In this paper the principle that the boundary of a boundary is identically zero (∂○∂≡0) is applied to a skeleton geometry. It is shown that the left-hand side of the Regge equation may be interpreted geometrically as the sum of the moments of rotation associated with the faces of a polyhedral domain. Here the polyhedron, warped though it may be, is located in a lattice dual to the original skeleton manifold. This sum is related to the amount of energy-momentum (E-p) (...) associated to the edge in question. In the establishment of this equation the ordinary Bianchi identity is rederived by applying the principle that the (∂○∂≡0) in its (1–2–3)-dimensional formulation to polyhedral domain. Steps toward the derivation of the contracted Bianchi identity using this principle in its (2–3–4)-dimensional form are discussed. Preliminary results in this direction indicate that there should be one vector identity per vertex of the skeleton geometry. “Space acts on matter, telling it how to move. In turn, matter reacts back on space, telling it how to curve.”—Ref. 3, Chap. 1. (shrink)

In this paper, we present a non-geometrodynamic quantum Yang–Mills theory of gravity based on the homogeneous Lorentz group within the general framework of the Poincare gauge theories. The obstacles of this treatment are that first, on the one hand, the gauge group that is available for this purpose is non-compact. On the other hand, Yang–Mills theories with non-compact groups are rarely healthy, and only a few instances exist in the literature. Second, it is not clear how the direct observations of (...) space–time waves can be explained when space–time has no dynamics. We show that the theory is unitary and is renormalizable to the one-loop perturbation. Although in our proposal, gravity is not associated with any elementary particle analogous to the graviton, classical helicity-two space–time waves are explained. Five essential exact solutions to the field equations of our proposal are presented as well. We also discuss a few experimental tests that can falsify the presented Yang–Mills theory. (shrink)

The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the (...) former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions. (shrink)

We review three broadly geometrodynamical---and in part, Machian or relational---projects, from the perspective of spacetime functionalism. We show how all three are examples of functionalist reduction of the type that was advocated by D. Lewis, and nowadays goes by the label `the Canberra Plan’. The projects are: the recovery of geometrodynamics by Hojman et al. ; the programme of Schuller and collaborators to deduce a metric from the physics of matter fields; the deduction of the ADM Hamiltonian by Gomes (...) and Shyam. We end by drawing a positive corollary about shape dynamics: namely, it has a good rationale for the Hamiltonian it postulates. (shrink)

By extending geometrodynamical phase space by embeddings and their conjugate momenta, one can homomorphically map the Lie algebra of space-time diffeomorphisms into the Poisson algebra of dynamical variables on the extended phase space.

The central conceptual idea of the contemporary theory of general relativity--or geometrodynamics--is the identification of matter with the structure of space-time. No entities foreign to space-time, like masses, charges, or independent fields are needed, and physics thus becomes identical with the geometry of space-time. This idea implies a philosophical description of the universe that is monistic and organic, characterized by an all-encompassing interdependence of events. Moreover, it is an idea with deep roots in the history of philosophy. For these (...) reasons, the author of this important study strives to clarify these philosophical and historical issues before proceeding to the details of the physical theory of geometrodynamics. (shrink)

The traditional standard quantum mechanics theory is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle”. A complete and straightforward solution of the spin–statistics problem is presented on the basis of the “conformal quantum geometrodynamics” theory. This theory provides a Weyl-gauge invariant formulation of the standard quantum mechanics and reproduces successfully all relevant quantum processes including the formulation of Dirac’s or Schrödinger’s equation, of Heisenberg’s uncertainty relations and of the nonlocal EPR correlations. When (...) the conformal quantum geometrodynamics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the “intrinsic helicity”. This property, not considered in the Standard Quantum Mechanics, determines the correct spin–statistics connection observed in Nature. (shrink)

The aim of this paper is to contribute to a more balanced judgement than the widespread impression that the changes which are called for in today's philosophy of physics and which centre around the concept of holism amount to a rupture with the framework of Cartesian philosophy of physics. I argue that this framework includes a sort of holism: As a result of the identification of matter with space, any physical property can be instantiated only if there is the whole (...) of matter. Relating this holism to general relativity, I maintain that this holism cannot be directly applied to today's philosophy of physics consequent upon the failure of geometrodynamics. I show in what respect precisely the holism in quantum physics amounts to a revision of the holism within Cartesianism. (shrink)

