point? We don't always know where our mathematical imagination, guided as far as possible by physical insight, is going to lead. Sometimes the mathematics and the physics get out of phase (which seems to be happening now); but I trust that that will be taken care of in the future.
...and he also got the prediction of anti-matter, too, which was a neat plus (er, minus?).
Actually, in the case of the positron, it was a plus!
IIRC, the Dirac equation allowed for the existence of magnetic monopoles as well.
IIRC (again), Van Vleck and others were insistent that there were no such beasts...