arXiv subjects

Tim Koslowski

Publications and source records attributed to Tim Koslowski.

At least 19 recordsLinked to original sources

arXiv2025

Pure Shape Dynamics: Relational General Relativity

We present a Pure Shape Dynamics (PSD) formulation of General Relativity (GR), which implements full relationalism by eliminating absolute scale and external time references from the fundamental description of gravity. Starting from the Arnowitt-Deser-Misner (ADM) formulation, we derive a decoupled dynamical system that governs the evolution of the spatial conformal geometry and relational matter degrees of freedom, while eliminating the total volume and York time as independent dynamical variables. This results in an autonomous subsystem describing an unparametrized trajectory in the conformal superspace of metric and matter configurations, with its evolution encoded in an equation of state that characterises the intrinsic geometric properties of the curve in shape space. We show that this equation of state is structurally analogous to the corresponding PSD description of the Newtonian $N$-body problem, reinforcing the fundamental similarity between gravity and relational particle dynamics. Our framework is applied to the homogeneous Bianchi IX cosmological model, demonstrating that the Janus point evolution through the Big Bang, as previously found in a symmetry-reduced setting, is a generic feature of the full inhomogeneous PSD description. This work establishes PSD as a fully scale- and reparametrization-invariant formulation of classical gravity and lays the foundation for addressing key open questions that are discussed at the end of the paper.

gr-qc↗

arXiv2024

A proposal for a metaphysics of self-subsisting structures. II. Quantum physics

The paper presents an extension of the metaphysics of self-subsisting structures set out in a companion paper to the realm of non-relativistic quantum physics. The discussion is centered around a Pure Shape Dynamics model representing a relational implementation of a de Broglie-Bohm $N$-body system. An interpretation of this model in terms of self-subsisting structures is proposed and assessed against the background of the debate on the metaphysics of quantum physics, with a particular emphasis on the nature of the wave function. The analysis shows that elaborating an appropriate Leibnizian/Machian metaphysics of the quantum world requires a substantial revision of the notion of world-building relation.

quant-ph↗

arXiv2024

Complexity and Its Creation

Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number of particles greater than or equal to the three needed to define triangle shapes. The resulting shape complexity is a simple scale-invariant quantity that measures the extent to which a collection of particles has a uniform or clustered distribution. As a positive-definite number with an absolute minimum realised on the most uniform distribution the particles can have, it not only characterises all physical structures from crystals to the most complex that can exist but also determines for them a measure that makes richly structured shapes more probable than bland ones. Strikingly, the criterion employed to define the shape complexity forces it to be the product of the two functions that define Newtonian universal gravitation. This suggests both the form and solutions the law of a universe of such particles should have and leads to a theory that not only determines the complexity and probability of any individual shape but also its creation from the maximally uniform shape. It does this moreover in a manner which makes it probable that the cosmological principle, according to which on a sufficiently large scale the universe should have the same appearance everywhere, holds. Our theory relies on universal group-theoretical principles that may allow generalisation to include all forces and general relativity.

gr-qc↗

arXiv2023

A de Broglie-Bohm Model of Pure Shape Dynamics: $N$-body system

We provide the construction of a de Broglie-Bohm model of the $N$-body system within the framework of Pure Shape Dynamics. The equation of state of the curve in shape space is worked out, with the instantaneous shape being guided by a wave function. In order to get a better understanding of the dynamical system, we also give some numerical analysis of the 3-body case. Remarkably enough, our simulations typically show the attractor-driven behaviour of complexity, well known in the classical case, thereby providing further evidence for the claim that the arrow of complexity is the ultimate cause of the experienced arrow of time.

gr-qc↗

arXiv2022

A Proposal for a Metaphysics of Self-Subsisting Structures. I. Classical Physics

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered -- and is thus susceptible to scientific progress -- , the empirically successful structural features of the framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space.

physics.hist-ph↗

arXiv2022

The Physics and Metaphysics of Pure Shape Dynamics

The goal of this essay is twofold. First, it provides a quick look at the foundations of modern relational mechanics by tracing its development from Julian Barbour and Bruno Bertotti's original ideas until present-day's pure shape dynamics. Secondly, it discusses the most appropriate metaphysics for pure shape dynamics, showing that relationalism is more of a nuanced thesis rather than an elusive one. The chapter ends with a brief assessment of the prospects of pure shape dynamics in light of quantum physics.

