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As title states, I wish to know whether fundamental symmetries (in the most general sense of the word, e.g. gauge symmetries, Lorentz invariance, diffeomorphism invariance, not necessarily just global symmetries/isometries) are believed to be exact or in fact just an approximation. I understand that arguments from symmetry are core to the development of many physical theories (e.g. gauge theories in general), but do we believe they should hold always. I.e. do we have evidence to suggest they hold at all energy scales, all times, etc. If not, does it make sense to think of them as approximations?

Moreover, this may be a misguided question, but if certain symmetries were fundamental, why do all physical theories across different fields/regimes not share the same ones?

An example to maybe clarify my meaning: in much of QFT Lorentz invariance is taken to be a fundamental guiding principle, but (without going into details) in GR we must do away with (global) Lorentz invariance. Should one really think of the flat-space Lorentz invariance of QFT as just an approximation/emergent symmetry, but not truly fundamental?

Any comments on clarification of question welcome, apologies for the wordiness. Here is a similar question What would it mean if symmetries are not fundamental at all? but the context is string theory and does not answer the question presented here.

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All symmetries are approximate; otherwise they may not be observed at all ;-)

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  • $\begingroup$ This is very true indeed! But we build our theories in a way that maintains these symmetries 'from the bottom up', so to speak - does it not make more sense [for the symmetries] to go 'from the top down'? $\endgroup$ – user290954 Apr 24 at 9:45
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    $\begingroup$ There are many ways of building theories. Some prefer an axiomatic approach, some others use a phenomenological way, and some use combinations. I wrote a paper containing some fresh ideas here: arxiv.org/abs/1409.8326 $\endgroup$ – Vladimir Kalitvianski Apr 24 at 11:14
  • $\begingroup$ see Anthony Zee's most excellent book, Fearful Symmetry. $\endgroup$ – niels nielsen Apr 24 at 18:54

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