>>183849857>Time crystals are defined by oscillation in their lowest-energy state
What? Time crystals are systems that break continuous time translation symmetry group into a discrete subgroup. One of the consequences of this is the fact that they need only conserve energy up to a "reciprocal time-scale" E0. This means that there is no single-valued definition of what energy is, let along what "low energy" means since any state with energy E and E + E0 are the same.
This lets systems acquire infinite degeneracy even in the absence of other discrete symmetries, which leads to macroscopic condensation, bosonization, fractional statistics, etc BUT no time travel capabilities.