Publications (30)57.05 Total impact
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ABSTRACT: We describe a MarkovChainMonteCarlo algorithm which can be used to generate naturally labeled nelement posets at random with a probability distribution of one's choice. Implementing this algorithm for the uniform distribution, we explore the approach to the asymptotic regime in which almost every poset takes on the threelayer structure described by Kleitman and Rothschild (KR). By tracking the ndependence of several orderinvariants, among them the height of the poset, we observe an oscillatory behavior which is very unlike a monotonic approach to the KR regime. Only around n=40 or so does this "finite size dance" appear to give way to a gradual crossover to asymptopia which lasts until n=85, the largest n we have simulated.  [Show abstract] [Hide abstract]
ABSTRACT: Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Belltype quantum nonlocality experiments. A derivation of this set from simple physical or information theoretic principles would represent an important step forward in our understanding of quantum mechanics, and this problem has been intensely investigated in recent years. "Macroscopic locality," which requires the recovery of locality in the limit of large numbers of trials, is one of several principles discussed in the literature that place a bound on the set of quantum probabilistic models. A similar question can also be asked about probabilistic models for the more general class of quantum contextuality experiments. Here, we extend the macroscopic locality principle to this more general setting, using the hypergraph approach of Acín, Fritz, Leverrier, and Sainz [Comm. Math. Phys. 334(2), 533628 (2015) 10.1007/s0022001422601], which provides a framework to study both phenomena of nonlocality and contextuality in a unified manner. We find that the set of probabilistic models allowed by our macroscopic noncontextuality principle is equivalent to an important and previously studied set in this formalism, which is slightly larger than the quantum set. In the particular case of Bell scenarios, this set is equivalent to the set of "almostquantum" models, which is of particular interest since the latter was recently shown to satisfy all but one of the principles that have been proposed to bound quantum probabilistic models, without being implied by any of them (or even their conjunction). Our condition is the first characterization of the almostquantum set from a simple physical principle.Physical Review A 01/2015; 91(4). DOI:10.1103/PhysRevA.91.042114 · 2.81 Impact Factor 
Article: Spacetime condensation in (2+1)dimensional CDT from a HoravaLifshitz minisuperspace model
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ABSTRACT: A spacetime condensation phenomenon underlies the emergence of a macroscopic universe in causal dynamical triangulations, where the time extension of the condensate is strictly smaller than the total time. It has been known for some time that the volumes of spatial slices in the bulk of the macroscopic universe follow a time evolution which resembles that of a sphere, and their effective dynamics is well described by a minisuperspace reduction of the general relativistic action. More recently, it has been suggested that the same minusuperspace model can also provide an understanding of the condensation phenomenon itself, thus explaining the presence of an extended droplet of spacetime connected to a stalk of minimal spatial extension. We show here that a minisuperspace model based on the general relativistic action fails in that respect for the (2+1)dimensional case, while a successful condensation is obtained from a minisuperspace model of HoravaLifshitz gravity.Classical and Quantum Gravity 10/2014; 32(21). DOI:10.1088/02649381/32/21/215007 · 3.17 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Recently much interest has been generated by the search for simple principles that can explain the quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments, as compared to more general theories. Approaching from considerations of quantum gravity, Sorkin has proposed lack of irreducible thirdorder interference as the most fundamental property of quantum mechanics. Here it is shown that this principle implies the principle known as consistent exclusivity or local orthogonality. This explains the previous result that lack of thirdorder interference (along with the condition that several independent copies of any realisable behaviour should again be realisable) rules out the existence of the PopescuRorlich box and the Wright pentagon, and implies new results such as bounds on violations of the CHSH inequality, and lack of quantum advantage in the Guess Your Neighbour's Input game.Physical Review Letters 06/2014; 114(22). DOI:10.1103/PhysRevLett.114.220403 · 7.51 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate nonclassical correlations in arbitrary causal structures. Our framework of `generalised Bayesian networks' replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, PopescuRohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$separation theorem to our setting. Secondly, we find that the theoryindependent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and generalprobabilistic correlations.New Journal of Physics 05/2014; 16(11). DOI:10.1088/13672630/16/11/113043 · 3.56 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate nonclassical correlations in arbitrary causal structures. Our framework of `generalised Bayesian networks' replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, PopescuRohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$separation theorem to our setting. Secondly, we find that the theoryindependent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and generalprobabilistic correlations.  [Show abstract] [Hide abstract]
