Noether's Theorem states that for every symmetry there exists a corresponding conservation law.pic.twitter.com/n9Gpaqeknt
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I don't think there's a simple answer to that (or at least I don't know of one). But there's some nice discussion of this here: https://physics.stackexchange.com/questions/24596/is-the-converse-of-noethers-first-theorem-true-every-conservation-law-has-a-sy … I'm assuming you meant converse by 'opposite'?
Though I will say that something being conserved makes one highly suspicious of a symmetry
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Definitely. In practice physicists will tend to work under the assumption that there is a symmetry underlying all conservation laws that they find and I think in certain settings that's even justifiable. I just don't think there's actually a theorem that guarantees this?
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