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I was having a discussion with a physicist asking him whether there could be any process, compatible with our current knowledge of physics, where the universe would be left without any fundamental symmetries (no Lorentz symmetry, no gauge symmetries, no conservation laws symmetries...etc).

This is what he told me:

If a vacuum decay would occur, and a high energy density is released, we would have a state far away indeed from the newly reached vacuum, and if the sate is not near the vacuum below then such a vacuum would not be relevant for physicists living in such a situation. They would hardly know if there were a vacuum ''behind'' the situation they would live in. They would rather think of something like the actual hot situation as the only state they could consider in reality. But this hot state would have no symmetries because there would be particles around breaking any symmetry. I think that what I am saying is that we only have the great amount of symmetries in our present theory becourse we are sufficiently close to a vacuum situation, with a huge amount of symmetries, but without such an almost realizable - but still just imagined - vacuum state with a lot of symmetry we would not ``see'' the many nice symmetries. So if one comes too far from a vacuum with high symmetry we can't conceive the symmetries.

However, this sounds to me as if, while in the state no symmetries would appear, there would be actually symmetries at the fundamental level (the vacuum). But perhaps I am making the wrong picture. So, even if there was so much heat produced that the state would be completely different from the vacuum where it would "rest upon", would that still mean that fundamentally there would be no symmetries?

And also, I've read some models and theories in physics that assume that, as we turn backwards the history of the universe and approach the Big Bang (and heat and energy density would continuously grow) we would find more and more symmetries. Even if that was true, could somehow the situation that this physicist described give as a result a state with no symmetries at all?

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  • $\begingroup$ Is the quoted text quoted verbatim or reconstructed from memory? Because there are a few loose ends. $\endgroup$ Commented Jul 9, 2022 at 21:52

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The question is a bit vague and conceptual, so allow me for a vague, conceptual and comment-like answer.

  • About your original question, before the quoted text.

    1. Regarding gauge symmetry. This is just a redundancy in the description. So it is not a physical symmetry. Nature doesn't know about gauge symmetry. Everything you see has to be gauge-invariant. So it should be excluded from the question of whether or not the universe has fundamental symmetries.

    2. Now to the interesting part. It is strongly believed, that once you turn on quantum gravity, any symmetry should be broken or gauged (and hence lost, cf. the above point).

      Originally, the argument for that goes as follows: Imagine you have a global symmetry and an associated conserved Noether charge $Q$. You can take a large number (say $N$) of particles with charge $q$ and collapse them into a black hole, with total charge $Q=N\, q$. Then let it evaporate completely until it is just Hawking radiation. But Hawking radiation cannot carry charge, so we lost our charge in the process. Thus we have a process violating charge conservation, and hence invalidating the assumption that we had a global symmetry to begin with.

      There are also more refined arguments, both for this and for a bit more general types of symmetries, but still, it is not a completely closed case whether or not quantum gravity can allow for global symmetries.

      In this, no-global-symmetries approach, however, this gives a precise answer to your question. The universe has no fundamental symmetries. All the global symmetries we see in nature are approximate/emergent and an artefact of us having access only to low energies, where quantum gravity is very very weak.

  • Now, for the false vacuum/metastable state question, if I understand correctly, the person you talked to implicitly assumes that the true vacuum preserves the symmetry, while the false vacuum in a symmetry breaking state. So you should think of this situation kind of like the usual Mexican hat potential, but with an extra, very deep dip in the centre. There, indeed, if we find ourselves in this metastable state, the symmetry would be broken. If that is the picture, then indeed at the fundamental level there would be symmetries. However, from a cosmology/pragmatical point of view, if we are in a metastable state which breaks the symmetry, it is impossible to know for sure whether or not the true vacuum preserves the symmetry. We'd have to go there to find out, but we'd die in the process.

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