arXiv subjects

Fay Dowker

Publications and source records attributed to Fay Dowker.

At least 19 recordsLinked to original sources

arXiv2026

O Nature, Where Art Thou?

Where does what happens happen in a quantum system? The standard textbook formulation of quantum mechanics provides a strange, imprecise and yet successful-in-practice answer to this question. In the struggle to unify our understanding of gravity with quantum theory, though, the textbook answer no longer suffices, and an alternative approach is needed. The Feynman Sum Over Histories approach provides an alternative that is particularly suited to quantum gravity because the Sum Over Histories and General Relativity are built on the same fundamental concepts of `event' and `history'.

gr-qc↗

arXiv2024

Timelike boundary and corner terms in the causal set action

The causal set action of dimension $d$ is investigated for causal sets that are Poisson sprinklings into submanifolds of $d$-dimensional Minkowski space. Evidence, both analytic and numerical, is provided for the conjecture that the mean of the causal set action over sprinklings into a manifold with a timelike boundary, diverges like $l^{-1}$ in the continuum limit as the discreteness length $l$ tends to zero. A novel conjecture for the contribution to the causal set action from co-dimension 2 corners, also known as joints, is proposed and justified.

gr-qc↗

arXiv2024

Visions in Quantum Gravity

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

hep-th↗

arXiv2024

In-in correlators and scattering amplitudes on a causal set

Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale and takes the form of a Lorentzian lattice, or "causal set", from which continuum spacetime emerges in a large-scale (low-energy) approximation. In this work, we present new developments in the framework of interacting quantum field theory on causal sets. We derive a diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. We outline how these same correlators can be computed using the double-path integral which acts as a generating functional for the in-in correlators. We modify the in-in generating functional to obtain a generating functional for in-out correlators. We define a notion of scattering amplitudes on causal sets with non-interacting past and future regions and verify that they are given by S-matrix elements (matrix elements of the time-evolution operator). We describe how these formal developments can be implemented to compute early universe observables under the assumption that spacetime is fundamentally discrete.

hep-th↗

arXiv2023

Observables for cyclic causal set cosmologies

In causal set theory, cycles of cosmic expansion and collapse are modelled by causal sets with "breaks" and "posts" and a special role is played by cyclic dynamics in which the universe goes through perpetual cycles. We identify and characterise two algebras of observables for cyclic dynamics in which the causal set universe has infinitely many breaks. The first algebra is constructed from the cylinder sets associated with finite causal sets that have a single maximal element and offers a new framework for defining cyclic dynamics as random walks on a novel tree. The second algebra is generated by a collection of stem-sets and offers a physical interpretation of the observables in these models as statements about unlabeled stems with a single maximal element. There are analogous theorems for cyclic dynamics in which the causal set universe has infinitely many posts.

gr-qc↗

arXiv2023

An intrinsic causality principle in histories-based quantum theory: a proposal

Relativistic causality (RC) is the principle that no cause can act outside its future lightcone, but any attempt to formulate this principle more precisely will depend on the foundational framework that one adopts for quantum theory. Adopting a histories-based (or "path integral") framework, we relate RC to a condition we term "Persistence of Zero" (PoZ), according to which an event $E$ of measure zero remains forbidden if one forms its conjunction with any other event associated to a spacetime region that is later than or spacelike to that of $E$. We also relate PoZ to the Bell inequalities by showing that, in combination with a second, more technical condition it leads to the quantal counterpart of Fine's patching theorem in much the same way as Bell's condition of Local Causality leads to Fine's original theorem. We then argue that RC per se has very little to say on the matter of which correlations can occur in nature and which cannot. From the point of view we arrive at, histories-based quantum theories are nonlocal in spacetime, and fully in compliance with relativistic causality.

quant-ph↗

arXiv2023

Causal Set Quantum Gravity and the Hard Problem of Consciousness

I develop Rafael D. Sorkin's proposal that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity provides an objective physical correlate of our perception of time passing. I argue that one cannot have a fully objective, external picture of the birth process because the order in which the spacetime atoms are born is a partial order. I propose that live experience in causal set theory is an internal view of the objective birth process in which events that are neural correlates of consciousness occur. In causal set theory, what ``breathes fire'' into a neural correlate of consciousness is that which breathes fire into the whole universe: the unceasing, partially ordered process of the birth of spacetime atoms.

gr-qc↗

arXiv2021

If time had no beginning: growth dynamics for past-infinite causal sets

We explore whether the growth dynamics paradigm of Causal Set Theory is compatible with past-infinite causal sets. We modify the Classical Sequential Growth dynamics of Rideout and Sorkin to accommodate growth "into the past" and discuss what form physical constraints such as causality could take in this new framework. We propose convex-suborders as the "observables" or "physical properties" in a theory in which causal sets can be past-infinite and use this proposal to construct a manifestly covariant framework for dynamical models of growth for past-infinite causal sets.

