arXiv subjects

Sean Gryb

Publications and source records attributed to Sean Gryb.

At least 19 recordsLinked to original sources

arXiv2026

Nomic Structure and Reduction

The canonical formulation of physical theories with irregular nomic structure is as constrained Hamiltonian theories within which ill-posedness of the equations of motion is connected to a pernicious form of surplus representational capacity. Such theories can be converted into theories with regular nomic structure and a well-posed initial value problem via the process of symplectic reduction. We analyse, synthesise, and contrast different approaches to the presentation and analysis of constrained Hamiltonian theories, drawing upon recent work on formalisation of nomic structure on model spaces (Gryb and Th\'ebault 2024) and comparisons of theoretical structure and representational capacity via category theory (Bradley and Weatherall 2020; Bradley 2025b). We suggest that the case of irregular nomic structure is most naturally suited to a category theoretic presentation in which state spaces are arrows and symplectic reduction is arrow composition (Landsman 2005). Under this approach one obtains the natural results that theories with isomorphic state spaces are equivalent and theories whose reduced state spaces are isomorphic are equivalent at the level of the regular representations of their nomic structure. This analysis provides a suitable foundation for the case of quantization of theories with irregular nomic structure, which will be in a companion paper.

physics.hist-ph↗

arXiv2025

An account of the arrow of time when scale is surplus

Existing accounts of the cosmological arrow of time face a dilemma: generalist approaches that posit time-asymmetric laws lack independent motivation, while particularist approaches that invoke a Past Hypothesis face serious conceptual and explanatory problems. We propose a novel account that dispenses with the need for both time-asymmetric laws and a Past Hypothesis. Instead, it is centred around a symmetry argument that reveals attractors and so-called 'Janus points'. The main idea is that the global spatial scale of the Universe is not empirically accessible, and should therefore be treated as surplus structure. By contrast, the Hubble parameter, which encodes the relative rate of change of scale, is empirically accessible. Once the scale redundancy is eliminated, the empirically meaningful description of cosmic dynamics involves a drag-like variable that transforms in a way that preserves time-reversal invariance. The resulting space of dynamical possibilities possesses universal attractors and Janus points, giving rise to particular states in which observers experience a cosmological arrow of time akin to our own. We illustrate the proposal by applying it to cosmological and gravitational N-body models, showing how it accounts, respectively, for the rapid cooling of the early universe and its relative smoothness.

physics.hist-ph↗

arXiv2025

Gauge symmetry and the arrow of time: How to count what counts

This thesis addresses two major problems in the philosophy of physics. The first is how to identify the minimal physical content of a theory; that is, what features of a theory are truly needed to make predictions, and what can be removed without changing its empirical consequences. The second is the problem of time's arrow: why time seems to have a direction, even though the fundamental laws of physics treat the past and future symmetrically. I show that answering the first question leads to insights about the second. In particular, I argue that the overall size of the Universe is not used to make predictions in cosmology, and so should not count as part of the theory's minimal physical content. Describing the Universe without this feature leads to a striking result: the arrow of time becomes a local phenomenon. Observers like us who see a Universe full of matter clumped together to form structures like stars and planets are statistically much more likely to see increasing clumpiness into the future than into the past. This tendency helps explain our experience of time's direction.

physics.hist-ph↗

arXiv2024

How closed is cosmology?

Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the focusing of measures along the dynamical flow. From these properties, we show that important dynamical features emerge that are not present in closed systems. In particular, a large and physically plausible class of cosmological models give rise to a natural arrow of time. We then argue that the appropriate notion of closure in cosmology is dynamical closure - that a system can be integrated without reference to external factors. This is realised in physical systems in terms of the algebraic closure of the equations of motion such that the system is autonomous. Remarkably, in a growing class of models it can be shown that the autonomous system obtained remains regular and can be integrated through the big bang.

gr-qc↗

arXiv2021

When scale is surplus

We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a system where the unit of Hamilton's principal function is rescaled, and therefore represent a kind of dynamical scaling symmetry with formal properties that differ from many standard symmetries. To study this symmetry, we develop a general framework for symmetries that distinguishes the observable and surplus structures of a theory by using the minimal freely specifiable initial data for the theory that is necessary to achieve empirical adequacy. This framework is then applied to well-studied examples including Galilean invariance and the symmetries of the Kepler problem. We find that our framework gives a precise dynamical criterion for identifying the observables of those systems, and that those observables agree with epistemic expectations. We then apply our framework to dynamical similarity. First we give a general definition of dynamical similarity. Then we show, with the help of some previous results, how the dynamics of our observables leads to singularity resolution and the emergence of an arrow of time in cosmology.

