## Publications

74 results found

Dowker F, Sorkin RD, 2023, An intrinsic causality principle in histories-based quantum theory: a proposal, *Journal of Physics A: Mathematical and Theoretical*, Vol: 56, ISSN: 1751-8113

Relativistic causality (RC) is the principle that no cause can act outside its future light cone, 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 RC.

Dowker F, Zalel S, 2023, Observables for cyclic causal set cosmologies, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 40, ISSN: 0264-9381

Dowker F, Wilkes H, 2022, An argument for strong positivity of the decoherence functional in the path integral approach to the foundations of quantum theory, *AVS Quantum Science*, Vol: 4, Pages: 012601-012601, ISSN: 2639-0213

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 Boës and Navascués that shows that the set of strongly positive quantum systems is maximal among 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 among the sets that are closed under tensor product composition.I. INTRODUCTION

Bento BV, Dowker F, Zalel S, 2022, If time had no beginning: growth dynamics for past-infinite causal sets, *Classical and Quantum Gravity*, Vol: 39, ISSN: 0264-9381

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.

Dowker F, 2021, Boundary contributions in the causal set action, *Classical and Quantum Gravity*, Vol: 38, ISSN: 0264-9381

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.

Dowker F, Sorkin RD, 2020, Symmetry-breaking and zero-one laws, *Classical and Quantum Gravity*, Vol: 37, ISSN: 0264-9381

We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré 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.

Dowker F, Imambaccus N, Owens A,
et al., 2020, A manifestly covariant framework for causal set dynamics, *Classical and Quantum Gravity*, Vol: 37, Pages: 085003-085003, ISSN: 0264-9381

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 -algebra generated by the stem sets.

Barton C, Counsell A, Dowker F,
et al., 2019, Horizon molecules in causal set theory, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 100, Pages: 1-17, ISSN: 1550-2368

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 behavior 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.

Wilkes H, Dowker H, Lewandowski C,
et al., 2017, A ``problem of time''' in the multiplicative scheme for the n-site hopper, *Journal of Physics A: Mathematical and Theoretical*, Vol: 50, ISSN: 1751-8113

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.

Ahmed SN, Dowker F, Surya S, 2017, Scalar field Green functions on causal sets, *Classical and Quantum Gravity*, Vol: 34, Pages: 1-19, ISSN: 0264-9381

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 2d 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 4d 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 de Sitter spacetime and the conformally flat patch of anti-de Sitter 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.

Clements K, Dowker F, Wallden P, 2017, Physical Logic, The Incomputable, Publisher: Springer International Publishing, Pages: 47-61

In R.D. Sorkin's framework for logic in physics a clear separation is madebetween the collection of unasserted propositions about the physical world andthe affirmation or denial of these propositions by the physical world. Theunasserted propositions form a Boolean algebra because they correspond tosubsets of an underlying set of spacetime histories. Physical rules ofinference, apply not to the propositions in themselves but to the affirmationand denial of these propositions by the actual world. This physical logic mayor may not respect the propositions' underlying Boolean structure. We provethat this logic is Boolean if and only if the following three axioms hold: (i)The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is deniedthen its negation, or complement, is affirmed. When a physical system isgoverned by a dynamical law in the form of a quantum measure with the rule thatevents of zero measure are denied, the axioms (i) - (iii) prove to be too rigidand need to be modified. One promising scheme for quantum mechanics as quantummeasure theory corresponds to replacing axiom (iii) with axiom (iv) Nature isas fine grained as the dynamics allows.

Dowker F, Zalel S, 2017, Evolution of universes in causal set cosmology, *Comptes Rendus Physique*, Vol: 18, Pages: 246-253, ISSN: 1631-0705

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.

Buck M, Dowker F, Jubb I,
et al., 2017, The Sorkin-Johnston state in a patch of the trousers spacetime, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 34, ISSN: 0264-9381

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.

