# Prof Fay Dowker

Faculty of Natural SciencesDepartment of Physics

Professor of Theoretical Physics

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### Assistant

Mrs Graziela De Nadai-Sowrey +44 (0)20 7594 7843

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### Location

Huxley BuildingSouth Kensington Campus

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## Publications

Publication Type
Year
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66 results found

Ahmed SN, Dowker F, Surya S, Nomaan Ahmed S, Dowker F, Surya S, Syed NA, Dowker F, Surya S, Ahmed SN, Dowker F, Surya Set al., 2017, Scalar field Green functions on causal sets, CLASSICAL AND QUANTUM GRAVITY, Vol: 34, ISSN: 0264-9381

© 2017 IOP Publishing Ltd. 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.

JOURNAL ARTICLE

Buck M, Dowker F, Jubb I, Sorkin R, Buck M, Dowker F, Jubb I, Sorkin R, Buck M, Dowker F, Jubb I, Sorkin R, Buck M, Dowker F, Jubb I, Sorkin Ret al., 2017, The Sorkin-Johnston state in a patch of the trousers spacetime, CLASSICAL AND QUANTUM GRAVITY, Vol: 34, Pages: 055002-055002, 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-Johnstonformalism. The isometry group of the patch is the dihedral group, the symmetrygroup of the square. The theory is shown to be pathological in a way that canbe interpreted as the topology change giving rise to a divergent energy, inagreement with previous results. In contrast to previous results, it is shownthat the infinite energy is localised not only on the future light cone of thetopology changing singularity, but also on the past cone, due to the timereversal symmetry of the Sorkin-Johnston state.

JOURNAL ARTICLE

Dowker F, Zalel S, Dowker F, Zalel S, Dowker F, Zalel Set al., 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 thehypothesis that spacetime is fundamentally discrete. Spacetime discretenessopens the door to novel types of dynamical law for cosmology and the ClassicalSequential Growth (CSG) models of Rideout and Sorkin form an interesting classof such laws. It has been shown that a renormalisation of the dynamicalparameters of a CSG model occurs whenever the universe undergoes a BigCrunch-Big Bang bounce. In this paper we propose a way to model the creation ofa new universe after the singularity of a black hole. We show thatrenormalisation of dynamical parameters occurs in a CSG model after such acreation event. We speculate that this could realise aspects of Smolin'sCosmological Natural Selection proposal.

JOURNAL ARTICLE

Belenchia A, Benincasa DMT, Dowker F, Belenchia A, Benincasa DMT, Dowker F, Belenchia A, Benincasa DMT, Dowker F, Belenchia A, Benincasa DMT, Dowker Fet al., 2016, The continuum limit of a 4-dimensional causal set scalar d'Alembertian, CLASSICAL AND QUANTUM GRAVITY, Vol: 33, Pages: 245018-245018, ISSN: 0264-9381

The continuum limit of a 4-dimensional, discrete d'Alembertian operator forscalar fields on causal sets is studied. The continuum limit of the mean ofthis operator in the Poisson point process in 4-dimensional Minkowski spacetimeis shown to be the usual continuum scalar d'Alembertian $\Box$. It is shownthat the mean is close to the limit when there exists a frame in which thescalar field is slowly varying on a scale set by the density of the Poissonprocess. The continuum limit of the mean of the causal set d'Alembertian in4-dimensional curved spacetime is shown to equal $\Box - \frac{1}{2}R$, where$R$ is the Ricci scalar, under certain conditions on the spacetime and thescalar field.

JOURNAL ARTICLE

Buck M, Dowker F, Jubb I, Surya S, Buck M, Dowker F, Jubb I, Surya S, Buck M, Dowker F, Jubb I, Surya S, Buck M, Dowker F, Jubb I, Surya Set al., 2015, Boundary terms for causal sets, CLASSICAL AND QUANTUM GRAVITY, Vol: 32, Pages: 205004-205004, ISSN: 0264-9381

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

JOURNAL ARTICLE

Benincasa DMT, Borsten L, Buck M, Dowker F, Benincasa DMT, Borsten L, Buck M, Dowker F, Benincasa DMT, Borsten L, Buck M, Dowker F, Benincasa DMT, Borsten L, Buck M, Dowker Fet al., 2014, Quantum information processing and relativistic quantum fields, CLASSICAL AND QUANTUM GRAVITY, Vol: 31, Pages: 075007-075007, ISSN: 0264-9381

It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom-qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light-crossing time of the cavity. © 2014 IOP Publishing Ltd.