physics.hist-ph↗

arXiv2020

Angular momentum without rotation: turbocharging relationalism

Newton's rotating bucket pours cold water on the naive relationalist by vividly illustrating how certain rotational effects, particularly those due to non-zero angular momentum, can depend on more than just relations between material bodies. Because of such effects, rotation has played a central role in the absolute-relational debate and poses a particularly difficult challenge to the relationalist. In this paper, we provide a qualified response to this challenge that significantly weakens the absolutist position. We present a theory that, contrary to orthodoxy, can account for all rotational effects without introducing, as the absolutist does, a fixed standard of rotation. Instead, our theory posits a universal SO(3) charge that plays the role of angular momentum and couples to inter-particle relations via terms commonly seen in standard gauge theories such as electromagnetism and the Standard Model of particle physics. Our theory makes use of an enriched form of relationalism: it adds an SO(3) structure to the traditional relational description. Our construction is made possible by the modern tools of gauge theory, which reveal a simple relational law describing rotational effects. In this way, we can save the phenomena of Newtonian mechanics using conserved charges and relationalism. In a second paper, we will further explore the ontological and explanatory implications of the theory developed here.

physics.hist-ph↗

arXiv2020

New Difficulties for the Past Hypothesis

Many macroscopic physical processes are known to occur in a time-directed way despite the apparent time-symmetry of the known fundamental laws. A popular explanation is to postulate an unimaginably atypical state for the early universe -- a "Past Hypothesis" (PH) -- that seeds the time-asymmetry from which all others follow. I will argue that such a PH faces serious new difficulties. First I strengthen the grounds for existing criticism by providing a systematic analytic framework for assessing the status of the PH. I outline three broad categories of criticism that put into question a list of essential requirements of the proposal. The resulting analysis paints a grim picture for the prospects of providing an adequate formulation for an explicit PH. I then provide a new argument that substantively extends this criticism by showing that any time-independent measure on the space of models of the universe must necessarily break one of its gauge symmetries. The PH then faces a new dilemma: reject a gauge symmetry of the universe and introduce a distinction without difference or reject the time-independence of the measure and lose explanatory power.

physics.hist-ph↗

arXiv2018

On the Universality of Hawking Radiation

A physically consistent semi-classical treatment of black holes requires universality arguments to deal with the `trans-Planckian' problem where quantum spacetime effects appear to be amplified such that they undermine the entire semi-classical modelling framework. We evaluate three families of such arguments in comparison with Wilsonian renormalization group universality arguments found in the context of condensed matter physics. Our analysis is framed by the crucial distinction between robustness and universality. Particular emphasis is placed on the quality whereby the various arguments are underpinned by `integrated' notions of robustness and universality. Whereas the principal strength of Wilsonian universality arguments can be understood in terms of the presence of such integration, the principal weakness of all three universality arguments for Hawking radiation is its absence.

physics.hist-ph↗

arXiv2018

On the Empirical Consequences of the AdS/CFT Duality

We provide an analysis of the empirical consequences of the AdS/CFT duality with reference to the application of the duality in a fundamental theory, effective theory and instrumental context. Analysis of the first two contexts is intended to serve as a guide to the potential empirical and ontological status of gauge/gravity dualities as descriptions of actual physics at the Planck scale. The third context is directly connected to the use of AdS/CFT to describe real quark-gluon plasmas. In the latter context, we find that neither of the two duals are confirmed by the empirical data.

physics.hist-ph↗

arXiv2018

Superpositions of the cosmological constant allow for singularity resolution and unitary evolution in quantum cosmology

A novel approach to quantization is shown to allow for superpositions of the cosmological constant in isotropic and homogeneous mini-superspace models. Generic solutions featuring such superpositions display unitary evolution and resolution of the classical singularity. Physically well-motivated cosmological solutions are constructed. These particular solutions exhibit characteristic features of a cosmic bounce including universal phenomenology that can be rendered insensitive to Planck-scale physics in a natural manner.

gr-qc↗

arXiv2018

Bouncing Unitary Cosmology I: Mini-Superspace General Solution

We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the cosmological constant. This possibility leads to a finite, bouncing unitary cosmology. Whereas the usual Wheeler--DeWitt cosmology generically displays pathological behaviour in terms of non-finite expectation values and non-unitary dynamics, the finiteness and unitarity of our model are formally guaranteed. For classically singular models with a massless scalar field and cosmological constant, we show that well-behaved quantum observables can be constructed and generic solutions to the universal Schr\"{o}dinger equation are singularity-free. Generic solutions of our model displays novel features including: i) superpositions of values of the cosmological constant; ii) universal effective physics due to non-trivial self-adjoint extensions of the Hamiltonian; and iii) bound `Efimov universe' states for negative cosmological constant. The last feature provides a new platform for quantum simulation of the early universe. A companion paper provides detailed interpretation and analysis of particular cosmological solutions that display a cosmic bounce due to quantum gravitational effects, a well-defined FLRW limit far from the bounce, and a semi-classical turnaround point in the dynamics of the scalar field which resembles an effective inflationary epoch.

