## Publications

67 results found

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, ISSN: 0264-9381

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.

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: 9

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: 7

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: 27

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: 29

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: 9

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: 11

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: 5

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: 5

Dowker F, Henson J, Sorkin RD, 2010, Discreteness and the transmission of light from distant sources, *PHYSICAL REVIEW D*, Vol: 82, ISSN: 2470-0010

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- Citations: 7

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: 7

Benincasa DMT, Dowker F, 2010, Scalar Curvature of a Causal Set, *PHYSICAL REVIEW LETTERS*, Vol: 104, ISSN: 0031-9007

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- Citations: 43

Philpott L, Dowker F, Sorkin RD, 2009, Energy-momentum diffusion from spacetime discreteness, *PHYSICAL REVIEW D*, Vol: 79, ISSN: 2470-0010

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- Citations: 20

Philpott L, Dowker F, Sorkin R, 2009, Massless particle diffusion in causal set theory, 4th International Workshop on Decoherence, Information, Complexity and Entropy (DICE) - From Quantum Mechanics through Complexity to Spacetime - The Role of Emergent Dynamical Structures, Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

Dowker F, Ghazi-Tabatabai Y, 2008, Dynamical wavefunction collapse models in quantum measure theory, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 41, ISSN: 1751-8113

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- Citations: 6

Dowker F, Ghazi-Tabatabai Y, 2008, The Kochen-Specker theorem revisited in quantum measure theory, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 41, ISSN: 1751-8113

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- Citations: 15

Adler SL, Bassi A, Dowker F,
et al., 2007, The Quantum Universe - Preface, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 40, ISSN: 1751-8113

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- Citations: 1

Craig D, Dowker F, Henson J,
et al., 2007, A Bell inequality analog in quantum measure theory, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 40, Pages: 501-523, ISSN: 1751-8113

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- Citations: 13

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