The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology

This letter is motivated by the recent papers by Dittrich and Thiemann and, respectively, by Rovelli discussing the status of Quantum Geometry in the dynamical sector of Loop Quantum Gravity. Since the papers consider model examples, we also study the issue in the case of an example, namely on the Loop Quantum Cosmology model of space-isotropic universe. We derive the Rovelli-Thiemann-Ditrich partial observables corresponding to the quantum geometry operators of LQC in both Hilbert spaces: the kinematical one and, respectively, the physical Hilbert space of solutions to the quantum constraints. We find, that Quantum Geometry can be used to characterize the physical solutions, and the operators of quantum geometry preserve many of their kinematical properties.Comment: Latex, 12 page

Non-singular Universes a la Palatini

It has recently been shown that f(R) theories formulated in the Palatini variational formalism are able to avoid the big bang singularity yielding instead a bouncing solution. The mechanism responsible for this behavior is similar to that observed in the effective dynamics of loop quantum cosmology and an f(R) theory exactly reproducing that dynamics has been found. I will show here that considering more general actions, with quadratic contributions of the Ricci tensor, results in a much richer phenomenology that yields bouncing solutions even in anisotropic (Bianchi I) scenarios. Some implications of these results are discussed.Comment: 4 pages, no figures. Contribution to the Spanish Relativity Meeting (ERE2010), 6-10 Sept. Granada, Spai

Classical Setting and Effective Dynamics for Spinfoam Cosmology

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasize

A Bell Inequality Analog in Quantum Measure Theory

One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or {\it measure}, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as ``screening off''. We show that if one assumes, more generally, a joint {\it quantal measure}, or ``decoherence functional'', one obtains instead an analogous inequality weaker by a factor of $\sqrt{2}$. The proof of this ``Tsirel'son inequality'' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a {\it question}: ``Does a joint measure follow from some quantal analog of `screening off'?'', and to the {\it observation} that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the meaning more clearly. Minor rewording and extra acknowledgements, now closer to published versio

Price dispersion: the case of pasta

Scopo della ricerca è indagare la possibilità di utilizzare scanner data sugli acquisti di pasta per costruire indici dei prezzi spaziali bilaterali e multilaterali utilizzando un approccio binario nella loro costruzione.The aim of our research is to explore the possibility of utilizing scanner data on pasta purchases to build bilateral and multilateral spatial price indexes, taking a binary approach in the latter.1 Pasta plays a major role in the Italian diet. Historically, pasta consumption was mainly concentrated in the Southern regions of the country but today pasta is perhaps the product most representative of the eating habits of the Italians. The range of pasta producers runs from firms of longstanding tradition (some of them mainly directed towards local markets, such as Mastromauro in Puglia) to well known international brands (such as Barilla and De Cecco). The marked increase in pasta prices over the last two years has aroused great interest, but with little focus on spatial price diversity. This study stems from the availability of an extremely detailed panel dataset (Nielsen data) on values and quantities of pasta purchased. This data was produced by the use of bar-code scanning at retail outlets and thus includes information which provides weights at an elementary level. The use of scanner data to construct price indexes is not new in literature and there is a widespread consensus on the advantages of this approach in achieving more representative indexes. Average prices (unit values) show a marked spatial price variability: even when only considering the five bestselling products, regional prices vary greatly. The paper is set out as follows: Sect. 2 provides a description of the pasta scanner dataset and briefly looks for price variability; in Sect. 3 the requirements of comparability and representativity in the case of pasta are discussed; Sect. 4 deals with the methods and formulas chosen to obtain indexes for the regional comparisons of prices; Sect. 5 shows empirical results; in Sect. 6 a brief conclusion and suggestions for future work are given

Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC

A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts.Comment: RevTex4, 32 page

Numerical loop quantum cosmology: an overview

A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key prediction of the bounce at the Planck scale in different models, and the numerical methods used to analyze the properties of the quantum difference operator and the von Neumann stability issues. Using the quantization of a massless scalar field in an isotropic spacetime as a template, an attempt is made to highlight the complementarity of different methods to gain understanding of the new physics emerging from the quantum theory. Open directions which need to be explored with more refined numerical methods are discussed.Comment: 33 Pages, 4 figures. Invited contribution to appear in Classical and Quantum Gravity special issue on Non-Astrophysical Numerical Relativit

Loop Quantum Cosmology: A Status Report

The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that, as described at the end of section I, each of these communities can read only the sections they are most interested in, without a loss of continuity.Comment: 138 pages, 15 figures. Invited Topical Review, To appear in Classical and Quantum Gravity. Typos corrected, clarifications and references adde

