/sci/ - Science & Math

>>11384179
The entire paradox is that everything past the horizon goes off to past infinity, hence no information regarding the prior entanglement can exit without violating locality. Anything inside the horizon is quite literally not part of the universe.
Incidentally the information paradox can be resolved with string theory
https://arxiv.org/abs/0810.4525
Please read up before making another post.
>>11384955
>some of the techniques seem like overkill
You [math]were[/math] looking for a rigorous proof after all. It's either that or I do variational calculus on the path space [math]P\mathfrak{A}[/math] to get the minimizers.
>>11385747
Here's the idea: for any irrep [math]\rho[/math] there's a conjugate irrep [math]\overline{\rho}[/math] with [math]\chi_\rho(c) = \chi_{\overline{\rho}}(c^{-1})[/math]. This arises because [math]\rho(c)\rho(c^{-1})[/math] lies in the conjugacy class of the centre of [math]{GL}_\mathbb{C}(V)[/math] so by Schur it must be similar to a multiple of the identity. The similarity transform then induces [math]\rho\mapsto \overline{\rho}[/math] with [math]\rho(c)\overline{\rho}(c) \sim \lambda\mathbb{C}[/math]. Hence [math]\chi_\rho(c) = \chi_{\overline{\rho}}(c^{-1}) = \overline{\chi_\rho(c^{-1})}[/math].