physics.hist-ph↗

arXiv2021

Pure shape dynamics: General framework

We put forward a general framework for describing relational physical theories, which we call Pure Shape Dynamics (PSD). Elaborating on the original insights brought about by the Shape Dynamics program, PSD's novel take on relationalism is its insistence on describing any dynamical system by means of the intrinsic geometry of its associated curve in the suitable relational configuration space of the theory, namely shape space, whereby the corresponding equation of state of the curve expresses the ratio of change of one of its geometric degrees of freedom with respect to another one. The mathematical structure underlying the equation of state is a local section over a natural generalization of the unit tangent bundle, which we call shape phase space.

gr-qc↗

arXiv2020

Renormalization Group Approach to the Continuum Limit of Matrix Models of Quantum Gravity with Preferred Foliation

This contribution is not intended as a review but, by suggestion of the editors, as a glimpse ahead into the realm of dually weighted tensor models for quantum gravity. This class of models allows one to consider a wider class of quantum gravity models, in particular one can formulate state sum models of spacetime with an intrinsic notion of foliation. The simplest one of these models is the one proposed by Benedetti and Henson, which is a matrix model formulation of two-dimensional Causal Dynamical Triangulations (CDT). In this paper we apply the Functional Renormalization Group Equation (FRGE) to the Benedetti-Henson model with the purpose of investigating the possible continuum limits of this class of models. Possible continuum limits appear in this FRGE approach as fixed points of the renormalization group flow where the size of the matrix acts as the renormalization scale. Considering very small truncations, we find fixed points that are compatible with analytically known results for CDT in two dimensions. By studying the scheme dependence of our results we find that precision results require larger truncations than the ones considered in the present work. We conclude that our work suggests that the FRGE is a useful exploratory tool for dually weighted matrix models. We thus expect that the FRGE will be a useful exploratory tool for the investigation of dually weighted tensor models for CDT in higher dimensions.

gr-qc↗

arXiv2018

Status of background-independent coarse-graining in tensor models for quantum gravity

A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual ideas underlying the use of the number of degrees of freedom as a scale for a Renormalization Group flow. We focus on tensor models, for which we explain how the tensor size serves as the scale for a background-independent coarse-graining flow. This flow provides a new probe of a universal continuum limit in tensor models. We review the development and setup of this tool and summarize results in the 2- and 3-dimensional case. Moreover, we provide a step-by-step guide to the practical implementation of these ideas and tools by deriving the flow of couplings in a rank-4-tensor model. We discuss the phenomenon of dimensional reduction in these models and find tentative first hints for an interacting fixed point with potential relevance for the continuum limit in four-dimensional quantum gravity.

gr-qc↗

arXiv2018

Towards background independent quantum gravity with tensor models

We explore whether the phase diagram of tensor models could feature a pregeometric, discrete and a geometric, continuum phase for the building blocks of space. The latter are associated to rank $d$ tensors of size $N$. We search for a universal large $N$ scaling limit in a rank-3 model with real tensors that could be linked to a transition between the two phases. We extend the conceptual development and practical implementation of the flow equation for the pregeometric setting. This provides a pregeometric "coarse-graining" by going from many microscopic to few effective degrees of freedom by lowering $N$. We discover several candidates for fixed points of this coarse graining procedure, and specifically explore the impact of a novel class of interactions allowed in the real rank-3 model. In particular, we explain how most universality classes feature dimensional reduction, while one candidate, involving a tetrahedral interaction, might potentially be of relevance for three-dimensional quantum gravity.

gr-qc↗

arXiv2017

Flowing to the continuum in discrete tensor models for quantum gravity

Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size N serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for three-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed points with a second relevant direction in a truncation of the Renormalization Group flow. The new relevant direction might hint at the presence of additional degrees of freedom in the corresponding continuum limit.

gr-qc↗

arXiv2016

Janus Points and Arrows of Time

We clarify and strengthen our demonstration that arrows of time necessarily arise in unconfined systems. Contrary to a recent claim, this does not require an improbable selection principle.

gr-qc↗

arXiv2015

Gravitational collapse of thin shells of dust in asymptotically flat Shape Dynamics

In a recent paper, one of us studied spherically symmetric, asymptotically flat solutions of Shape Dynamics, finding that the spatial metric has characteristics of a wormhole - two asymptotically flat ends and a minimal-area sphere, or `throat', in between. In this paper we investigate whether that solution can emerge as a result of gravitational collapse of matter. With this goal, we study the simplest kind of spherically-symmetric matter: an infinitely-thin shell of dust. Our system can be understood as a model of a star accreting a thin layer of matter. We solve the dynamics of the shell exactly and find that, indeed, as it collapses, the shell leaves in its wake the wormhole metric. In the maximal-slicing time we use for asymptotically flat solutions, the shell only approaches the throat asymptotically and does not cross it in a finite amount of time (as measured by a clock `at infinity'). This leaves open the possibility that a more realistic cosmological solution of Shape Dynamics might see this crossing happening in a finite amount of time (as measured by the change of relational/shape degrees of freedom).