JOURNAL ARTICLE

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

In the following discussion I suggest that the reason there is no consensus on whether the passage of time is physical is that our current best theory of spacetime, general relativity, lacks such a concept. This means that the sense-experience of passage, appealed to by those who claim it is physical, cannot be properly expressed: it is not even a fact. I draw attention to work in the literature on a model of a growing, granular spacetime--arising within a proposed theory of quantum spacetime called causal set theory--that does contain the concept of passage as the coming into being or birth of atoms of spacetime. I present an example from the history of science of a sense-experience that cannot be understood within one theory but is revealed to be an important fact within a better successor theory.

JOURNAL ARTICLE

Dowker F, Henson J, Wallden P, Dowker F, Henson J, Wallden P, Dowker F, Henson J, Wallden Pet al., 2014, A histories perspective on characterizing quantum non-locality, NEW JOURNAL OF PHYSICS, Vol: 16, Pages: 033033-033033, ISSN: 1367-2630

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Dowker F, Glaser L, Dowker F, Glaser L, Dowker F, Glaser Let al., 2013, Causal set d'Alembertians for various dimensions, CLASSICAL AND QUANTUM GRAVITY, Vol: 30, Pages: 195016-195016, ISSN: 0264-9381

We propose, for dimension d, a discrete Lorentz invariant operator on scalarfields that approximates the Minkowski spacetime scalar d'Alembertian. For eachdimension, this gives rise to a scalar curvature estimator for causal sets, andthence to a proposal for a causal set action.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Afshordi N, Buck M, Dowker F, Rideout D, Sorkin RD, Yazdi YK, Afshordi N, Buck M, Dowker F, Rideout D, Sorkin RD, Yazdi YK, Afshordi N, Buck M, Dowker F, Rideout D, Sorkin RD, Yazdi YKet al., 2012, A ground state for the causal diamond in 2 dimensions, JOURNAL OF HIGH ENERGY PHYSICS, Vol: 2012, ISSN: 1029-8479

We apply a recent proposal for a distinguished ground state of a quantumfield in a globally hyperbolic spacetime to the free massless scalar field in acausal diamond in two-dimensional Minkowski space. We investigate the twolimits in which the Wightman function is evaluated (i) for pairs of points thatlie in the centre of the diamond (i.e. far from the boundaries), and (ii) forpairs of points that are close to the left or right corner. We find that in thecentre, the Minkowski vacuum state is recovered, with a definite value of theinfrared cutoff. Interestingly, the ground state is not the Rindler vacuum inthe corner of the diamond, as might have been expected, but is instead thevacuum of a flat space in the presence of a static mirror on that corner. Weconfirm these results by numerically evaluating the Wightman function of amassless scalar field on a causal set corresponding to the continuum causaldiamond.

JOURNAL ARTICLE

Clements K, Dowker F, Wallden P, 2012, Physical Logic

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.

BOOK CHAPTER

Dowker F, Elizalde E, Kirsten K, Dowker F, Elizalde E, Kirsten Ket al., 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, Pages: 370301-370301, ISSN: 1751-8113

JOURNAL ARTICLE

Benincasa DMT, Dowker F, Schmitzer B, Benincasa DMT, Dowker F, Schmitzer B, Benincasa DMT, Dowker F, Schmitzer Bet al., 2011, The random discrete action for two-dimensional spacetime, CLASSICAL AND QUANTUM GRAVITY, Vol: 28, Pages: 105018-105018, ISSN: 0264-9381

A one-parameter family of random variables, called the Discrete Action, isdefined for a 2-dimensional Lorentzian spacetime of finite volume. The singleparameter is a discreteness scale. The expectation value of this DiscreteAction is calculated for various regions of 2D Minkowski spacetime. When acausally convex region of 2D Minkowski spacetime is divided into subregionsusing null lines the mean of the Discrete Action is equal to the alternatingsum of the numbers of vertices, edges and faces of the null tiling, up tocorrections that tend to zero as the discreteness scale is taken to zero. Thisresult is used to predict that the mean of the Discrete Action of the flatLorentzian cylinder is zero up to corrections, which is verified. Thetopological'' character of the Discrete Action breaks down for causallyconvex regions of the flat trousers spacetime that contain the singularity andfor non-causally convex rectangles.

