Einstein gravity as a 3D conformally invariant theory

We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is irrelevant. The dual theory is invariant under foliation preserving 3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume (for the spatially compact case). Locally, this symmetry is identical to that of Horava-Lifshitz gravity in the high energy limit but our theory is equivalent to Einstein gravity. Specifically, we find that the solutions of general relativity, in a gauge where the spatial hypersurfaces have constant mean extrinsic curvature, can be mapped to solutions of a particular gauge fixing of the dual theory. Moreover, this duality is not accidental. We provide a general geometric picture for our procedure that allows us to trade foliation invariance for conformal invariance. The dual theory provides a new proposal for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections

Quantum Machian Time in Toy Models of Gravity

General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints. These constraints can be thought of as a way of imposing temporal and spatial relationalism. The same type of constraints can be used in non-relativistic particle models to produce relational theories that suffer from the same Problem of Time as that encountered in General Relativity. As a result, these simple toy models are well suited for studying the Problem of Time in quantum gravity. In this paper, a version of these particle models is studied where we "best-match" the time translational invariance of the theory. Using insights gained from this procedure, we can move back and forth between absolute and relational time by changing the way in which the relational fields are varied. We then proceed to quantize this theory using Dirac and path integral quantizations. We discover that one of the constraints of the theory, which we call the Mach constraint, is responsible for removing the dependence of the theory on a background structure. It is this Mach constraint that is responsible for making the theory temporally relational. Because of the deep relationship between these models and General Relativity, this work may shed new light on the Problem of Time in quantum gravity and how one might expect time to emerge on quantum subsystems of the universe.Comment: 27 pages, references added, typos fixed, additional comments added to abs/intro/concl, journal ref adde

Singularity resolution depends on the clock

We study the quantum cosmology of a flat Friedmann–Lemaître–Robertson–Walker Universe filled with a (free) massless scalar field and a perfect fluid that represents radiation or a cosmological constant whose value is not fixed by the action, as in unimodular gravity. We study two versions of the quantum theory: the first is based on a time coordinate conjugate to the radiation/dark energy matter component, i.e., conformal time (for radiation) or unimodular time. As shown by Gryb and Thébault, this quantum theory achieves a type of singularity resolution; we illustrate this and other properties of this theory. The theory is then contrasted with a second type of quantisation in which the logarithm of the scale factor serves as time, which has been studied in the context of the 'perfect bounce' for quantum cosmology. Unlike the first quantum theory, the second one contains semiclassical states that follow classical trajectories and evolve into the singularity without obstruction, thus showing no singularity resolution. We discuss how a complex scale factor best describes the semiclassical dynamics. This cosmological model serves as an illustration of the problem of time in quantum cosmology

Background-Independence

Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.Comment: Forthcoming in General Relativity and Gravitatio

Quantum Cosmological Relational Model of Shape and Scale in 1-d

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues 1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schrodinger interpretation and records theory). 2) In quantum cosmology, such as in the investigation of uniform states, robustness, and the qualitative understanding of the origin of structure formation.Comment: References and some more motivation adde

Triangleland. II. Quantum Mechanics of Pure Shape

Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for resolving the problem of time in quantum general relativity. Moreover, to date there are few explicit examples of these at the quantum level. In this paper I exploit recent geometrical and classical dynamics work to provide such a study based on reduced quantization in the case of pure shape (no scale) in 2-d for 3 particles (triangleland) with multiple harmonic oscillator type potentials. I explore solutions for these making use of exact, asymptotic, perturbative and numerical methods. An analogy to the mathematics of the linear rigid rotor in a background electric field is useful throughout. I argue that further relational models are accessible by the methods used in this paper, and for specific uses of the models covered by this paper in the investigation of the problem of time (and other conceptual and technical issues) in quantum general relativity.Comment: Journal Reference added, minor updates to References and Figure

Extended Thromboprophylaxis with Betrixaban in Acutely Ill Medical Patients

Background Patients with acute medical illnesses are at prolonged risk for venous thrombosis. However, the appropriate duration of thromboprophylaxis remains unknown. Methods Patients who were hospitalized for acute medical illnesses were randomly assigned to receive subcutaneous enoxaparin (at a dose of 40 mg once daily) for 10±4 days plus oral betrixaban placebo for 35 to 42 days or subcutaneous enoxaparin placebo for 10±4 days plus oral betrixaban (at a dose of 80 mg once daily) for 35 to 42 days. We performed sequential analyses in three prespecified, progressively inclusive cohorts: patients with an elevated d-dimer level (cohort 1), patients with an elevated d-dimer level or an age of at least 75 years (cohort 2), and all the enrolled patients (overall population cohort). The statistical analysis plan specified that if the between-group difference in any analysis in this sequence was not significant, the other analyses would be considered exploratory. The primary efficacy outcome was a composite of asymptomatic proximal deep-vein thrombosis and symptomatic venous thromboembolism. The principal safety outcome was major bleeding. Results A total of 7513 patients underwent randomization. In cohort 1, the primary efficacy outcome occurred in 6.9% of patients receiving betrixaban and 8.5% receiving enoxaparin (relative risk in the betrixaban group, 0.81; 95% confidence interval [CI], 0.65 to 1.00; P=0.054). The rates were 5.6% and 7.1%, respectively (relative risk, 0.80; 95% CI, 0.66 to 0.98; P=0.03) in cohort 2 and 5.3% and 7.0% (relative risk, 0.76; 95% CI, 0.63 to 0.92; P=0.006) in the overall population. (The last two analyses were considered to be exploratory owing to the result in cohort 1.) In the overall population, major bleeding occurred in 0.7% of the betrixaban group and 0.6% of the enoxaparin group (relative risk, 1.19; 95% CI, 0.67 to 2.12; P=0.55). Conclusions Among acutely ill medical patients with an elevated d-dimer level, there was no significant difference between extended-duration betrixaban and a standard regimen of enoxaparin in the prespecified primary efficacy outcome. However, prespecified exploratory analyses provided evidence suggesting a benefit for betrixaban in the two larger cohorts. (Funded by Portola Pharmaceuticals; APEX ClinicalTrials.gov number, NCT01583218. opens in new tab.

Weak interaction symmetries with atom traps

Neutral atoms trapped with modern laser cooling techniques offer the promise of improving several broad classes of weak interaction experiments with radioactive isotopes. For nuclear β decay, demonstrated trap techniques include neutrino momentum measurements from beta-recoil coincidences, along with methods to produce highly polarized samples. These techniques enable experiments to search for non-Standard Model interactions, test whether parity symmetry is maximally violated, search for 2nd-class tensor and other tensor interactions, and search for new sources of time reversal violation. Ongoing efforts at TRIUMF, Berkeley, and Los Alamos will be highlighted. Trap experiments involving fundamental symmetries in atomic physics, such as time-reversal violating electric dipole moments and neutral current weak interactions, will be briefly mentioned