gr-qc↗

arXiv2018

Bouncing Unitary Cosmology II: Mini-Superspace Phenomenology

A companion paper provides a proposal for cosmic singularity resolution based upon general features of a bouncing unitary cosmological model in the mini-superspace approximation. This paper analyses novel phenomenology that can be identified within particular solutions of that model. First, we justify our choice of particular solutions based upon a clearly articulated and observationally-motivated principle. Second, we demonstrate that the chosen solutions follow a classical mini-superspace cosmology before smoothly bouncing off the classically singular region. Third, and most significantly, we identify a `Rayleigh-scattering' limit for physically reasonable choices of parameters within which the solutions display effective behaviour that is insensitive to the details of rapidly oscillating Planck-scale physics. This effective physics is found to be compatible with an effective period of cosmic inflation well below the Planck scale. The detailed effective physics of this Rayleigh-scattering limit is provided via: i) an exact analytical treatment of the model in the de~Sitter limit; and ii) numerical solutions of the full model.

gr-qc↗

arXiv2016

$\Psi$-Epistemic Quantum Cosmology?

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a $\Psi$-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity, upon causally-symmetric local hidden variable theories, and upon a dynamical origin for the cosmological arrow of time. Our conclusion weighs the strengths and weaknesses of the approach and points towards paths for future development.

gr-qc↗

arXiv2015

Regarding the `Hole Argument' and the `Problem of Time'

The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical and quantum gravity. In this paper, we examine the connection between these two much discussed problems in the foundations of spacetime theory along two interrelated lines. First, from a formal perspective, we consider the extent to which the two problems can and cannot be precisely and distinctly characterised. Second, from a philosophical perspective, we consider the implications of various responses to the problems, with a particular focus upon the viability of a `deflationary' attitude to the relationalist/substantivalist debate regarding the ontology of spacetime. Conceptual and formal inadequacies within the representative language of canonical gravity will be shown to be at the heart of both the canonical hole argument and the problem of time. Interesting and fruitful work at the interface of physics and philosophy relates to the challenge of resolving such inadequacies.

gr-qc↗

arXiv2015

Schrodinger Evolution for the Universe: Reparametrization

Starting from a generalized Hamilton-Jacobi formalism, we develop a new framework for constructing observables and their evolution in theories invariant under global time reparametrizations. Our proposal relaxes the usual Dirac prescription for the observables of a totally constrained system (`perennials') and allows one to recover the influential partial and complete observables approach in a particular limit. Difficulties such as the non-unitary evolution of the complete observables in terms of certain partial observables are explained as a breakdown of this limit. Identification of our observables (`mutables') relies upon a physical distinction between gauge symmetries that exist at the level of histories and states (`Type 1'), and those that exist at the level of histories and not states (`Type 2'). This distinction resolves a tension in the literature concerning the physical interpretation of the partial observables and allows for a richer class of observables in the quantum theory. There is the potential for the application of our proposal to the quantization of gravity when understood in terms of the Shape Dynamics formalism.

gr-qc↗

arXiv2015

Is Spacetime Countable?

Is there a number for every bit of spacetime, or is spacetime smooth like the real line? The ultimate fate of a quantum theory of gravity might depend on it. The troublesome infinities of quantum gravity can be cured by assuming that spacetime comes in countable, discrete pieces which one could simulate on a computer. But, perhaps there is another way? In this essay, we propose a picture where scale is meaningless so that there can be no minimum length and, hence, no fundamental discreteness. In this picture, Einstein's Special Relativity, suitably modified to accommodate an expanding Universe, can be reinterpreted as a theory where only the instantaneous shapes of configurations count.

gr-qc↗

arXiv2014

Observing Shape in Spacetime

The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms - namely hypersurface deformations - are, in a certain sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of "Shape Observer" that represents a conformal reference frame that is dual to the notion of inertial reference frame in spacetime. We then provide a precise dictionary relating the two notions. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.

gr-qc↗

arXiv2014

Time Remains

On one popular view, the general covariance of gravity implies that change is relational in a strong sense, such that all it is for a physical degree of freedom to change is for it to vary with regard to a second physical degree of freedom. At a quantum level, this view of "change as relative variation" leads to a "fundamentally timeless" formalism for quantum gravity. Here, we will show how one may avoid this acute `problem of time'. Under our view, duration is still regarded as relative, but temporal succession is taken to be absolute. Following our approach, which is presented in more formal terms in arXiv:1303.7139, it is possible to conceive of a genuinely dynamical theory of quantum gravity within which time, in a substantive sense, remains.

gr-qc↗