Weekly Papers on Quantum Foundations (39)

Authors: Suvrat Raju

A sharp version of the information paradox involves a seeming violation of the monogamy of entanglement during black hole evaporation. We construct an analogous paradox in empty anti-de Sitter space. In a local quantum field theory, Bell correlations between operators localized in mutually spacelike regions are monogamous. We show, through a controlled calculation, that this property can be violated by an order-1 factor in a theory of gravity. This example demonstrates that what appears to be a violation of the monogamy of entanglement may just be a subtle violation of locality in quantum gravity.

Authors: D. F. Ramírez JiménezN. G. Kelkar

Methods based on the use of Green’s functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock-Krylov amplitude in terms of the coefficients introduced in the Green’s functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective to understand the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, $t_c$, from the exponential to the inverse power law behaviour at large times. Evaluating $\tau_c = \Gamma t_c$ for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.

Authors: Thomas UndenDaniel LouzonMichael ZwolakWojciech ZurekFedor Jelezko

The origin of classical reality in our quantum world is a long-standing mystery. Here, we examine a nitrogen vacancy center evolving naturally in the presence of its environment to study quantum Darwinism – the proliferation of information about preferred quantum states throughout the world via the environment. This redundantly imprinted information accounts for the perception of objective reality, as it is independently accessible by many without perturbing the system of interest. To observe the emergence of redundant information, we implement a novel dynamical decoupling scheme that enables the measurement/control of several nuclear spins (the environment E) interacting with a nitrogen vacancy (the system S). In addition to showing how to create entangled SE states relevant to quantum metrology, we demonstrate that under the decoherence of S, redundant information is imprinted onto E, giving rise to classical objectivity – a consensus of the nuclear spins about the state of S. This provides the first laboratory verification of the objective classical world emerging from the underlying quantum substrate.

Authors: Henry Wilkes

We introduce and explore Rafael Sorkin’s \textit{evolving co-event scheme}: a theoretical framework for determining completely which events do and do not happen in evolving quantum, or indeed classical, systems. The theory is observer-independent and constructed from discrete histories, making the framework a potential setting for discrete quantum cosmology and quantum gravity, as well as ordinary discrete quantum systems. The foundation of this theory is Quantum Measure Theory, which generalises (classical) measure theory to allow for quantum interference between alternative histories; and its co-event interpretation, which describes whether events can or can not occur, and in what combination, given a system and a quantum measure. In contrast to previous co-event schemes, the evolving co-event scheme is applied in stages, in the stochastic sense, without any dependence on later stages, making it manifestly compatible with an evolving block view. It is shown that the co-event realities produced by the basic evolving scheme do not depend on the inclusion or exclusion of zero measure histories in the history space, which follows non-trivially from the basic rules of the scheme. It is also shown that this evolving co-event scheme will reduce to producing classical realities when it is applied to classical systems.

Authors: Detlef DürrSheldon GoldsteinStefan TeufelRoderich TumulkaNino Zanghì

Recently, there has been progress in developing interior-boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while treating space as a continuum and electrons as point particles. An IBC can be expressed in the particle-position representation of a Fock vector $\psi$ as a condition on the values of $\psi$ on the set of collision configurations, and the corresponding Hamiltonian is defined on a domain of vectors satisfying this condition. We describe here how Bohmian mechanics can be extended to this type of Hamiltonian. In fact, part of the development of IBCs was inspired by the Bohmian picture. Particle creation and annihilation correspond to jumps in configuration space; the annihilation is deterministic and occurs when two particles (of the appropriate species) meet, whereas the creation is stochastic and occurs at a rate dictated by the demand for the equivariance of the $|\psi|^2$ distribution, time reversal symmetry, and the Markov property. The process is closely related to processes known as Bell-type quantum field theories.

Jaramillo, José Luis and Lam, Vincent (2018) Counterfactuals in the initial value formulation of general relativity. [Preprint]
Gillies, Donald (2018) Indeterministic Causality and Simpson’s Paradox. In: UNSPECIFIED.
Morganti, Matteo (2018) From Ontic Structural Realism to Metaphysical Coherentism. [Preprint]

Author(s): Ezad Shojaee, Christopher S. Jackson, Carlos A. Riofrío, Amir Kalev, and Ivan H. Deutsch

The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively me…

[Phys. Rev. Lett. 121, 130404] Published Wed Sep 26, 2018

Authors: T. P. Shestakova

It is generally accepted that the Copenhagen interpretation is inapplicable to quantum cosmology, by contrast with the many worlds interpretation. I shall demonstrate that the two basic principles of the Copenhagen interpretation, the principle of integrity and the principle of complementarity, do make sense in quantum gravity, since we can judge about quantum gravitational processes in the very early Universe by their vestiges in our macroscopic Universe. I shall present the extended phase space approach to quantum gravity and show that it can be interpreted in the spirit of the Everett’s `relative states’ formulation, while there is no contradiction between the `relative states’ formulation and the mentioned basic principles of the Copenhagen interpretation.

