Sorry, but no. First, who cares that the fractional quantum Hall effect breaks Lorentz invariance? Tons of things do that—turn on a strong electric field in your lab and WHAM! Lorentz invariance broken. Great. That doesn’t mean you can’t make general statements about Lorentz-invariant systems, which our fundamental theories are. (If you actually, y'know, read literally any textbook on the spin-statistics theorem (e.g. Schwartz), you'll see that there is a dimension restriction in the theorem statement for this very reason.) This is just a category error coming from a total lack of understanding of the theorem.
Second, I don’t know where you’ve been getting your information from, but that’s simply not true. Locality... (read more)
Sorry, but no. First, who cares that the fractional quantum Hall effect breaks Lorentz invariance? Tons of things do that—turn on a strong electric field in your lab and WHAM! Lorentz invariance broken. Great. That doesn’t mean you can’t make general statements about Lorentz-invariant systems, which our fundamental theories are. (If you actually, y'know, read literally any textbook on the spin-statistics theorem (e.g. Schwartz), you'll see that there is a dimension restriction in the theorem statement for this very reason.) This is just a category error coming from a total lack of understanding of the theorem.
Second, I don’t know where you’ve been getting your information from, but that’s simply not true. Locality... (read more)