Or even 4 dimensional quantum time crystals (which surprisingly, doesn't appear to be completely mental) - http://arxiv.org/abs/1202.2539
Course, you can't take any power off them and you have to put them somewhere very very cold, but they will keep going, apparently.
As for the second, we know there are issues with the current physics and I think that might just be what stuff like CERN is for. Or to prove it really really well.
First one, liquids with zero viscosity, such as helium superfluids. - http://www.sciencemag.org/content/286/5438/213.summary
Or even 4 dimensional quantum time crystals (which surprisingly, doesn't appear to be completely mental) - http://arxiv.org/abs/1202.2539
Course, you can't take any power off them and you have to put them somewhere very very cold, but they will keep going, apparently.
As for the second, we know there are issues with the current physics and I think that might just be what stuff like CERN is for. Or to prove it really really well.