STUDI DESKRIPTIF LEVEL BERPIKIR GEOMETRI VAN HIELE SISWA DI SMP NEGERI PERCONTOHAN DI LEMBANG

Geometri sekolah mempunyai peluang besar untuk dipahami oleh siswa dibandingkan dengan cabang ilmu matematika yang lainnya. Hal ini dikarenakan pengenalan konsep dasar geometri sudah dikenal oleh siswa sejak usia dini, seperti mengenal bangun-bangun geometri. Namun beberapa penelitian menunjukkan bahwa masih banyak siswa yang mengalami kesulitan dalam belajar geeometri, khususnya pada tingkat SMP. Oleh karena itu diperlukan penelitian terhadap level berpikir geometri siswa. Penelitian ini bertujuan untuk mengetahui: (1) level berpikir geometri siswa di SMP Negeri percontohan di Lembang, dan (2) menelaah apakah pembelajaran geometri yang berlangsung di sekolah menerapkan tahapan pembelajaran Van Hiele atau tidak. Metode dalam penelitian ini merupakan studi deskriptif dengan subjek penelitian adalah siswa kelas IX dari dua sekolah menengah pertama di Lembang. Instrumen dalam penelitian ini terdiri dari: (1) instrumen tes, yaitu tes level berpikir geometri Van Hiele pada materi bangun datar. Hasil dari tes ini dianalisis dengan kategori level berpikir sebagai berikut: level 0 adalah tahap pengenalan; level 1 adalah tahap analisis; level 2 adalah tahap pengurutan; level 3 adalah tahap deduksi formal; dan level 4 adalah tahap akurasi. (2) Instrumen non tes, yaitu berupa wawancara terhadap guru dan murid. Berdasarkan hasil penelitian diperoleh kesimpulan bahwa: (1) secara keseluruhan siswa SMP telah memasuki tahap berpikir geometri Van Hiele. Sebagian besar siswa berada pada tahap pengenalan (level 0) yaitu 81,16%, sedangkan sisanya telah memasuki tahap analisis (level 1) sebesar 17,39% dan tahap pengurutan (level 2) sebesar 1,45%. (2) Pembelajaran geometri di sekolah kurang memperhatikan tahapan pembelajaran geometri Van Hiele---------- Student has a big opportunity to understand geometry because the basic concept has early familiar, such as know the geometry’s objects. However, some of the research were show that many student difficult to learn geometry, specifically for junior high school. Because of that, it necessary to research about the geometry level thinking. The goal of the research are to know: (1) student geometry level thinking at the model of junior high school in Lembang, and (2) observe the lesson geometry at school by use the phase of Van Hiele geometry learning. The method is descriptive study with the subject are the student from IX class of two junior high school in Lembang. The instrument is: (1) test instrument, is Van Hiele geometry level test. The result will be analysis by categories of Van Hiele: level 0 is visualization; level 1 is analysis; level 2 is informal deduction; level 3 is deduction; and level 4 is rigor. (2) Non-test instrument, is interview to the teacher and student. Base of the research, the conclusion are: (1) by and large the student has include the Van Hiele geometry level. Student at level 0 is 81, 16%, at level 1 is 17,3% and at level 2 is 1,45%. (2) School did’nt use the phase of Van Hiele geometry learning

Circulating levels of dickkopf-1, osteoprotegerin and sclerostin are higher in old compared with young men and women and positively associated with whole-body bone mineral density in older adults

Summary: Bone mineral density declines with increasing older age. We examined the levels of circulating factors known to regulate bone metabolism in healthy young and older adults. The circulating levels of dickkopf-1, osteocalcin, osteoprotegerin and sclerostin were positively associated with WBMD in older adults, despite the average WBMD being lower and circulating dickkopf-1, osteoprotegerin and sclerostin being higher in old than young. Purpose: To investigate the relationship between whole-body bone mineral density (WBMD) and levels of circulating factors with known roles in bone remodelling during 'healthy' ageing. Methods: WBMD and fasting plasma concentrations of dickkopf-1, fibroblast growth factor-23, osteocalcin, osteoprotegerin, osteopontin and sclerostin were measured in 272 older subjects (69 to 81 years; 52% female) and 171 younger subjects (18-30 years; 53% female). Results: WBMD was lower in old than young. Circulating osteocalcin was lower in old compared with young, while dickkopf-1, osteoprotegerin and sclerostin were higher in old compared with young. These circulating factors were each positively associated with WBMD in the older adults and the relationships remained after adjustment for covariates (r-values ranging from 0.174 to 0.254, all p<0.01). In multivariate regression, the body mass index, circulating sclerostin and whole-body lean mass together accounted for 13.8% of the variation with WBMD in the older adults. In young adults, dickkopf-1 and body mass index together accounted for 7.7% of variation in WBMD. Conclusion: Circulating levels of dickkopf-1, osteocalcin, osteoprotegerin and sclerostin are positively associated with WBMD in community-dwelling older adults, despite the average WBMD being lower and circulating dickkopf-1, osteoprotegerin and sclerostin being higher in old than young