The procedures of canonical quantization of the gravitational field apparently lead to entities for which any interpretation in terms of spatio-temporal localization or spatio-temporal extension seems difficult. This fact is the main ground for the suggestion that can often be found in the physics literature on canonical quantum gravity according to which spacetime may not be fundamental in some sense. This paper aims to investigate this radical suggestion from an ontologically serious point of view in the cases of two standard (...) forms of canonical quantum gravity, quantum geometrodynamics and loop quantum gravity. We start by discussing the physical features of the quantum wave functional of quantum geometrodynamics and of the spin networks of loop quantum gravity that motivate the view according to which spacetime is not fundamental. We then point out that, by contrast, for any known ontologically serious understanding of quantum entanglement, the commitment to spacetime seems indispensable. Against this background, we then critically discuss the idea that spacetime may emerge from more fundamental entities. As a consequence, we finally suggest that the emergence of classical spacetime in canonical quantum gravity faces a dilemma: either spacetime ontologically emerges from more fundamental non-spatio-temporal entities or it already belongs to the fundamental quantum gravitational level and the emergence of the classical picture is merely a matter of levels of description. On the first horn of the dilemma, it is unclear how to make sense of concrete physical entities that are not in spacetime and of the notion of ontological emergence that is involved. The second horn runs into the difficulties raised by the physics of canonical quantum gravity. (shrink)

The traditional standard theory of quantum mechanics is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper :858–873, 2015) we presented a proof of the spin–statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics”. In the present paper, by the same theory the proof of the spin–statistics theorem is extended to the relativistic (...) domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin–statistics connection observed in Nature :858–873, 2015). The present proof of the spin–statistics theorem is simpler than the one presented in Santamato and De Martini :858–873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary. (shrink)

Beyond Peaceful Coexistence: The Emergence of Space, Time and Quantum brings together leading academics in mathematics and physics to address going beyond the 'peaceful coexistence' of space-time descriptions (local and continuous ones) and quantum events (discrete and non-commutative ones). Formidable challenges waiting beyond the Standard Model require a new semantic consistency within the theories in order to build new ways of understanding, working and relating to them. The original A. Shimony meaning of the peaceful coexistence (the collapse postulate and non-locality) (...) appear to be just the tip of the iceberg in relation to more serious fundamental issues across physics as a whole. Chapters in this book present perspectives on emergent, discrete, geometrodynamic and topological approaches, as well as a new interpretative spectrum of quantum theories after Copenhagen, discrete time theories, time-less approaches and 'super-fluid' pictures of space-time. As well as stimulating further research among established theoretical physicists, the book can also be used in courses on the philosophy and mathematics of theoretical physics. (shrink)

This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular (...) for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond. (shrink)

The purpose of this paper is to shed some fresh light on the long-standing conceptual question of the origin of the well-known Poisson bracket structure of the constraints that govern the canonical dynamics of generally relativistic field theories, i.e. geometrodynamics. This structure has long been known to be the same for a wide class of fields that inhabit the space-time, namely those with non-differential coupling to gravity. It has also been noticed that an identical bracket structure can be derived (...) independently of any dynamical theory, by purely geometrical considerations in Lorentzian geometry. Here we attempt to provide the missing link between the dynamics and geometry, which we understand to be the reason for this structure to be of the specific kind. We achieve this by a careful analysis of the geometrodynamical approach, which allows us to derive the structure in question and understand it as a consistency requirement for any such theory. In order to stay close to the classical literature on the subject we stick to the metric formulation of general relativity, but the reasoning should carry over to any other formulation as long as the non-metricity tensor vanishes. The discussion section is devoted to derive some interesting consequences of the presented result in the context of reconstructing the Arnowitt–Deser–Misner framework, thus providing a precise sense to the inevitability of the Einstein’s theory under minimal assumptions. (shrink)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time. We then introduce the search for a quantum theory of gravity ; and review some general interpretative issues about space, time and matter. We then discuss the emergence of time in simple quantum geometrodynamics, and in the Euclidean approach. Section (...) 6 concludes. (shrink)

