If crystals exist in spatial dimensions, then they ought to exist in the dimension of time too, says Nobel prize-winning physicist.
One of the most powerful ideas in modern physics is that the Universe is governed by symmetry. This is the idea that certain properties of a system do not change when it undergoes a transformation of some kind.
For example, if a system behaves the same way regardless of its orientation or movement in space, it must obey the law of conservation of momentum.
If a system produces the same result regardless of when it takes place, it must obey the law of conservation of energy.
We have the German mathematician, Emmy Noether, to thank for this powerful way of thinking. According to her famous theorem, every symmetry is equivalent to a conservation law. And the laws of physics are essentially the result of symmetry.
Equally powerful is the idea of symmetry breaking. When the universe displays less symmetry than the equations that describe it, physicists say the symmetry has been broken.
A well known example is the low energy solution associated with the precipitation of a solid from a solution—the formation of crystals, which have a spatial periodicity. In this case the spatial symmetry breaks down.
Spatial crystals are well studied and well understood. But they raise an interesting question: does the universe allow the formation of similar periodicities in time?
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