Qubit transport model for unitary black hole evaporation without firewalls

Abstract

We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon, and it avoids a counterargument that has been raised for subsystem transfer models as resolutions of the firewall paradox. Furthermore, it fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector. Although the qubit model is too crude to be quantitatively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.

Are quantum corrections on horizon scale physically motivated?

“…There are also attempts to set a framework of fundamental principles to constraint the type of non-local interactions needed to solve the paradox [58,59]. A toy model along these lines has been proposed [60], see also [61]. Such scenarii have been argued to lead to O(1) corrections of any signal propagating around the horizon scale [62].…”

Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory

“…This is not surprising since we were modeling the physics in a manner to match against expectations on the dual supergravity side. We also noted that the qubit action we arrived at has some of the features of the qubit evolution toy model proposed in the work of Osuga and Page [65]. The latter consisted of a proof-of-concept system that circumvents the need of a firewall by positing non-local interactions at the horizon and an exchange mechanism of qubits within a direct product of three Hilbert spaces.…”

“…The dynamics of the marginal bound states in Matrix theory is a complicated strong coupling problem that remains an open issue, and we will not be able to tackle the full problem here. Instead, given the spirit of an effective approximate scaling analysis, we will next engage in a speculative analysis that is inspired by a recent toy model of black hole qubit evaporation due to Osuga and Page [65]. We will argue that the Matrix theory qubit evolution operator has the hallmarks of the toy model presented in [65], under a series of assumptions.…”

“…In [65], a toy model was proposed whereby the black hole Hilbert space is augmented to a tensor product that involves the black hole qubit sector and two other sectors, one for in-falling and another for outgoing radiation modes just inside and just outside the event horizon. Each black hole qubit is paired with two qubits that are in the singlet Bell state.…”

“…Looking at the form of (119), we see a structure that has the right general form to potentially generate such an evolution of qubits. The analogue of the exchange operator from [65] in our language takes the form exp [i α t (ψ + − ψ + bh )(ψ − − ψ − bh )]. Our effective Hamiltonian involves in addition the mediation of the light δψ modes in combinations of the form ∼ (ψ + −ψ + bh )δψ − and its complex conjugate.…”