One of Julian Barbour’s main aims is to solve the problem of time that appears in quantum geometrodynamics (QG). QG involves the application of canonical quantization procedure to the Hamiltonian formulation of General Relativity. The problem of time arises because the quantization of the Hamiltonian constraint results in an equation that has no explicit time parameter. Thus, it appears that the resulting equation, as apparently timeless, cannot describe evolution of quantum states. Barbour attempts to resolve the problem by allegedly (...) eliminating time from his interpretation of QG. In order to evaluate the efficacy of his solution, it is necessary to ascertain in what sense time has been eliminated from his theory. I proceed to do so by developing a form of conceptual analysis that is applicable to the concept of time in physical theories and applying this analysis to Barbour’s account. (shrink)

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of contemporary physics: general relativity, quantum mechanics and some attempts at quantizing gravity (especially geometrodynamics and its recent successors in the form of various pregeometry conceptions). It turns out that all big interpretative issues involved in this problem point towards the (...) necessity of changing from the standard space-time geometry to some radically new, most probably non-local, generalization. We argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. Noncommutative spaces are, in general, non-local, and their applications to physics, known at present, seem very promising. One would expect that beneath the Planck threshold there reigns a "noncommutative pregeometry", and only when crossing this threshold does the usual space-time geometry emerges. (shrink)

I discuss Julian Barbour's Machian theories of dynamics, and his proposal that a Machian perspective enables one to solve the problem of time in quantum geometrodynamics (by saying that there is no time!). I concentrate on his recent book, The End of Time (1999). A shortened version will appear in The British Journal for Philosophy of Science}.

The procedures of canonical quantization of the gravitational field apparently lead to entities for which any interpretation in terms of spatio-temporal localization or spatio-temporal extension seems difficult. This fact is the main ground for the suggestion that can often be found in the physics literature on canonical quantum gravity according to which spacetime may not be fundamental in some sense. This paper aims to investigate this radical suggestion from an ontologically serious point of view in the cases of two standard (...) forms of canonical quantum gravity, quantum geometrodynamics and loop quantum gravity. We start by discussing the physical features of the quantum wave functional of quantum geometrodynamics and of the spin networks of loop quantum gravity that motivate the view according to which spacetime is not fundamental. We then point out that, by contrast, for any known ontologically serious understanding of quantum entanglement, the commitment to spacetime seems indispensable. Against this background, we then critically discuss the idea that spacetime may emerge from more fundamental entities. As a consequence, we finally suggest that the emergence of classical spacetime in canonical quantum gravity faces a dilemma: either spacetime ontologically emerges from more fundamental non-spatio-temporal entities or it already belongs to the fundamental quantum gravitational level and the emergence of the classical picture is merely a matter of levels of description. On the first horn of the dilemma, it is unclear how to make sense of concrete physical entities that are not in spacetime and of the notion of ontological emergence that is involved. The second horn runs into the difficulties raised by the physics of canonical quantum gravity. (shrink)

