Canonical formalism for simplicial gravity

We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in particular.Comment: 4 pages, 5 figures, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

Encoding Possible Final States of the Universe with Conformal Structures

The concept of an Isotropic (Past) Singularity (IPS) was defined by Goode and Wainwright in 1985 as a mathematical formalisation of quiescent cosmology and the Weyl Curvature Hypothesis (WCH) for the isotropic initial state of the universe. ¶ In this thesis it is argued that the framework of an IPS is not sufficient to guarantee a future behaviour which is compatible with the future anisotropy implied by quiescent cosmology and the WCH. Therefore it is necessary to complete and combine the framework of an IPS with new definitions, in order to assure an appropriate past and future behaviour of a cosmology satisfying the respective combination of definitions. Since it is not yet clear whether our universe will expand indefinitely or recontract, it is reasonable to provide a new definition for the scenario of an ever expanding cosmos and one for a recollapsing universe. ¶ Specific example space-times are explored for their conformal structure, future evolution and compatibility with the WCH as guidance in the quest for the new definitions. Motivated by these particular models, we present for the first time the definitions for the conformal structure of an Anisotropic Future Endless Universe (AFEU) and an Anisotropic Future Singularity (AFS). For the purpose of completeness and comparison, we furthermore define the physically less realistic Isotropic Future Singularity (IFS) and the Future Isotropic Universe (FIU). ¶ A number of essential technical implications of the new de nitions are derived. It is explicitly shown that a conformal structure, whose conformal factor is a function of cosmic time, necessarily leads to an asymptotically Ricci dominated Weyl curvature and asymptotically expansion dominated kinematics, if the conformal metric remains regular. This condition is satis ed by the IFS and FIU. Based on this, it is argued that a conformal structure for an anisotropic nal state of the universe requires a degenerate conformal metric, as is the case for the AFS and AFEU. ¶ This degeneracy complicates the derivation of physical attributes of the concepts of an AFEU and an AFS and, consequently, new approaches are unavoidable. Some physical properties are examined, such as the behaviour of the expansion scalar and the curvature. It is proven that the conformal space-times always possess a future singularity, which under reasonable assumptions corresponds to a strong curvature singularity. Finally, we reveal sufficient conditions for the AFS, as well as the IPS, to be a strong curvature singularity. ¶ The combination of the IPS with the AFEU and the AFS could provide a possible first version of a complete mathematical formalisation of quiescent cosmology

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks

Effective relational dynamics

We provide a synopsis of an effective approach to the problem of time in the semiclassical regime. The essential features of this new approach to evaluating relational quantum dynamics in constrained systems are illustrated by means of a simple toy model.Comment: 4 pages, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

Quantum Relativity of Subsystems

One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. We further demonstrate that subalgebras which commute before imposing the symmetry constraint can translate into non-commuting algebras in a given QRF perspective after symmetry imposition. Such a QRF perspective does not inherit the distinction between subsystems in terms of the corresponding tensor factorizability of the kinematical Hilbert space and observable algebra. Since the condition for this to occur is contingent on the choice of QRF, the notion of subsystem locality is frame-dependent

Effective approach to the problem of time: general features and examples

The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the quantum constrained system can be truncated to finite size and solved by the reduced phase space or gauge-fixing methods. In particular, the classical feasibility of local internal times is directly generalized to quantum systems, overcoming the main difficulties associated with the general problem of time in the semiclassical realm. The key features of local internal times and the procedure of patching global solutions using overlapping intervals of local internal times are described and illustrated by two quantum mechanical examples. Relational evolution in a given choice of internal time is most conveniently described and interpreted in a corresponding choice of gauge at the effective level and changing the internal clock is, therefore, essentially achieved by a gauge transformation. This article complements the conceptual discussion in arXiv:1009.5953.Comment: 42 pages, 9 figures; v2: streamlined discussions, more compact manuscrip

Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař\u27s criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks

Trinity of relational quantum dynamics

The problem of time in quantum gravity calls for a relational solution. Using quantum reduction maps, we establish a previously unknown equivalence between three approaches to relational quantum dynamics: (1) relational observables in the clock-neutral picture of Dirac quantization, (2) Page and Wootters’ (PW) Schrödinger picture formalism, and (3) the relational Heisenberg picture obtained via symmetry reduction. Constituting three faces of the same dynamics, we call this equivalence the trinity. In the process, we develop a quantization procedure for relational Dirac observables using covariant positive operator-valued measures which encompass nonideal clocks and resolve the nonmonotonicity issue of realistic quantum clocks reported by Unruh and Wald. The quantum reduction maps reveal this procedure as the quantum analog of gauge-invariantly extending gauge-fixed quantities. We establish algebraic properties of these relational observables. We extend a recent “clock-neutral” approach to changing temporal reference frames, transforming relational observables and states, and demonstrate a clock dependent temporal nonlocality effect. We show that Kuchař’s criticism, alleging that the conditional probabilities of the PW formalism violate the constraint, is incorrect. They are a quantum analog of a gauge-fixed description of a gauge-invariant quantity and equivalent to the manifestly gauge-invariant evaluation of relational observables in the physical inner product. The trinity furthermore resolves a previously reported normalization ambiguity and clarifies the role of entanglement in the PW formalism. The trinity finally permits us to resolve Kuchař’s criticism that the PW formalism yields wrong propagators by showing how conditional probabilities of relational observables give the correct transition probabilities. Unlike previous proposals, our resolution does not invoke approximations, ideal clocks or ancilla systems, is manifestly gauge invariant, and easily extends to an arbitrary number of conditionings

The ophthalmic branch of the Gutenberg Health Study: study design, cohort profile and self-reported diseases

This paper describes the study design, methodology, cohort profile and self-reported diseases in the ophthalmological branch of the Gutenberg Health Study (GHS).The GHS is an ongoing, prospective, interdisciplinary, single-center, population-based cohort study in Germany. The main goals of the ophthalmological section are to assess the prevalence and incidence of ocular diseases and to explore risk factors, genetic determinants and associations with systemic diseases and conditions. The eye examination at baseline included a medical history, self-reported eye diseases, visual acuity, refractive errors, intraocular pressure, visual field, pachymetry, keratometry, fundus photography and tear sampling. The 5-year follow-up visit additionally encompassed optical coherence tomography, anterior segment imaging and optical biometry. The general examination included anthropometry; blood pressure measurement; carotid artery ultrasound; electrocardiogram; echocardiography; spirometry; cognitive tests; questionnaires; assessment of mental conditions; and DNA, RNA, blood and urine sampling.Of 15,010 participants (aged 35-74 years at the time of inclusion), ocular data are available for 14,700 subjects (97.9%). The mean visual acuity (standard deviation), mean spherical equivalent, median decimal visual acuity, and mean intraocular pressure were 0.08 (0.17) logMar, -0.42 (2.43) diopters, 0.9 and 14.24 (2.79) mm Hg, respectively. The frequencies of self-reported strabismus, glaucoma, surgery for retinal detachment and retinal vascular occlusions were 2.7%, 2.3%, 0.2% and 0.4%, respectively.The GHS is the most extensive dataset of ophthalmic diseases and conditions and their risk factors in Germany and one of the largest cohorts worldwide. This dataset will provide new insight in the epidemiology of ophthalmic diseases and related medical specialties

Gender Bias in Urology: How Do Patients Really Choose Their Urologist?

Purpose: The present study aimed to investigate the influence of patients’ and urologists’ gender when choosing a urologist. With rising population diversity through immigration and generational differences, patient-centered healthcare has recently moved to the focus of European healthcare systems. As healthcare in urology often concentrates on sensitive topics, and often involves gender-specific diseases, research on the influence of gender on decision-making processes is of high importance. Understanding influence of gender on patients’ choices in real life would provide patients, and physicians alike, with the means to provide better resources to achieve greater satisfaction from visits to a urologist. Patients and Methods: A questionnaire was prepared, and patients at our tertiary referral center were given the opportunity to voluntarily participate in our survey. We collected questionnaires from 1012 patients during their visits from June 2021 to October 2021. Results: Patients were divided into groups according to their gender: male (n=763), female (n=246), and non-binary (n=3). Our patient cohort consisted of more men than women (75% vs 24%), with only three patients identifying as non-binary. Irrespective of the patients’ own gender, patients preferred a male urologist when problems were considered embarrassing, limiting daily activities, or when worrisome. When problems were considered painful, all patients preferred a female urologist. When patients had had a previous positive experience with a female or male urologist, they preferred to be treated by a female or male urologist, respectively. Overall, 65% of patients stated a gender preference for at least one given situation, or consultation scenario. Conclusion: As the majority of our patients stated a gender preference, urological departments should be considerate of potential patients’ preferences for urologist gender that may be based on the individual patient’s history, taking a comprehensive approach to fulfill the patients’ need for same gender urologists in educational hospitals and health care services