128,128 research outputs found
The hidden horizon and black hole unitarity
We motivate through a detailed analysis of the Hawking radiation in a
Schwarzschild background a scheme in accordance with quantum unitarity. In this
scheme the semi-classical approximation of the unitary quantum - horizonless -
black hole S-matrix leads to the conventional description of the Hawking
radiation from a classical black hole endowed with an event horizon. Unitarity
is borne out by the detailed exclusive S-matrix amplitudes. There, the fixing
of generic out-states, in addition to the in-state, yields in asymptotic
Minkowski space-time saddle-point contributions which are dominated by
Planckian metric fluctuations when approaching the Schwarzschild radius. We
argue that these prevent the corresponding macroscopic "exclusive backgrounds"
to develop an event horizon. However, if no out-state is selected, a distinct
saddle-point geometry can be defined, in which Planckian fluctuations are
tamed. Such "inclusive background" presents an event horizon and constitutes a
coarse-grained average over the aforementioned exclusive ones. The classical
event horizon appears as a coarse-grained structure, sustaining the
thermodynamic significance of the Bekenstein-Hawking entropy. This is
reminiscent of the tentative fuzzball description of extremal black holes: the
role of microstates is played here by a complete set of out-states. Although
the computations of unitary amplitudes would require a detailed theory of
quantum gravity, the proposed scheme itself, which appeals to the metric
description of gravity only in the vicinity of stationary points, does not.Comment: 29 pages, 4 figures. Typos corrected. Two footnotes added (footnotes
3 and 5
Rate Limitations of Unitary Event Analysis
Unitary event analysis is a new method for detecting episodes of synchronized neural activity (Riehle, GrĂĽun, Diesmann, & Aertsen, 1997). It detects time intervals that contain coincident firing at higher rates than would be expected if the neurons fired as independent inhomogeneous Poisson processes; all coincidences in such intervals are called unitary events (UEs). Changes in the frequency of UEs that are correlated with behavioral states may indicate synchronization of neural firing that mediates or represents the behavioral state.
We show that UE analysis is subject to severe limitations due to the underlying discrete statistics of the number of coincident events. These limitations are particularly stringent for low (0–10 spikes/s) firing rates. Under these conditions, the frequency of UEs is a random variable with a large variation relative to its mean. The relative variation decreases with increasing firing rate, and we compute the lowest firing rate, at which the 95% confidence interval around the mean frequency of UEs excludes zero.
This random variation in UE frequency makes interpretation of changes in UEs problematic for neurons with low firing rates. As a typical example, when analyzing 150 trials of an experiment using an averaging window 100 ms wide and a 5ms coincidence window, firing rates should be greater than 7 spikes per second
Evolution in Quantum Causal Histories
We provide a precise definition and analysis of quantum causal histories
(QCH). A QCH consists of a discrete, locally finite, causal pre-spacetime with
matrix algebras encoding the quantum structure at each event. The evolution of
quantum states and observables is described by completely positive maps between
the algebras at causally related events. We show that this local description of
evolution is sufficient and that unitary evolution can be recovered wherever it
should actually be expected. This formalism may describe a quantum cosmology
without an assumption of global hyperbolicity; it is thus more general than the
Wheeler-DeWitt approach. The structure of a QCH is also closely related to
quantum information theory and algebraic quantum field theory on a causal set.Comment: 20 pages. 8 figures. (v3: minor corrections, additional references
[2,3]) to appear in CQ
A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties
Within ordinary ---unitary--- quantum mechanics there exist global protocols
that allow to verify that no definite event ---an outcome to which a
probability can be associated--- occurs. Instead, states that start in a
coherent superposition over possible outcomes always remain as a superposition.
We show that, when taking into account fundamental errors in measuring length
and time intervals, that have been put forward as a consequence of a
conjunction of quantum mechanical and general relativity arguments, there are
instances in which such global protocols no longer allow to distinguish whether
the state is in a superposition or not. All predictions become identical as if
one of the outcomes occurs, with probability determined by the state. We use
this as a criteria to define events, as put forward in the Montevideo
Interpretation of Quantum Mechanics. We analyze in detail the occurrence of
events in the paradigmatic case of a particle in a superposition of two
different locations. We argue that our approach provides a consistent (C)
single-world (S) picture of the universe, thus allowing an economical way out
of the limitations imposed by a recent theorem by Frauchiger and Renner showing
that having a self-consistent single-world description of the universe is
incompatible with quantum theory. In fact, the main observation of this paper
may be stated as follows: If quantum mechanics is extended to include
gravitational effects to a QG theory, then QG, S, and C are satisfied.Comment: thoughts and comments more than welcom
Unitarity issue in BTZ black holes
We study the wave equation for a massive scalar in three-dimensional
AdS-black hole spacetimes to understand the unitarity issues in a semiclassical
way. Here we introduce four interesting spacetimes: the non-rotating BTZ black
hole (NBTZ), pure AdS spacetime (PADS), massless BTZ black hole (MBTZ), and
extremal BTZ black hole (EBTZ). Our method is based on the potential analysis
and solving the wave equation to find the condition for the frequency
exactly. In the NBTZ case, one finds the quasinormal (complex and discrete)
modes which signals for a non-unitary evolution. Real and discrete modes are
found for the PADS case, which means that it is unitary obviously. On the other
hand, we find real and continuous modes for the two extremal black holes of
MBTZ and EBTZ. It suggests that these could be candidates for the unitary
system.Comment: 14 pages, contracted version to appear in MPL
Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory
We develop an microscopic model of the M-theory Schwarzschild black hole
using the Banks-Fischler-Shenker-Susskind Matrix formulation of quantum
gravity. The underlying dynamics is known to be chaotic, which allows us to use
methods from Random Matrix Theory and non-equilibrium statistical mechanics to
propose a coarse-grained bottom-up picture of the event horizon -- and the
associated Hawking evaporation phenomenon. The analysis is possible due to a
hierarchy between the various timescales at work. Event horizon physics is
found to be non-local at the Planck scale, and we demonstrate how non-unitary
physics and information loss arise from the process of averaging over the
chaotic unitary dynamics. Most interestingly, we correlate the onset of
non-unitarity with the emergence of spacetime geometry outside the horizon. We
also write a mean field action for the evolution of qubits -- represented by
polarization states of supergravity modes. This evolution is shown to have
similarities to a recent toy model of black hole evaporation proposed by Osuga
and Page -- a model aimed at developing a plausible no-firewall scenario.Comment: 37 pages, 3 figures; v2: clarifications added, typos correcte
Quantum Jump from Singularity to Outside of Black Hole
Considering the role of black hole singularity in quantum evolution, a
resolution to the firewall paradox is presented. It is emphasized that if an
observer has the singularity as a part of his spacetime, then the
semi-classical evolution would be non-unitary as viewed by him. Specifically, a
free-falling observer inside the black hole would have a Hilbert space with
non-unitary evolution; a quantum jump for particles encountering the
singularity to outside of the horizon as late Hawking radiations. The
non-unitariness in the jump resembles the one in collapse of wave function, but
preserves entanglements. Accordingly, we elaborate the first postulate of black
hole complementarity: freely falling observers who pass through the event
horizon would have non-unitary evolution, while it does not have physically
measurable effects for them. Besides, no information would be lost in the
singularity. Taking the modified picture into account, the firewall paradox can
be resolved, respecting No Drama. A by-product of our modification is that
roughly half of the entropy of the black hole is released close to the end of
evaporation in the shape of very hot Hawking radiation.Comment: 7 figures, v2 more comprehensive, v3 matches the published versio
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