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 co... (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 co... (read more)