A crystal with cubic symmetry moving at a relativistic speed would appear to have lost that symmetry as viewed from the stationary frame due to Lorentz contraction of its axis in the direction of movement. How can we account for this illusory change of symmetry group?
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$\begingroup$ Why do we need to account for it? Surely the explanation is simply length contraction? $\endgroup$– Professor SushingCommented Nov 4 at 10:31
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$\begingroup$ How is the at-rest symmetry formally captured? Is it a Lagrangian with some set of translation operators that leave it invariant? $\endgroup$– JEBCommented Nov 4 at 13:13
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$\begingroup$ My question is whether we should accept as a fact that a crystal that we know full well to be cubic, in another frame of reference must be treated as tetragonal (with the same level of reality) and, if so, how we should modify the analysis of interactions between atoms in the crystal. $\endgroup$– victor kazanskiyCommented Nov 4 at 13:59
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$\begingroup$ Sounds like a bunch of messy math to arrive at the answer in the rest frame of the crystal. $\endgroup$– Jon CusterCommented Nov 4 at 17:11
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$\begingroup$ Hi Victor. Understood. I tend to agree with Jon's comment. I modelled crystalline solids for my PhD and it was hard enough in an implicitly assumed rest frame. $\endgroup$– Professor SushingCommented Nov 5 at 6:36
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