And while spacetime symmetries still seem scale invariant, considering the above argument they might also break down at small scales. It seems exceedingly unlikely that they would not! The initial parameters of the theory would have to be chosen just so as to be a fixed point. It seems much more likely that these symmetries emerged through RG flow rather than being fundamental.
While this is an interesting idea, I do still think space symmetries are likely to remain fundamental features of physics, rather than being emergent out of some other process.
Sadly my claim is somewhat unfalsifiable because the emergence might always be hiding at some smaller scale, but I would be surprised if we find the theory that the standard model emerges from and it’s contains classical spacetime.
I don’t know if that is a meaningful question. Consider this: a cube is something that is symmetric under the octahedral group—that’s what *makes* it a cube. If it wasn’t symmetric under these transformations, it wouldn’t be a cube. So also with spacetime—it’s something that transforms according to the Poincaré group (plus some other mathematical properties, metric etc.). That’s what makes it spacetime.
While this is an interesting idea, I do still think space symmetries are likely to remain fundamental features of physics, rather than being emergent out of some other process.
I’ll bet you! ;)
Sadly my claim is somewhat unfalsifiable because the emergence might always be hiding at some smaller scale, but I would be surprised if we find the theory that the standard model emerges from and it’s contains classical spacetime.
I did a little search, and if it’s worth anything Witten and Wheeler agree: https://www.quantamagazine.org/edward-witten-ponders-the-nature-of-reality-20171128/ (just search for ‘emergent’ in the article)
Can you have emergent spacetime while space symmetry remains a bedrock fundamental principle, and not emergent of something else?
I don’t know if that is a meaningful question.
Consider this: a cube is something that is symmetric under the octahedral group—that’s what *makes* it a cube. If it wasn’t symmetric under these transformations, it wouldn’t be a cube. So also with spacetime—it’s something that transforms according to the Poincaré group (plus some other mathematical properties, metric etc.). That’s what makes it spacetime.
So space symmetry is always assumed when we talk about spacetime, and if space symmetry didn’t hold, spacetime as we know it would not work/exist?