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Symmetry becomes much more easy to grasp if you think of it only in terms of transformations - in this case coordinate transformations. If you for example rotat

Symmetry becomes much more easy to grasp if you think of it only in terms of transformations - in this case coordinate transformations. If you for example rotate your system by a few degrees, does it look the same if you were to overlay it with the initial state (imagine the crystal as an infinite lattice). If yes, you have found a symmetry. For a crystal structure, you usually only have some discrete symmetries, i.e. you can maybe rotate by multiples of 90 degrees or shift axes by multiples of a certain length, but apart from these things the "inherent" rotational and translational symmetry of empty space is gone. What they're calling "spontaneous symmetry breaking" here is technically correct, but in this context it's a pretty trivial observation (I mean, yeah, it is a lattice after all) without any deep insight, as opposed to the Higgs mechanism for example.

zarzavat 4y ago
It’s counterintuitive because most people are more familiar with the mathematical concept of symmetry whereby a lattice has more symmetry than a random set of points (which almost certainly has no symmetry at all). However from the physics point of view, the random set of points is more symmetrical than the lattice because there’s no way of telling which way a random set of points is oriented.
- sigmoid10 4y ago
  Symmetry in physics is not just about orientations in space. This notion rather comes from the fact that large systems of discrete points are often described using continuum mechanics or field theory, which naturally has a lot more symmetries. But even a set of randomly distributed point-like particles can have symmetries. If the set was made up of identical bosons for example, it would have a wave function symmetry under particle permutations. And real particles would also exhibit a whole lot of other discrete symmetries, like CPT symmetry at the very least.

zarzavat 4y ago

It’s counterintuitive because most people are more familiar with the mathematical concept of symmetry whereby a lattice has more symmetry than a random set of points (which almost certainly has no symmetry at all). However from the physics point of view, the random set of points is more symmetrical than the lattice because there’s no way of telling which way a random set of points is oriented.

sigmoid10 4y ago
Symmetry in physics is not just about orientations in space. This notion rather comes from the fact that large systems of discrete points are often described using continuum mechanics or field theory, which naturally has a lot more symmetries. But even a set of randomly distributed point-like particles can have symmetries. If the set was made up of identical bosons for example, it would have a wave function symmetry under particle permutations. And real particles would also exhibit a whole lot of other discrete symmetries, like CPT symmetry at the very least.