Can matter cycle through shapes eternally?

@article{Powell2013CanMC,
  title={Can matter cycle through shapes eternally?},
  author={Devin Powell},
  journal={Nature},
  year={2013}
}
'Time crystals' idea is challenged but its proponent doubles down. 
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References

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Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that…
Impossibility of spontaneously rotating time crystals: a no-go theorem.
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  • Physics
    Physical review letters
  • 2013
TLDR
A "no-go theorem" is proved, rigorously ruling out the possibility of spontaneous ground-state rotation for a broad class of systems.
Classical time crystals.
TLDR
This work considers the possibility that classical dynamical systems display motion in their lowest-energy state, forming a time analogue of crystalline spatial order, and exhibits models of that kind, including a model with traveling density waves.
Space-time crystals of trapped ions.
TLDR
The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter and are robust for direct experimental observation.