ABSTRACT: We introduce a framework for studying nonlocality 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 NavascuesPironioAcin (NPA) condition $Q^1$ and is implied by the stronger NPA condition $Q^{1+AB}$. A related condition is shown to be equivalent to $Q^{1+AB}$.New Journal of Physics 11/2013; 16(3). DOI:10.1088/13672630/16/3/033033 · 3.56 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This paper addresses arguments that "separability" is an assumption of Bell's theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as "holism") will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately. In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (b) the definition of Bell's locality condition does not rely on separability in any way; (c) the proof of Bell's theorem does not use separability as an assumption. If, inspired by considerations of nonseparability, the assumptions of Bell's theorem are weakened, what remains no longer embodies the locality principle. Teller's argument for "relational holism" and Howard's arguments concerning separability are criticised in the light of these results. Howard's claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem.Foundations of Physics 02/2013; 43(8). DOI:10.1007/s1070101397308 · 1.03 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Rédei and San Pedro discuss my “Comparing Causality Principles,” their main aim being to distinguish reasonable weakened versions of two causality principles presented there, “SO1” and “SO2”. They also argue that the proof that SO1 implies SO2 contains a flaw. Here, a reply is made to a number of points raised in their paper. It is argued that the “intuition” that SO1 should be stronger than SO2 is implicitly based on a false premise. It is pointed out that a similar weakening of SO2 was already considered in the original paper. The technical definition of the new conditions is shown to be defective. The argument against the stronger versions of SO1 and SO2 given by Rédei and San Pedro is criticised. The flaw in the original proof is shown to be an easily corrected mistake in the wording. Finally, it is argued that some cited results on causal conditions in AQFT have little relevance to these issues, and are, in any case, highly problematic in themselves.Studies In History and Philosophy of Science Part B Studies In History and Philosophy of Modern Physics 02/2013; 44(1):17–19. DOI:10.1016/j.shpsb.2012.09.002 · 0.60 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS inequality as quantum mechanics, and also rules out PRbox nonlocality. He conjectures that the condition will also reproduce quantum limits on contextuality in other scenarios. Here we show that the proposed principle is actually too weak to derive these results. Cabello has implicitly assumed in the proofs that if all pairs in a set of events are pairwise exclusive (so that their probabilities must sum to less than 1), the set can itself be considered exclusive. Perhaps surprisingly, this is not in general true in the general probabilistic framework under discussion. We call this hidden assumption "Consistent Exclusivity" or CE. With this extra assumption Cabello's proofs are sound. Furthermore, it is established that CE holds in quantum mechanics, providing a reasonable and simple new principle that may characterise quantum noncontextuality in many scenarios.  [Show abstract] [Hide abstract]
ABSTRACT: Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One proposed application of causal sets is to use them as the histories in a quantum sumoverhistories, i.e. to construct a quantum theory of spacetime. It is expected by many that quantum gravity will introduce some kind of 'fuzziness', uncertainty and perhaps discreteness into spacetime, and generic effects of this fuzziness are currently being sought. Applied as a model of discrete spacetime, causal sets can be used to construct simple phenomenological models which allow us to understand some of the consequences of this general expectation. Introduction: seeing atoms with the naked eye At present, one of the most important tasks in theoretical physics is to understand the nature of spacetime at the Planck scale. Various indications from our current most successful theories point to this scale: quantum effects are to be expected to invalidate the general theory of relativity here. What should replace our current best understanding of spacetime? This question remains controversial as no theory of quantum gravity can yet be claimed to be complete. For example, some researchers are convinced that the kinematical structure used to replace the continuous manifolds of GR should be discrete, but others do not adhere to this requirement. George Ellis' great contribution to our understanding of spacetime, and his interest in the issue of spacetime discreteness, make this a very appropriate topic for these proceedings.  [Show abstract] [Hide abstract]
ABSTRACT: Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while dropping any of the betterknown assumptions of Bell's theorem. However, another assumption of Bell's theorem is the use of classical logic. One part of this assumption is the principle of "ontic definiteness", that is, that it must in principle be possible to assign definite truth values to all propositions treated in the theory. Once the logical setting is clarified somewhat, it can be seen that rejecting this principle does not in any way undermine the type of causal principle used by Bell. Without ontic definiteness, the deterministic causal condition known as Einstein Locality succeeds in banning superluminal influence (including signalling) whilst allowing correlations that violate Bell's inequalities. Objections to altering logic, and the consequences for operational and realistic viewpoints, are also addressed.  [Show abstract] [Hide abstract]
