I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to check this? Have any of them been performed?
I know that there are indirect tests of time reversal invariance by observing CP violation, in the decay $K_L \to 2\pi$ for example. Then if you assume that the necessary conditions for CPT symmetry are satisfied in our universe, that means there must be time reversal symmetry violation as well. But I'm curious about ways to test time reversal invariance without relying on CPT.
Basically, how could we distinguish between the standard model, which predicts T violation, and some hypothetical other theory that matches current experimental results as well as the SM, but in which CPT symmetry does not hold?
P.S. This may be more of a research-level question, but I'm hoping it won't be too obscure for this site ;-)