Prompted by the "Panel Discussion of Grünbaum's Philosophy of Science" (Philosophy of Science 36, December, 1969) and other recent literature, this essay ranges over major issues in the philosophy of space, time and space-time as well as over problems in the logic of ascertaining the falsity of a scientific hypothesis. The author's philosophy of geometry has recently been challenged along three main distinct lines as follows: (i) The Panel article by G. J. Massey calls for a more precise and more (...) coherent account of the Riemannian conception of an intrinsic as opposed to an extrinsic metric, which the author has invoked as his basis for the distinction between non-conventional and convention-laden ascriptions of metrical equality and inequality; (ii) the latter distinction has been claimed to suffer from the liabilities of the so-called "standard conception" of scientific theories [36]; and (iii) pursuant to H. Putnam's "An Examination of Grünbaum's Philosophy of Geometry" [56], J. Earman [16, 17] and R. Swinburne [65] have contended that the difference between intrinsic and extrinsic metrics is scientifically unilluminating, and that the associated distinction between non-conventional and convention-laden metrical comparisons does not have the kind of relevance to extant scientific theories that the author has claimed for it. The essay consists of two installments. The present installment, comprising the Introduction and Part A, is devoted to the clarification, correction and further development of the author's prior writings on the philosophy of geometry. Its main objective is constructive elaboration rather than offering polemics. But rebuttals to Earman, [16, 17], Swinburne [65] and Demopoulos [13] are included, because their inclusion conduced to clarity in giving the new exposition. Part B is to appear in a subsequent issue and will be devoted to replies to critiques contained in the Panel Discussion and in other recent literature. It will range over issues in the philosophy of geometry and in the logic of ascertaining the falsity of a scientific hypothesis. By way of merely elliptical anticipation of much more precise statements given in Part A, section 3(ii), the Introduction dissociates the notion of convention-ladenness developed in Part A from the quite different notion integral to the so-called "standard conception" of scientific theories. Thereby, the Introduction prepares the ground for seeing, as a corollary to Part A, section 3(ii), that the notion advocated in the present essay has nothing to fear from the following fact, noted by C. G. Hempel ([36]; cf. also his 1970 Carus Lectures): "even though a sentence may originally be introduced as true by stipulation, it soon joins the club of all other member-statements of the theory and becomes subject to revision in response to further empirical findings and theoretical developments." Part A, which begins with a fairly detailed table of contents, endeavors to meet the aforementioned three-fold challenge to the author's philosophy of geometry. Massey's call for the provision of clear and detailed characterizations of intrinsic and extrinsic metrics is answered with the invaluable aid rendered personally by Massey himself. These characterizations are shown to permit a precise explication of the portions of Riemann's Inaugural Dissertation relevant to (1) Riemann's brilliant anticipation of Einstein's dynamical conception of physical geometry, and (2) the author's philosophical characterization of the metrics and geometries of space, time, and space-time {section 2(c)}. A byproduct of the analysis is to raise two major philosophical doubts concerning Clifford's sketch of a so-called "space-theory of matter" as elaborated in J. A. Wheeler's relativistic geometrodynamics. That theory's vision of understanding matter as a manifestation of empty curved space is questioned in regard to (1) the existence of an intra-geometrodynamic basis for individuating the metrically homogeneous world points of its space-time manifold {section 1(a)}, and (2) the compatibility of the theory with the Riemannian metrical philosophy apparently espoused by its proponents {section 2(c)(i)}. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The “erasing race” effect is the reduction of the salience of “race” as an alliance cue when recalling coalition membership, once more accurate information about coalition structure is presented. We conducted a random-effects model meta-analysis of this effect using five United States studies (containing nine independent effect sizes). The effect was found (ρ = 0.137, K = 9, 95% CI = 0.085 to 0.188). However, no decline effect or moderation effects were found (a “decline effect” in this context would be (...) a decrease in the effect size over time). Furthermore, we found little evidence of publication bias. Synthetically correcting the effect size for bias stemming from the use of an older method for calculating error base rates reduced the magnitude of the effect, but the it remained significant. Taken together, these findings indicate that the “erasing race” effect generalizes quite well across experimental contexts and would, therefore, appear to be quite robust. We reinterpret the theoretical basis for these effects in line with Brunswikian evolutionary-developmental theory and present a series of predictions to guide future research in this area. (shrink)

This article investigates an intertwined systematic and historical view on theories of matter. It follows an approach brought forward by Hermann Weyl around 1925, applies it to recent theories of matter in physics (including geometrodynamics and quantum gravity), and embeds it into a more general philosophical framework. First, I shall discuss the physical and philosophical problems of a unified field theory on the basis of Weyl's own abandonment of his 1918 ‘pure field theory’ in favour of an ‘agent theory’ (...) of matter. The difference between agent and field theories of matter is then used to establish a sort of dialectic meta-view. With reference to Weyl this view can be understood as being a particular Fichtean transcendental idealist approach which attempts to combine the strengths of the Husserlian phenomenology and Cassirer's neo-Kantianism. (shrink)

