>>10938947>I'm not asking for a statistical approach to answering the question.So you're not looking for an answer at all. Or do you have some sort of quantum vortex supercomputer that can store every single qubit in the universe?
>everyone can agree there is no symmetry in the observable universe. Who's this "everyone"? What happened to Lorentz? Gauge symmetries? Even at the cosmic level, the Einstein action is invariant under reparameterizations of the metric. Where do you think these symmetries went?
>why is the universe not fractal-like?This is asking for a very specific symmetry, namely scaling symmetry. Scaling is extremely special and only shows up in e.g. systems near criticality, for which conformal symmetry emerges. In fact, it can be taken as the definition: scaling symmetry emerges iff the system reaches criticality, as scaling directly implies the proliferation of some macroscopic state throughout the system. In this sense, it would be quite far-fetched to expect the observable universe now, even as a statistical system, to have scaling symmetry.
There have been people, especially string theorists, who argue that scaling emerges as an internal symmetry of a "hidden" fundamental degree of freedom (i.e. strings), for which CFT was used extensively to make computations. The problem with this is that the theory criticality of the universe's fundamental degrees of freedom; this is where the (SUSY)-string transition occurs in which strings condense into actual particles and their worldsheets become heavily compactified. A priori, we have nothing to compare the coherence length of this phase transition to, and hence no understanding of the RG "time scale" to determine if our universe is actually near criticality, let along a SUSY string criticality. There hasn't even been proof that such a RG flow into string criticality is necessary.
Besides, you wouldn't be able to see this with deep space pictures anyway.
