scholarly journals QUANTUM STATE OF WORMHOLES AND TOPOLOGICAL ARROW OF TIME

1994 ◽  
Vol 03 (03) ◽  
pp. 549-568 ◽  
Author(s):  
PEDRO F. GONZÁLEZ-DĺAZ
Keyword(s):  
Quantum Gravity ◽  
Quantum State ◽  
Semiclassical Approximation ◽  
Asymptotic Region ◽  
Analytic Extension ◽  
Arrow Of Time ◽  
Quantum Uncertainty ◽  
Time Symmetry ◽  
Low Energies ◽  
Symmetry Problem

This paper studies the time-symmetry problem in quantum gravity. The issue depends critically on the choice of the quantum state and has been considered in this paper by restricting it to the case of quantum wormholes. It is seen that pure states represented by a wave functional are time symmetric. However, a maximal analytic extension of the wormhole manifold is found that corresponds to a mixed state describable by a nondegenerate density-matrix functional that involves an extra quantum uncertainty for the three-metric, and is free from the divergences encountered so far in statistical states formulated in quantum gravity. It is then argued that, relative to one asymptotic region, the statistical quantum state of single Euclidean wormholes in semiclassical approximation is time-asymmetric and gives rise to a topological arrow of time which will reflect in the set of all quantum fields at low energies of the asymptotically flat region.

scholarly journals LARGE QUANTUM GRAVITY EFFECTS: CYLINDRICAL WAVES IN FOUR DIMENSIONS

2000 ◽  
Vol 09 (06) ◽  
pp. 669-686 ◽  
Author(s):  
MARÍA E. ANGULO ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Quantum Gravity ◽  
Symmetry Axis ◽  
Point Of View ◽  
Three Dimensions ◽  
Asymptotic Region ◽  
Four Dimensions ◽  
Cylindrical Waves ◽  
Significant Difference ◽  
Gravity Effects ◽  
Linearly Polarized

Linearly polarized cylindrical waves in four-dimensional vacuum gravity are mathematically equivalent to rotationally symmetric gravity coupled to a Maxwell (or Klein–Gordon) field in three dimensions. The quantization of this latter system was performed by Ashtekar and Pierri in a recent work. Employing that quantization, we obtain here a complete quantum theory which describes the four-dimensional geometry of the Einstein–Rosen waves. In particular, we construct regularized operators to represent the metric. It is shown that the results achieved by Ashtekar about the existence of important quantum gravity effects in the Einstein–Maxwell system at large distances from the symmetry axis continue to be valid from a four-dimensional point of view. The only significant difference is that, in order to admit an approximate classical description in the asymptotic region, states that are coherent in the Maxwell field need not contain a large number of photons anymore. We also analyze the metric fluctuations on the symmetry axis and argue that they are generally relevant for all of the coherent states.

scholarly journals Symmetry and the Arrow of Time in Theoretical Black Hole Astrophysics

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
David Garofalo
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Active Galactic Nuclei ◽  
Accretion Disks ◽  
Time Reversal ◽  
Large Scale ◽  
Galactic Nuclei ◽  
Arrow Of Time ◽  
Time Symmetry ◽  
The Universe

While the basic laws of physics seem time-reversal invariant, our understanding of the apparent irreversibility of the macroscopic world is well grounded in the notion of entropy. Because astrophysics deals with the largest structures in the Universe, one expects evidence there for the most pronounced entropic arrow of time. However, in recent theoretical astrophysics work it appears possible to identify constructs with time-reversal symmetry, which is puzzling in the large-scale realm especially because it involves the engines of powerful outflows in active galactic nuclei which deal with macroscopic constituents such as accretion disks, magnetic fields, and black holes. Nonetheless, the underlying theoretical structure from which this accreting black hole framework emerges displays a time-symmetric harmonic behavior, a feature reminiscent of basic and simple laws of physics. While we may expect such behavior for classical black holes due to their simplicity, manifestations of such symmetry on the scale of galaxies, instead, surprise. In fact, we identify a parallel between the astrophysical tug-of-war between accretion disks and jets in this model and the time symmetry-breaking of a simple overdamped harmonic oscillator. The validity of these theoretical ideas in combination with this unexpected parallel suggests that black holes are more influential in astrophysics than currently recognized and that black hole astrophysics is a more fundamental discipline.

