Recent experiments at ultra-cold temperatures have shown a phenomenon known as "neutron loss," in which we somehow lose track of these subatomic particles for short periods. This probably has a mundane explanation...but just for fun, here's an awesomely insane explanation.
The idea put forward by Zurab Berezhiani and Fabrizio Nesti, a pair of theoretical physicists at Italy's University of l'Aquila, is that these neutrons have mirror particle twins that exist in some sort of parallel world. Any neutron could theoretically transition from one world to the other, swapping places with its mirror particle twin - which would be invisible to us, explaining why we seem to "lose" the neutrons - and then returning in a period lasting anywhere from a few seconds to ten minutes.
It's definitely an out there hypothesis, but Berezhiani and Nesti point out that it can't be ruled out by what we currently know experimentally. Of course, that's a pretty weak argument in and of itself, but there do seem to be a few pieces of evidence that support their idea - and, even better, there might be a way to test the hypothesis experimentally.
Specifically, Anatoly Serebrov's research group at France's Institut Laue-Langevin found evidence that the loss rate of neutrons appeared to be dependent on the surrounding magnetic field, with the field's direction and strength both able to affect how the neutrons disappeared. According to Berezhiani and Nesti, we can't currently explain that apparent effect in terms of known physics - but their physics might just do the trick.
Basically, if Earth is surrounded by a "mirror" magnetic field with a flux density of about 0.1 Gauss, then it would be able to facilitate neutrons' oscillations between worlds in the way that Serebrov's research group observed. Earth could have built up such a mirror magnetic field by capturing stray mirror particles floating through the galaxy - and those particles might well be one of the components of the still mysterious dark matter.
It's an exotic explanation for what could very well a very mundane sort of problem, but still - any hypothesis that combines parallel worlds, mirror particles, and dark matter is always worth a look. You can check out the entire original paper right here at the European Physical Journal.