gr-qc↗

arXiv2015

Entropy and the Typicality of Universes

The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by inappropriate transfer of the traditional concept of entropy to the whole universe. Use of what we call the relational $N$-body problem as a model indicates the need to employ two distinct entropy-type concepts to describe the universe. One, which we call entaxy, is novel. It is scale-invariant and decreases as the observable universe evolves. The other is the algebraic sum of the dimensionful entropies of branch systems (isolated subsystems of the universe). This conventional additive entropy increases. In our model, the decrease of entaxy is fundamental and makes possible the emergence of branch systems and their increasing entropy. We have previously shown that all solutions of our model divide into two halves at a unique `Janus point' of maximum disorder. This constitutes a common past for two futures each with its own gravitational arrow of time. We now show that these arrows are expressed through the formation of branch systems within which conventional entropy increases. On either side of the Janus point, this increase is in the same direction in every branch system. We also show that it is only possible to specify unbiased solution-determining data at the Janus point. Special properties of these `mid-point data' make it possible to develop a rational theory of the typicality of universes whose governing law, as in our model, dictates the presence of a Janus point in every solution. If our self-gravitating universe is governed by such a law, then the second law of thermodynamics is a necessary direct consequence of it and does not need any special initial condition.

gr-qc↗

arXiv2015

The shape dynamics description of gravity

Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than GR) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of spacetime in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of spacetime geometry, the role of local Minkowski space, universality of spacetime geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincare group. In this contribution I derive effective spacetime structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an "experienced spacetime geometry." This leads (in an idealized approximation) to local Minkowski space and causal relations. The small scale structure of the emergent geometric picture depends on the specific probes used to experience spacetime, which limits the applicability of effective spacetime to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski spacetime emerges from the evolution of quantum particles.

gr-qc↗

arXiv2014

Identification of a gravitational arrow of time

It is widely believed that special initial conditions must be imposed on any time-symmetric law if its solutions are to exhibit behavior of any kind that defines an `arrow of time'. We show that this is not so. The simplest non-trivial time-symmetric law that can be used to model a dynamically closed universe is the Newtonian $N$-body problem with vanishing total energy and angular momentum. Because of special properties of this system (likely to be shared by any law of the Universe), its typical solutions all divide at a uniquely defined point into two halves. In each a well-defined measure of shape complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows and act as `records'. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of the records of one branch and deduce a unique past and future direction from inspection of the available records.

gr-qc↗

arXiv2014

Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group

We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the analysis of [1], we study three new aspects of the double-scaling limit of matrix models as Renormalization Group fixed points: Firstly, we investigate multicritical fixed points, which are associated with quantum gravity coupled to conformal matter. Secondly, we discuss an approximation that reduces the scheme dependence of our results as well as computational effort while giving good numerical results. This is a consequence of the approximation being a solution to the unitary Ward-identity associated to the U(N) symmetry of the hermitian matrix model. Thirdly, we discuss a scenario that relates the double scaling limit to fixed points of continuum quantum gravity.

gr-qc↗

arXiv2013

A Gravitational Origin of the Arrows of Time

The only widely accepted explanation for the various arrows of time that everywhere and at all epochs point in the same direction is the `past hypothesis': the Universe had a very special low-entropy initial state. We present the first evidence for an alternative conjecture: the arrows exist in all solutions of the gravitational law that governs the Universe and arise because the space of its true degrees of freedom (shape space) is asymmetric. We prove our conjecture for arrows of complexity and information in the Newtonian N-body problem. Except for a set of measure zero, all of its solutions for non-negative energy divide at a uniquely defined point into two halves. In each a well-defined measure of complexity fluctuates but grows irreversibly between rising bounds from that point. Structures that store dynamical information are created as the complexity grows. Recognition of the division is a key novelty of our approach. Each solution can be viewed as having a single past and two distinct futures emerging from it. Any internal observer must be in one half of the solution and will only be aware of one past and one future. The `paradox' of a time-symmetric law that leads to observationally irreversible behaviour is fully resolved. General Relativity shares enough architectonic structure with the N-body problem for us to prove the existence of analogous complexity arrows in the vacuum Bianchi IX model. In the absence of non-trivial solutions with matter we cannot prove that arrows of dynamical information will arise in GR, though they have in our Universe. Finally, we indicate how the other arrows of time could arise.

gr-qc↗