Violations of the Born rule in cool state-dependent horizons

Abstract

Abstract:The black hole information problem has motivated many proposals for new physics. One idea, known as state-dependence, is that quantum mechanics must be generalized to describe the physics of black holes, and that fixed linear operators do not provide the fundamental description of experiences for infalling observers. Instead, such experiences are to be described by operators with an extra dependence on the global quantum state. By generalizing a previous argument for firewalls in generic black holes, we show that any implementation of this idea strong enough to remove firewalls from generic states requires massive violations of the Born rule. We also demonstrate a sense in which such violations are visible to infalling observers involved in preparing the initial state of the black hole. We emphasize the generality of our results; no details of any specific proposal for state-dependence are required.

Spacetime and universal soft modes: Black holes and beyond

“…We also explain why the Born rule problem of Ref. [13] does not apply to the current framework. We will focus on Schwarzschild black holes in 4-dimensional asymptotically flat spacetime (or small black holes in 4-dimensional asymptotically AdS spacetime), though the restriction on specific spacetime dimensions or on non-rotating, non-charged black holes is not essential.…”

“…We also discuss why the present framework does not suffer from the "Born rule problem" of Ref. [13] and describe a mechanism with which a black hole "self-repairs" itself to restore the smooth horizon.…”

“…We emphasize that in order to obtain the correct Boltzmann-weight coefficients in Eqs. (12,13), ∝ e −En 2T H , it is important that the black hole has soft modes with the density of states given by e S BH (E soft ) , and that the hard and soft modes are well scrambled, giving c nina that take values statistically independent of n. 4 We also stress that the operation of coarse-graining, i.e. ignoring the detailed structure of c nina 's, is different from tracing out degrees of freedom.…”

One-loop universality of holographic codes

“…According to this paradigm, full recovery of standard bulk physics can occur only on a 'code subspace' H code in the CFT Hilbert space H CFT . Consistent with either the firewall [9][10][11][12] or state-dependent observables [13][14][15][16][17][18] hypotheses, the orthogonal complement of H code is presumed to contain states describing generic black holes inside which at least any given code will fail to reconstruct standard bulk physics.…”

“…It is straightforward to generalize the discussion to include matter fields with standard twoderivative actions 12. For example, E ij differs from R ij only by 2Λ d−1 g ij ∈ [0] ⊂[1] which can be absorbed into (A.50).…”