ABSTRACT: We model the classical transmission of a massless scalar field from a source to a detector on a background causal set. The predictions do not differ significantly from those of the continuum. Thus, introducing an intrinsic inexactitude to lengths and durations  or more specifically, replacing the Lorentzian manifold with an underlying discrete structure  need not disrupt the usual dynamics of propagation. Comment: 16 pages, 1 figure. Version 2: reference addedPhysical review D: Particles and fields 09/2010; 82(10). DOI:10.1103/PHYSREVD.82.104048 · 4.86 Impact Factor 
Article: Discovering the Discrete Universe
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ABSTRACT: This paper presents an brief review of some recent work on the causal set approach to quantum gravity. Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One proposed application of causal sets is to use them as the histories in a quantum sumoverhistories, i.e. to construct a quantum theory of spacetime. It is expected by many that quantum gravity will introduce some kind of "fuzziness", uncertainty and perhaps discreteness into spacetime, and generic effects of this fuzziness are currently being sought. Applied as a model of discrete spacetime, causal sets can be used to construct simple phenomenological models which allow us to understand some of the consequences of this general expectation. Comment: 24 pages, 4 figures. Based on a proceedings article for the "Foundations of Space and Time" conference, Cape Town, August 2009, in honour of George Ellis' 70th birthday.  [Show abstract] [Hide abstract]
ABSTRACT: Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of threedimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large scale behaviour to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity  the first time this has been done for threedimensional causal dynamical triangulations. In this case, the value for the shortscale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and HoravaLifshitz gravity, among other approaches to quantum gravity. Comment: 25 pages, 6 figures. Version 2: references to figures added, acknowledgment added.Physical review D: Particles and fields 11/2009; 80(12). DOI:10.1103/PhysRevD.80.124036 · 4.86 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A new procedure for coarsegraining dynamical triangulations is presented. The procedure provides a meaning for the relevant value of observables when "probing at large scales", e.g. the average scalar curvature. The scheme may also be useful as a starting point for a new type of renormalisation procedure, suitable for dynamically triangulated quantum gravity. Random Delaunay triangulations have previously been used to produce discretisations of continuous Euclidean manifolds, and the coarsegraining scheme is an extension of this idea, using random simplicial complexes produced from a dynamical triangulation. In order for a coarsegraining process to be useful, it should preserve the properties of the original dynamical triangulation that are relevant when probing at large scales. Some general discussion of this point is given, along with some arguments in favour of the proposed scheme. Comment: 19 pages (14 main body), 3 figures. Accepted for publication in Class. Quant. GravClassical and Quantum Gravity 07/2009; 26(17). DOI:10.1088/02649381/26/17/175019 · 3.17 Impact Factor 
Article: Imposing causality on a matrix model
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ABSTRACT: We introduce a new matrix model that describes Causal Dynamical Triangulations (CDT) in two dimensions. In order to do so, we introduce a new, simpler definition of 2D CDT and show it to be equivalent to the old one. The model makes use of ideas from dually weighted matrix models, combined with multimatrix models, and can be studied by the method of character expansion.Physics Letters B 07/2009; 678(2678):222226. DOI:10.1016/j.physletb.2009.06.027 · 6.13 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A 2d model of causal set quantum gravity is constructed using a continuuminspired dynamics. Apart from a restriction to causal set dimension and topology, the model is fully dynamical and includes all relevant 2d conformally flat degrees of freedom. Surprisingly, in the large N limit the partition function is dominated by causal sets that resemble 2d Minkowski spacetime. Thus, in this model the "entropy problem" of causal set theory is overcome and a sensible low energy limit is obtained.Journal of Physics Conference Series 06/2009; 174(1):2049. DOI:10.1088/17426596/174/1/012049  [Show abstract] [Hide abstract]
ABSTRACT: This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of "emergent geometry", are discussed. Comment: 35 pages (29 pages main body), two figuresJournal of Physics Conference Series 01/2009; 174(1). DOI:10.1088/17426596/174/1/012020  [Show abstract] [Hide abstract]
ABSTRACT: Nonperturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this "entropy problem" in a model of causal set quantum gravity corresponding to a discretisation of 2D spacetimes. Using results from the theory of partial orders we show that, in the large volume or continuum limit, its partition function is dominated by causal sets which approximate to a region of 2D Minkowski space. This model of causal set quantum gravity thus overcomes the entropy problem and predicts the emergence of a physically reasonable geometry.Classical and Quantum Gravity 07/2007; 25(10). DOI:10.1088/02649381/25/10/105025 · 3.17 Impact Factor
Publication Stats
451  Citations  
57.05  Total Impact Points  
Top Journals
Institutions

20142015

University of Bristol
 School of Physics
Bristol, England, United Kingdom


2013

Imperial College London
Londinium, England, United Kingdom


2009

Perimeter Institute for Theoretical Physics
Waterloo, Ontario, Canada


2006

Utrecht University
 Institute for Theoretical Physics
Utrecht, Utrecht, Netherlands


20042005

University of California, San Diego
 Department of Mathematics
San Diego, California, United States


2002

University of London
Londinium, England, United Kingdom
