quantum field theory - What sort of experiment would directly test time reversal invariance?

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?

Answer

As an update on this old thread, the 2015 version of the Particle Data Group review on tests of conservation laws (the 2009 version of which was rightly pointed to by invisiblerhino) has an interesting update:

The BABAR experiment has reported the first direct observation of $T$ violation in the $B$ system. The measured $T$-violating parameters in the time evolution of the neutral $B$ mesons are $∆S^+_T = −1.37±0.15$ and $∆S^−_T = 1.17±0.21$, with a significance of $14σ$ [4]. This observation of $T$ violation, with exchange of initial and final states of the neutral $B$, was made possible in a $B$-factory using the Einstein-Podolsky-Rosen Entanglement of the two $B$'s produced in the decay of the $\Upsilon(4S)$ and the two time-ordered decays of the $B$'s as filtering measurements of the meson state [5].

Pointing to the reference

[4] J.P. Lees et al., Observation of Time-Reversal Violation in the $B^0$ Meson System, Phys. Rev. Lett. 109, 211801 (2012), arXiv:1207.5832.

which has pretty much what it says. For an entry-level explanation of that paper, the APS Physics Viewpoint: Particle Decays Point to an Arrow of Time is probably a good place to start. That article probably does a much better job than I could at explaining the particulars, but I'll note here that, with a $14σ$ significance, this experiment does seem to mean that

the long wait for an unequivocal time-reversal violation in particle physics is finally over.