The Continuous Parameter Estimation Model is applied to develop individual genomic-level heritabilities for the latent hierarchical structure and developmental dynamics of Life History (LH) strategy LH strategies relate to the allocations of bioenergetic resources into different domains of fitness. LH has moderate to high population-level heritability in humans, both at the level of the high-order Super-K Factor and the lower-order factors, the K-Factor, Covitality Factor, and General Factor of Personality (GFP). Several important questions remain unexplored. We developed measures of genome-level (...) heritabilities employing an American sample of 316 monozygotic (MZ) and 274 dizygotic (DZ) twin dyads and a Swedish sample of 863 MZ and 475 DZ twin dyads. This novel heritability index measures individual genetic transmissibility, therefore opening new avenues for analyzing complex interactions among heritable traits inaccessible to standard structural equations methods. For these samples: (1) moderate to high heritability of factor loadings of Super-K on its lower-order factors is demonstrated, evidencing biological preparedness, genetic accommodation, and the gene-culture coevolution of biased epigenetic rules of development; (2) moderate to high heritability of the magnitudes of the effect of the higher-order factors upon their loadings on their constituent factors, evidencing genetic constraints upon phenotypic plasticity; and (3) that heritability of the LH factors, of factor loadings, and of the magnitudes of the correlations among factors are weaker among those with slower LH speeds, demonstrating that inter-individual variation in transmissibility is a function of individual socioecological selection pressures. (shrink)

Objective Apeiron was founded in 1966 and has developed into one of the oldest and most distinguished journals dedicated to the study of ancient philosophy, ancient science, and, in particular, of problems that concern both fields. Apeiron is committed to publishing high-quality research papers in these areas of ancient Greco-Roman intellectual history; it also welcomes submission of articles dealing with the reception of ancient philosophical and scientific ideas in the later western tradition. The journal appears quarterly. Articles are peer-reviewed on (...) a double-blind basis. Topics ancient philosophy ancient science reception of ancient philosophical and scientific ideas in the later western tradition Article formats Original Articles. (shrink)

This volume offers an English translation of John of St. Thomas's Cursus theologicus I, question I, disputation 2. In this particular text, the Dominican master raises questions concerning the scientific status and nature of theology. At issue, here, are a number of factors: namely, Christianity's continual coming to terms with the "Third Entry" of Aristotelian thought into Western Christian intellectual culture - specifically the Aristotelian notion of 'science' and sacra doctrina's satisfaction of those requirements - the Thomistic-commentary tradition, and the (...) larger backdrop of the Iberian Peninsula's flourishing "Second Scholasticism." In this latter context, John of St. Thomas applies the theological principles of Thomas Aquinas to the Scholastic disputes preoccupying Thomist, Franciscan, and Jesuit theologians, such as Cajetan, Bañez, Luis de Molina, Vazquez, Suárez - to name only a few - in a tour de force of theological thinking throughout the entire period of Scholasticism. In the process - and not insignificantly - the status quaestionis of theology's scientific character is clearly framed and answered according to John's satisfaction. Key to John of St. Thomas's resolution of the question is his understanding of the continuity of the power of human reason with the super-intelligibility of divine revelation spelled out in terms of what he calls "virtual revelation." This text presented in this volume is a quintessential example of the deep and abiding harmony that flourished between faith and reason as well as grace and nature within the golden era of Baroque Scholasticism. (shrink)

"End-Of-Law week drinkS @ ACT Magistrates Court: Friday 20 May 2005." Ethos: Official Publication of the Law Society of the Australian Capital Territory, (198), pp. 24.

A critical edition with facing-page translation, of Guglielmo Ebreo's treatise of 1463. It also contains dance tunes in facsimile and in annotated transcriptions based on the choreographies.

This volume contains the first critical edition of the Scriptum super III-VIII libros Politicorum by Peter of Auvergne as well as a pragmatical edition of Books III-VIII of the medieval Latin translation of Aristotle's Politics. Intended as the continuation of Aquinas' unfinished commentary on the first three books of the Politics, the Scriptum became-together with Aquinas' commentary-the commentary on the Politics. From its appearance in the late thirteenth century to the end of the sixteenth century, the Scriptum represented the most (...) authoritative and influential interpretation of Books III-VIII of the Politics.The introduction to the volume provides both an overview of Peter's political thought and a case study of the production and dissemination of a university text. An examination of the manuscripts traces the preparation of the text from its first transcription and revision by a scribe close to the author-if not the author himself-to the preparation of the finished exemplar and its diffusion through the system of peciae. The introduction also explains how the text was adapted to fit the standards of humanistic Latin when it was first printed in the fifteenth century: its language was adjusted to humanistic standards, many formulations were reshaped, and passages were suppressed. These changes were subsequently preserved in all later editions of the text. Freed from this humanistic patina with which it has been transmitted since the early age of printing age, the Scriptum is now restored to its original version. (shrink)