gr-qc↗

arXiv2021

Recovering General Relativity from a Planck scale discrete theory of quantum gravity

An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis. We show in particular that an apparent alternative to causal sets, viz. a certain sort of discrete Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way. For it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.

gr-qc↗

arXiv2020

An Argument for Strong Positivity of the Decoherence Functional

We give an argument for strong positivity of the decoherence functional as the correct, physical positivity condition in formulations of quantum theory based fundamentally on the path integral. We extend to infinite systems work by Boes and Navascues that shows that the set of strongly positive quantum systems is maximal amongst sets of systems that are closed under tensor product composition. We show further that the set of strongly positive quantum systems is the unique set that is maximal amongst sets that are closed under tensor product composition.

quant-ph↗

arXiv2020

Boundary contributions in the causal set action

Evidence is provided for a conjecture that, in the continuum limit, the mean of the causal set action of a causal set sprinkled into a globally hyperbolic Lorentzian spacetime, M, of finite volume equals the Einstein Hilbert action of M plus the volume of the co-dimension 2 intersection of the future boundary with the past boundary. We give the heuristic argument for this conjecture and analyse some examples in 2 dimensions and one example in 4 dimensions.

gr-qc↗

arXiv2020

A manifestly covariant framework for causal set dynamics

We propose a manifestly covariant framework for causal set dynamics. The framework is based on a structure, dubbed covtree, which is a partial order on certain sets of finite, unlabeled causal sets. We show that every infinite path in covtree corresponds to at least one infinite, unlabeled causal set. We show that transition probabilities for a classical random walk on covtree induce a classical measure on the $σ$-algebra generated by the stem sets.

gr-qc↗

arXiv2019

Horizon Molecules in Causal Set Theory

We propose a new definition of "horizon molecules" in Causal Set Theory following pioneering work by Dou and Sorkin. The new concept applies for any causal horizon and its intersection with any spacelike hypersurface. In the continuum limit, as the discreteness scale tends to zero, the leading behaviour of the expected number of horizon molecules is shown to be the area of the horizon in discreteness units, up to a dimension dependent factor of order one. We also determine the first order corrections to the continuum value, and show how such corrections can be exploited to obtain further geometrical information about the horizon and the spacelike hypersurface from the causal set.

gr-qc↗

arXiv2019

Symmetry-breaking and zero-one laws

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincar{é} invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based.

gr-qc↗

arXiv2018

Scalar Field Green Functions on Causal Sets

We examine the validity and scope of Johnston's models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2-d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2 dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4-d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker's continuum Green function. We find that the same prescription can also be used for deSitter spacetime and the conformally flat patch of anti deSitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston's model for the Green function for a causal set approximated by 3 dimensional flat spacetime.

gr-qc↗

arXiv2017

A "problem of time" in the multiplicative scheme for the $n$-site hopper

Quantum Measure Theory (QMT) is an approach to quantum mechanics, based on the path integral, in which quantum theory is conceived of as a generalised stochastic process. One of the postulates of QMT is that events with zero quantum measure do not occur, however this is not sufficient to give a full picture of the quantum world. Determining the other postulates is a work in progress and this paper investigates a proposal called the Multiplicative Scheme for QMT in which the physical world corresponds, essentially, to a set of histories from the path integral. This scheme is applied to Sorkin's $n$-site hopper, a discrete, unitary model of a single particle on a ring of $n$ sites, motivated by free Schrödinger propagation. It is shown that the multiplicative scheme's global features lead to the conclusion that no non-trivial, time-finite event can occur.

quant-ph↗

arXiv2017

Evolution of Universes in Causal Set Cosmology

The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential Growth (CSG) models of Rideout and Sorkin form an interesting class of such laws. It has been shown that a renormalisation of the dynamical parameters of a CSG model occurs whenever the universe undergoes a Big Crunch-Big Bang bounce. In this paper we propose a way to model the creation of a new universe after the singularity of a black hole. We show that renormalisation of dynamical parameters occurs in a CSG model after such a creation event. We speculate that this could realise aspects of Smolin's Cosmological Natural Selection proposal.

gr-qc↗

arXiv2017

The Sorkin-Johnston State in a Patch of the Trousers Spacetime

A quantum scalar field in a patch of a fixed, topology-changing, $1+1$ dimensional "trousers" spacetime is studied using the Sorkin-Johnston formalism. The isometry group of the patch is the dihedral group, the symmetry group of the square. The theory is shown to be pathological in a way that can be interpreted as the topology change giving rise to a divergent energy, in agreement with previous results. In contrast to previous results, it is shown that the infinite energy is localised not only on the future light cone of the topology changing singularity, but also on the past cone, due to the time reversal symmetry of the Sorkin-Johnston state.

gr-qc↗