The main source of scale-invariance itself probably would have to do with symmetry meaning that an object has a particular property that is preserved across scales.
Space symmetry is an example, where the basic physical laws are preserved across all scales of spacetime, and in particular means that scaling a system down doesn’t mean different laws of physics apply at different scales, there is only 1 physical law, which produces varied consequences at all scales.
You’re making an interesting connection to symmetry! But scale invariance as discussed here is actually emergent—it arises when theories reach fixed points under coarse-graining, rather than being a fundamental symmetry of space. This is why quantities like electric charge can change with scale, despite spacetime symmetries remaining intact.
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.
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.
The main source of scale-invariance itself probably would have to do with symmetry meaning that an object has a particular property that is preserved across scales.
Space symmetry is an example, where the basic physical laws are preserved across all scales of spacetime, and in particular means that scaling a system down doesn’t mean different laws of physics apply at different scales, there is only 1 physical law, which produces varied consequences at all scales.
You’re making an interesting connection to symmetry! But scale invariance as discussed here is actually emergent—it arises when theories reach fixed points under coarse-graining, rather than being a fundamental symmetry of space. This is why quantities like electric charge can change with scale, despite spacetime symmetries remaining intact.
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.
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?