scholarly journals Spacetime and Deformations of Special Relativistic Kinematics

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1401 ◽  
Author(s):  
José Manuel Carmona ◽  
José Luis Cortés ◽  
José Javier Relancio
Keyword(s):  
Quantum Gravity ◽  
Classical Level ◽  
Relativistic Kinematics ◽  
Interaction Processes ◽  
Low Energies ◽  
Decomposition Principle

A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a model including single- or multi-interaction processes, for which absolute locality in terms of canonical spacetime coordinates is lost. We discuss the different alternatives for observable effects in the propagation of a particle over very large distances that emerge from the new notion of spacetime. A central ingredient in the discussion is the cluster decomposition principle, which can be used to favor some alternatives over the others.

scholarly journals Is a time symmetric interpretation of quantum theory possible without retrocausality?

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160607 ◽  
Author(s):  
Matthew S. Leifer ◽  
Matthew F. Pusey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
General Framework ◽  
Bell Inequalities ◽  
Time Symmetry ◽  
Causality Criterion ◽  
The Status ◽  
Interpretation Of Quantum Theory ◽  
Huw Price ◽  
New Interpretation

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ -mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.

scholarly journals Quick Quantum Circuit Simulation

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Daniel Evans
Keyword(s):  
Quantum State ◽  
Quantum Computer ◽  
Circuit Simulation ◽  
Matrix Multiplication ◽  
Quantum Circuit ◽  
Machine Language ◽  
Unitary Matrix ◽  
Initial State ◽  
Final State ◽  
Quantum Uncertainty

Quick Quantum Circuit Simulation (QQCS) is a software system for computing the result of a quantum circuit using a notation that derives directly from the circuit, expressed in a single input line. Quantum circuits begin with an initial quantum state of one or more qubits, which are the quantum analog to classical bits. The initial state is modified by a sequence of quantum gates, quantum machine language instructions, to get the final state. Measurements are made of the final state and displayed as a classical binary result. Measurements are postponed to the end of the circuit because a quantum state collapses when measured and produces probabilistic results, a consequence of quantum uncertainty. A circuit may be run many times on a quantum computer to refine the probabilistic result. Mathematically, quantum states are 2n -dimensional vectors over the complex number field, where n is the number of qubits. A gate is a 2n ×2n unitary matrix of complex values. Matrix multiplication models the application of a gate to a quantum state. QQCS is a mathematical rendering of each step of a quantum algorithm represented as a circuit, and as such, can present a trace of the quantum state of the circuit after each gate, compute gate equivalents for each circuit step, and perform measurements at any point in the circuit without state collapse. Output displays are in vector coefficients or Dirac bra-ket notation. It is an easy-to-use educational tool for students new to quantum computing.

scholarly journals Generalised Uncertainty Relations for Angular Momentum and Spin in Quantum Geometry

Universe ◽  
2020 ◽  
Vol 6 (4) ◽  
pp. 56 ◽  
Author(s):  
Matthew J. Lake ◽  
Marek Miller ◽  
Shi-Dong Liang
Keyword(s):  
Angular Momentum ◽  
Dark Energy ◽  
Quantum Gravity ◽  
Quantum State ◽  
Orbital Angular Momentum ◽  
Uncertainty Principle ◽  
Minimum Length ◽  
Uncertainty Relations ◽  
Quantum Geometry ◽  
Space Model

We derive generalised uncertainty relations (GURs) for orbital angular momentum and spin in the recently proposed smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum and recovers both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), previously proposed in the quantum gravity literature, within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum and obtain generalisations of the canonical so ( 3 ) and su ( 2 ) algebras. We find that, although SO ( 3 ) symmetry is preserved on three-dimensional slices of an enlarged phase space, corresponding to a superposition of background geometries, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for orbital angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, ħ → ħ + β . The value of the new parameter, β ≃ ħ × 10 − 61 , is determined by the ratio of the dark energy density to the Planck density, and its existence is required by the presence of both minimum length and momentum uncertainties. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum ∼ ħ Λ , where Λ is the cosmological constant, which is consistent with the existence of a finite cosmological horizon. In the smeared-space model, ħ and β are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with a flat background to be fermionic, with spin eigenvalues ± β / 2 . Finally, the modified spin algebra leads to GURs for spin measurements. The potential implications of these results for cosmology and high-energy physics, and for the description of spin and angular momentum in relativistic theories of quantum gravity, including dark energy, are briefly discussed.

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