- Not all three statements are consistent it is claimed.
- 1) Hawking radiation is in a pure state.
- 2) The information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon.
- 3) The infalling observer encounters nothing unusual at the horizon.
Well 1) cannot be true since if Hawking radiation is black body it is not in a pure state it is a mixed state with a reduced density matrix that is not an idempotent projection operator.
So what is all the fuss about? ;-)
Throw away 1) and keep 2) and 3)?
Furthermore, there is no reason to go hog wild that the universe obeys unitarity at all levels of organization. Why should probability be conserved in the first place? Life does not seem to conserve probabilities. When Feynman gave an early lecture on his Lagrangian formulation of quantum theory Dirac was there with Einstein and Dirac asked Feynman if his theory was “unitary.” Feynman said he had no idea of what Dirac even meant at that time. Valentini has an extended quantum theory that is definitely not unitary for example. Feynman also asked why observables have to be Hermitian operators. Hermitian operators generate unitary transformations.
Unitarity is in Hilbert qubit pilot wave space what orthogonality is in the spacetime continuum. There is nothing sacred and absolute in either. There is no compelling reason to say that inner products of quantum states are invariant under time evolution. It works in a limited range of experiments - scattering experiments - very primitive smashing of things together - brute force not very subtle.
The S-MATRIX is a crude tool that has been elevated into The Golden Calf by the Priests of Orthodox Physics.