, 2017, The Incomputable, Publisher: Springer International Publishing, ISBN: 9783319436678

Belenchia A, Benincasa DMT, Dowker F, 2016, The continuum limit of a 4-dimensional causal set scalar d’Alembertian, *Classical and Quantum Gravity*, Vol: 33, ISSN: 0264-9381

The continuum limit of a 4-dimensional, discrete d'Alembertian operator for scalar fields on causal sets is studied. The continuum limit of the mean of this operator in the Poisson point process in 4-dimensional Minkowski spacetime is shown to be the usual continuum scalar d'Alembertian $\square $ . It is shown that the mean is close to the limit when there exists a frame in which the scalar field is slowly varying on a scale set by the density of the Poisson process. The continuum limit of the mean of the causal set d'Alembertian in 4-dimensional curved spacetime is shown to equal $\square -\frac{1}{2}R$ , where R is the Ricci scalar, under certain conditions on the spacetime and the scalar field.

Buck M, Dowker F, Jubb I,
et al., 2015, Boundary terms for causal sets, *Classical and Quantum Gravity*, Vol: 32, ISSN: 1361-6382

We propose a family of boundary terms for the action of a causal set with a spacelike boundary. We show that in the continuum limit one recovers the Gibbons–Hawking–York boundary term in the mean. We also calculate the continuum limit of the mean causal set action for an Alexandrov interval in flat spacetime. We find that it is equal to the volume of the codimension-2 intersection of the two light-cone boundaries of the interval.

Benincasa DMT, Borsten L, Buck M,
et al., 2014, Quantum information processing and relativistic quantum fields, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 31, ISSN: 0264-9381

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- Citations: 34

Dowker F, Henson J, Wallden P, 2014, A histories perspective on characterizing quantum non-locality, *New Journal of Physics*, Vol: 16, ISSN: 1367-2630

We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum measure—the quantum analogue of a joint probability measure—on a set of experimental probabilities implies the Navascues–Pironio–Acin (NPA) condition ${{Q}^{1}}$ and is implied by the stronger NPA condition ${{Q}^{1+AB}}$. A related condition is shown to be equivalent to ${{Q}^{1+AB}}$.

Dowker F, 2014, The birth of spacetime atoms as the passage of time, *FLOW OF TIME*, Vol: 1326, Pages: 18-25, ISSN: 0077-8923

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- Citations: 24

Dowker F, Glaser L, 2013, Causal set d'Alembertians for various dimensions, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 30, ISSN: 0264-9381

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- Citations: 43

Dowker F, 2013, Introduction to causal sets and their phenomenology, *GENERAL RELATIVITY AND GRAVITATION*, Vol: 45, Pages: 1651-1667, ISSN: 0001-7701

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- Citations: 54

Dowker F, 2013, Physics meets the big C, *PHYSICS WORLD*, Vol: 26, Pages: 20-20, ISSN: 0953-8585

Afshordi N, Buck M, Dowker F,
et al., 2012, A ground state for the causal diamond in 2 dimensions, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 18

Dowker F, Elizalde E, Kirsten K, 2012, Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker's 75th birthday PREFACE, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 45, ISSN: 1751-8113

Benincasa DMT, Dowker F, Schmitzer B, 2011, The random discrete action for two-dimensional spacetime, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 28, ISSN: 0264-9381

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- Citations: 17

Dowker F, 2011, Spacetime discreteness, Lorentz invariance and locality, 5th International Workshop on Decoherence, Information, Complexity and Entropy (DICE) - Space-Time-Matter - Current Issues in Quantum Mechanics and Beyond, Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

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- Citations: 8

Dowker F, Johnston S, Surya S, 2010, On extending the quantum measure, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 43, ISSN: 1751-8113

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- Citations: 13

Dowker F, Henson J, Sorkin RD, 2010, Discreteness and the transmission of light from distant sources, *PHYSICAL REVIEW D*, Vol: 82, ISSN: 1550-7998

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- Citations: 10

Contaldi C, Dowker F, Philpott L, 2010, Polarization Diffusion from Spacetime Uncertainty, *Classical and Quantum Gravity*, Vol: 27, ISSN: 0264-9381

A model of Lorentz invariant random fluctuations in photon polarization ispresented. The effects are frequency dependent and affect the polarization ofphotons as they propagate through space. We test for this effect by confrontingthe model with the latest measurements of polarization of Cosmic MicrowaveBackground (CMB) photons.

Dowker F, Johnston S, Sorkin RD, 2010, Hilbert spaces from path integrals, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 43, ISSN: 1751-8113

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- Citations: 9

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