JOURNAL ARTICLE

Dowker F, 2011, Useless Qubits in "Relativistic Quantum Information"

I draw attention to previous work that shows that the observablescorresponding to relativistic quantum field modes commonly employed in paperson "relativistic quantum information" cannot be measured by ideal measurements.

JOURNAL ARTICLE

Dowker F, 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, Pages: 012016-012016, ISSN: 1742-6588

CONFERENCE PAPER

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

A one parameter family of retarded linear operators on scalar fields on causal sets is introduced. When the causal set is well approximated by 4 dimensional Minkowski spacetime, the operators are Lorentz invariant but nonlocal, are parametrized by the scale of the nonlocality, and approximate the continuum scalar D'Alembertian square when acting on fields that vary slowly on the nonlocality scale. The same operators can be applied to scalar fields on causal sets which are well approximated by curved spacetimes in which case they approximate square-(1/2)R where R is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.

JOURNAL ARTICLE

Contaldi CR, Dowker F, Philpott L, Contaldi C, Dowker F, Philpott L, Contaldi C, Dowker F, Philpott Let al., 2010, Polarization diffusion from spacetime uncertainty, Classical and Quantum Gravity, Vol: 27, Pages: 172001-172001, 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.

JOURNAL ARTICLE

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

We model the classical transmission of a massless scalar field from a sourceto a detector on a background causal set. The predictions do not differsignificantly from those of the continuum. Thus, introducing an intrinsicinexactitude to lengths and durations - or more specifically, replacing theLorentzian manifold with an underlying discrete structure - need not disruptthe usual dynamics of propagation.

JOURNAL ARTICLE

Dowker F, Johnston S, Sorkin RD, Dowker F, Johnston S, Sorkin RD, Dowker F, Johnston S, Sorkin RDet al., 2010, Hilbert spaces from path integrals, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, Pages: 275302-275302, ISSN: 1751-8113

It is shown that a Hilbert space can be constructed for a quantum systemstarting from a framework in which histories are fundamental. The DecoherenceFunctional provides the inner product on this "History Hilbert space". It isalso shown that the History Hilbert space is the standard Hilbert space in thecase of non-relativistic quantum mechanics.

JOURNAL ARTICLE

Dowker F, Johnston S, Surya S, Dowker F, Johnston S, Surya S, Dowker F, Johnston S, Surya Set al., 2010, On extending the quantum measure, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, Pages: 505305-505305, ISSN: 1751-8113

We point out that a quantum system with a strongly positive quantum measureor decoherence functional gives rise to a vector valued measure whose domain isthe algebra of events or physical questions. This gives an immediate handle onthe question of the extension of the decoherence functional to the sigmaalgebra generated by this algebra of events. It is on the latter that thephysical transition amplitudes directly give the decoherence functional. Sincethe full sigma algebra contains physically interesting questions, like thereturn question, extending the decoherence functional to these more generalquestions is important. We show that the decoherence functional, and hence thequantum measure, extends if and only if the associated vector measure does. Wegive two examples of quantum systems whose decoherence functionals do notextend: one is a unitary system with finitely many states, and the other is aquantum sequential growth model for causal sets. These examples fail to extendin the formal mathematical sense and we speculate on whether the conditions forextension are unphysically strong.

