scholarly journals Violation of unitarity in gravitational subregions

2021 ◽  
Author(s):  
Aron C. Wall
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Path Integral ◽  
Cpt Symmetry ◽  
Negative Norm ◽  
Trapped Surfaces ◽  
Negative Probability

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, “states” with negative probability can be identified on either side of trapped surfaces. I argue that these negative norm states are tolerable, by analogy to quantum mechanics. This viewpoint suggests a resolution of the firewall paradox, similar to black hole complementarity. Implications for cosmology are briefly discussed.

scholarly journals From the black hole conundrum to the structure of quantum gravity

2021 ◽  
pp. 2130007
Author(s):  
Yasunori Nomura
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Quantum System ◽  
Path Integral ◽  
Recent Progress ◽  
Black Hole Physics ◽  
Interior Volume

We portray the structure of quantum gravity emerging from recent progress in understanding the quantum mechanics of an evaporating black hole. Quantum gravity admits two different descriptions, based on Euclidean gravitational path integral and a unitarily evolving holographic quantum system, which appear to present vastly different pictures under the existence of a black hole. Nevertheless, these two descriptions are physically equivalent. Various issues of black hole physics — including the existence of the interior, unitarity of the evolution, the puzzle of too large interior volume, and the ensemble nature seen in certain calculations — are addressed very differently in the two descriptions, still leading to the same physical conclusions. The perspective of quantum gravity developed here is expected to have broader implications beyond black hole physics, especially for the cosmology of the eternally inflating multiverse.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

scholarly journals Ontology in Quantum Mechanics

2021 ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Evolution Equations ◽  
Black Hole Physics ◽  
Special Kind ◽  
Quantum Evolution ◽  
The Standard Model ◽  
Low Energies

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is given by elements of the permutation group. This would restore an ontological interpretation. It is shown how, at low energies per particle degree of freedom, almost any quantum system allows for such a transformation. This contradicts Bell’s theorem, and we emphasise why some of the assumptions made by Bell to prove his theorem cannot hold for the models studied here. We speculate how an approach of this kind may become helpful in isolating the most likely version of the Standard Model, combined with General Relativity. A link is suggested with black hole physics.

Polymer quantization effects on gauge-flation

2018 ◽  
Vol 15 (10) ◽  
pp. 1850169
Author(s):  
M. Mardaani ◽  
K. Nozari
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Abelian Gauge ◽  
Friedmann Equations ◽  
Cosmological Inflation

Polymer quantum mechanics, as a non-standard representation of quantum mechanics, is based on a symmetric sector of loop quantum gravity known as loop quantum cosmology. In this work, by analyzing the Hamiltonian and Friedmann equations in the standard Hilbert space and polymer Hilbert space, we show that polymer quantization is a successful formalism for a non-Abelian gauge field driving the cosmological inflation, the so-called gauge-flation, in order to remove initial singularity and also keeping the inflationary trajectories in this model as attractors of dynamics after the bounce.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

STATIONARY PHASE, QUANTUM MECHANICS AND SEMI-CLASSICAL LIMIT

1996 ◽  
Vol 08 (08) ◽  
pp. 1161-1185 ◽  
Author(s):  
JORGE REZENDE
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Stationary Phase ◽  
Finite Number ◽  
Path Integral ◽  
Critical Points ◽  
Classical Limit ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path

A method of stationary phase for the normalized-oscillatory integral on Hilbert space is developed in the case where the phase function has a finite number of critical points which are non-degenerate. Applications to the Feynman path integral and the semi-classical limit of quantum mechanics are given.

scholarly journals Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study

2015 ◽  
Vol 24 (10) ◽  
pp. 1550073 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Valerio Astuti
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Recent Progress ◽  
Covariant Formulation ◽  
Specific Context ◽  
Intrinsic Interest ◽  
Alternative Approaches

Alternative approaches to the study of the quantum gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics, suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.

GEOMETRIC STRUCTURES IN PHYSICS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260026 ◽  
Author(s):  
L. J. BOYA
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Mechanics ◽  
Path Integral ◽  
Riemannian Manifolds ◽  
Symplectic Geometry ◽  
Gauge Theories ◽  
Classical Mechanics ◽  
The Past ◽  
Modern Physics

Geometry and Physics developed independently, until the past twentieth century, where physicists realized geometry is rather flexible and can adapt itself to the needs and characteristics of modern physics. Besides the use of Riemannian manifolds to describe General Relativity, classical mechanics encounters symplectic geometry, not to speak of the bundle connection ingredient of modern gauge theories; even Quantum Mechanics, after the initial Hilbert space period, is seeking nowadays to adapt itself better to a geometrical interpretation, by imperatives of the path integral description and also to incorporate more clearly the symplectic aspects of its classical antecedent.

scholarly journals On the spectrum of pure higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Jin-Beom Bae ◽  
Nathan Benjamin ◽  
Carmen Jorge-Diaz
Keyword(s):  
Black Hole ◽  
Partition Function ◽  
Path Integral ◽  
Higher Spin Gravity ◽  
Central Charge ◽  
Modular Invariance ◽  
Light Spectrum ◽  
Negative Norm ◽  
Deficit Angle ◽  
Higher Spin

Abstract We study the spectrum of pure massless higher spin theories in AdS3. The light spectrum is given by a tower of massless particles of spin s = 2, ⋯ , N and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the $$ {\mathcal{W}}_N $$ W N algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle 2π(1 − 1/M). Unitarity allows the inclusion of such defects into the path integral provided M ≥ N.

scholarly journals Quantum groups and polymer quantum mechanics

2021 ◽  
Author(s):  
G. Acquaviva ◽  
A. Iorio ◽  
L. Smaldone
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Quantum Groups ◽  
Loop Quantum Gravity ◽  
Quantization Scheme ◽  
Creation And Annihilation Operators

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows that the [Formula: see text]-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of [Formula: see text] is of topological nature.

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