Authors: Mariam Bouhmadi-LópezManuel KraemerJoão MoraisSalvador Robles-Pérez

We study a toy model of a multiverse consisting of canonically quantized universes that interact with each other on a quantum level based on a field-theoretical formulation of the Wheeler-DeWitt equation. This interaction leads to the appearance of a pre-inflationary phase in the evolution of the individual universes. We analyze scalar perturbations within the model and calculate the influence of the pre-inflationary phase onto the power spectrum of these perturbations. The result is that there is a suppression of power on large scales, which can describe well the Planck 2018 data for the cosmic microwave background anisotropies and could thus indicate a possible solution to the observed quadrupole discrepancy.

Authors: George SavvidyKonstantin Savvidy

We demonstrate that the Riemann zeta function zeros define the position and the widths of the resonances of the quantised Artin dynamical system. The Artin dynamical system is defined on the fundamental region of the modular group on the Lobachevsky plane. It has a finite volume and an infinite extension in the vertical direction that correspond to a cusp. In classical regime the geodesic flow in the fundamental region represents one of the most chaotic dynamical systems, has mixing of all orders, Lebesgue spectrum and non-zero Kolmogorov entropy. In quantum-mechanical regime the system can be associated with the narrow infinitely long waveguide stretched out to infinity along the vertical axis and a cavity resonator attached to it at the bottom. That suggests a physical interpretation of the Maass automorphic wave function in the form of an incoming plane wave of a given energy entering the resonator, bouncing inside the resonator and scattering to infinity. As the energy of the incoming wave comes close to the eigenmodes of the cavity a pronounced resonance behaviour shows up in the scattering amplitude.

Authors: C.P. PanosCh.C. Moustakidis

It is shown that the entropic force formula $F_e=-\lambda\partial S/\partial A$ leads to a Newtonian $r^{-2}$ dependence. Here we employ the universal property of the information entropy $S=a+b\ln N$ ($N$ is the number of particles of a quantum system and $A$ is the area containing the system). This property was previously obtained for fermionic systems (atoms, atomic clusters, nuclei and infinite Fermi systems) and bosonic ones (correlated boson-atoms in a trap). A similar dependence of the entropic force has been derived very recently by Plastino et al with a Bose gas entropy, inspired by Verlinde’s conjecture~\cite{Verlide-11} that gravity is an emergent entropic force.

Authors: Carlo Maria ScandoloRoberto SalazarJarosław K. KorbiczPaweł Horodecki

We investigate the emergence of classicality and objectivity in arbitrary physical theories. First we provide an explicit example of a theory where there are no objective states. Then we characterize classical states of generic theories, and show how classical physics emerges through a decoherence process, which always exists in causal theories as long as there are classical states. We apply these results to the study of the emergence of objectivity, here recast as a multiplayer game. In particular, we prove that the so-called Spectrum Broadcast Structure characterizes all objective states in every causal theory, in the very same way as it does in quantum mechanics. This shows that the structure of objective states is valid across an extremely broad range of physical theories. Finally we show that, unlike objectivity, the emergence of local observers is not generic among physical theories, but it is only possible if a theory satisfies two axioms that rule out holistic behavior in composite systems.

Authors: Joshua RosalerRobert Harlander

In light of the increasingly strong violations of the Higgs naturalness principle revealed at the LHC, we examine the assumptions underlying one influential argument for naturalness in the sense that prohibits fine-tuning of bare Standard Model (SM) parameters. We highlight the dependence of this argument on the interpretation of these bare parameters as “fundamental parameters,” by direct physical analogy with the interpretation of microscopic lattice parameters in condensed matter physics. We emphasize that while the notion of fundamental parameters is appropriate to some applications in condensed matter physics, it plays no essential role in the effective field theories (EFT’s) of high-energy physics. We distinguish two ways of understanding high-energy EFT’s within the Wilsonian framework, the first of which takes an EFT to be uniquely defined by a single set of physical, fundamental bare parameters, and the second of which dispenses entirely with the notion of fundamental parameters. In this latter view, an EFT is instead defined by a one-parameter class of physically equivalent parametrizations related by Wilsonian renormalization group flows. From this perspective, the delicate cancellation between bare Higgs mass and quantum corrections appears as an eliminable artifact of mathematical convention, rather than as a physical coincidence calling out for explanation by a deeper theory. Thus, we aim to clarify the distinction between two physical interpretations of Wilsonian EFT’s and bare parameters in high energy physics, and to show in light of this distinction how one formulation of the naturalness requirement, based on the notion that bare parameters at an EFT’s physical cutoff constitute “fundamental parameters,” may be rooted in an excessively literal reading of the high-energy/condensed-matter analogy.

Authors: Jorge PullinParampreet Singh

We summarize the talks presented at the QG3 session (loop quantum gravity: cosmology and black holes) of the 15th Marcel Grossmann Meeting held in Rome, Italy on July 1-7 2018.

Crowther, Karen (2018) Defining a crisis: The roles of principles in the search for a theory of quantum gravity. [Preprint]
Damiano, Anselmi (2018) The correspondence principle in quantum field theory and quantum gravity. [Preprint]

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