JOURNAL ARTICLE

Philpott L, Dowker F, Sorkin R, Philpott L, Dowker F, Sorkin Ret al., 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, Pages: 012048-012048, ISSN: 1742-6588

CONFERENCE PAPER

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

We study potentially observable consequences of spatiotemporal discretenessfor the motion of massive and massless particles. First we describe some simpleintrinsic models for the motion of a massive point particle in a fixed causalset background. At large scales, the microscopic swerves induced by theunderlying atomicity manifest themselves as a Lorentz invariant diffusion inenergy-momentum governed by a single phenomenological parameter, and we derivein full the corresponding diffusion equation. Inspired by the simplicity of theresult, we then derive the most general Lorentz invariant diffusion equationfor a massless particle, which turns out to contain two phenomenologicalparameters describing, respectively, diffusion and drift in the particle'senergy. The particles do not leave the light cone however: their worldlinescontinue to be null geodesics. Finally, we deduce bounds on the drift anddiffusion constants for photons from the blackbody nature of the spectrum ofthe cosmic microwave background radiation.

JOURNAL ARTICLE

Dowker F, Ghazi-Tabatabai Y, Dowker F, Ghazi-Tabatabai Y, Dowker F, Ghazi-Tabatabai Yet al., 2008, Dynamical wavefunction collapse models in quantum measure theory, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, Pages: 205306-205306, ISSN: 1751-8113

The structure of Collapse Models is investigated in the framework of QuantumMeasure Theory, a histories-based approach to quantum mechanics. The underlyingstructure of coupled classical and quantum systems is elucidated in thisapproach which puts both systems on a spacetime footing. The nature of thecoupling is exposed: the classical histories have no dynamics of their own butare simply tied, more or less closely, to the quantum histories.

JOURNAL ARTICLE

Dowker F, Ghazi-Tabatabai Y, Dowker F, Ghazi-Tabatabai Y, Dowker F, Ghazi-Tabatabai Yet al., 2008, The Kochen-Specker theorem revisited in quantum measure theory, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, Pages: 105301-105301, ISSN: 1751-8113

The Kochen-Specker Theorem is widely interpreted to imply that non-contextualhidden variable theories that agree with the predictions of Copenhagen quantummechanics are impossible. The import of the theorem for a novel observerindependent interpretation of quantum mechanics, due to Sorkin, isinvestigated.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Barnett M, Dowker F, Rideout D, Barnett M, Dowker F, Rideout D, Barnett M, Dowker F, Rideout D, Barnett M, Dowker Fet al., 2007, Popescu-Rohrlich boxes in quantum measure theory, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 40, Pages: 7255-7264, ISSN: 1751-8113

Two results are proved at the quantal level in Sorkin's hierarchy of measuretheories. One is a strengthening of an existing bound on the correlations inthe EPR-Bohm setup under the assumption that the probabilities admit a stronglypositive joint quantal measure. It is also proved that any set of no-signallingprobabilities, for two distant experimenters with a choice of two alternativeexperiments each and two possible outcomes per experiment, admits a jointquantal measure, though one that is not necessarily strongly positive.

JOURNAL ARTICLE

Craig D, Dowker F, Henson J, Major S, Rideout D, Sorkin RDet 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

JOURNAL ARTICLE

Craig D, Dowker F, Henson J, Major S, Rideout D, Sorkin R, Craig D, Dowker F, Henson J, Major S, Rideout D, Sorkin RD, Craig D, Dowker F, Henson J, Major S, Rideout D, Sorkin RDet al., 2007, A Bell inequality analog in quantum measure theory, J. Phys. A: Math. Theor., Vol: 40, Pages: 501-523, ISSN: 1751-8113

One obtains Bell's inequalities if one posits a hypothetical jointprobability distribution, or {\it measure}, whose marginals yield theprobabilities produced by the spin measurements in question. The existence of ajoint measure is in turn equivalent to a certain causality condition known asscreening off''. We show that if one assumes, more generally, a joint {\itquantal measure}, or decoherence functional'', one obtains instead ananalogous inequality weaker by a factor of $\sqrt{2}$. The proof of thisTsirel'son inequality'' is geometrical and rests on the possibility ofassociating a Hilbert space to any strongly positive quantal measure. Theseresults lead both to a {\it question}: Does a joint measure follow from somequantal analog of `screening off'?'', and to the {\it observation} thatnon-contextual hidden variables are viable in histories-based quantummechanics, even if they are excluded classically.

JOURNAL ARTICLE

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