Publications (23)21.55 Total impact
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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 $Q^{1+AB}$.11/2013; 16(3).  [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; · 1.17 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. · 0.85 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.10/2012;  [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.02/2011;  [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; 
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.03/2010;  [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;  [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; · 3.56 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.  [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; 
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 01/2009; · 4.57 Impact Factor  [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; · 3.56 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: This article concerns the fate of local Lorentz invariance in quantum gravity, particularly for approaches in which a discrete structure replaces continuum spacetime. Some features of standard quantum mechanics, presented in a sumoverhistories formulation, are reviewed, and their consequences for such theories are discussed. It is argued that, if the individual histories of a theory give bad approximations to macroscopic continuum properties in some frames, then it is inevitable that the theory violates Lorentz symmetry.05/2006;  [Show abstract] [Hide abstract]
ABSTRACT: This paper concerns sprinklings into Minkowski space (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to ``Lorentz breaking'' effects like modified dispersion relations. Another consequence is that there is no way to associate a finitevalency graph to a sprinkling consistently with Lorentz invariance. Comment: 7 pages, laTeXModern Physics Letters A 05/2006; · 1.11 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or {\it measure}, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as ``screening off''. We show that if one assumes, more generally, a joint {\it quantal measure}, or ``decoherence functional'', one obtains instead an analogous inequality weaker by a factor of $\sqrt{2}$. The proof of this ``Tsirel'son inequality'' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a {\it question}: ``Does a joint measure follow from some quantal analog of `screening off'?'', and to the {\it observation} that noncontextual hidden variables are viable in historiesbased quantum mechanics, even if they are excluded classically. Comment: 38 pages, TeX. Several changes and added comments to bring out the meaning more clearly. Minor rewording and extra acknowledgements, now closer to published versionJournal of Physics A Mathematical and Theoretical 04/2006; · 1.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The causal set is a discrete structure which avoids this problem and provides a possible history space on which to build a ``path integral'' type quantum gravity theory. Motivation, results and open problems are discussed and some comparisons to other approaches are made. Some recent progress on recovering locality in causal sets is recounted.02/2006;  [Show abstract] [Hide abstract]
ABSTRACT: The ClauserHorneShimonyHoltBell inequalities are necessary conditions for a set of nosignalling probabilities for two measurers each with two alternative experiments each with two possible outcomes to admit a joint probability distribution. An analogue of these inequalities in the context of quantum measure theory is presented. Talk given by Fay Dowker.01/2006;  [Show abstract] [Hide abstract]
ABSTRACT: A criticism sometimes made of the causal set quantum gravity program is that there is no practical scheme for identifying manifoldlike causal sets and finding embeddings of them into manifolds. A computational method for constructing an approximate embedding of a small manifoldlike causal set into Minkowski space (or any spacetime that is approximately flat at short scales) is given, and tested in the twodimensional case. This method can also be used to determine how manifoldlike a causal set is, and conversely to define scales of manifoldlikeness.Classical and Quantum Gravity 01/2006; 23(4). · 3.56 Impact Factor 
Article: Comparing causality principles
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ABSTRACT: The principle of common cause is discussed as a possible fundamental principle of physics. Some revisions of Reichenbach's formulation of the principle are given, which lead to a version given by Bell. Various similar forms are compared and some equivalence results proved. The further problems of causality in a quantal system, and indeterministic causal structure, are addressed, with a view to defining a causality principle applicable to quantum gravity.Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics. 01/2005;
Publication Stats
313  Citations  
21.55  Total Impact Points  
Top Journals
Institutions

2006–2013

Imperial College London
Londinium, England, United Kingdom


2009

Perimeter Institute for Theoretical Physics
Waterloo, Ontario, Canada


2004–2006

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


2002

University of London
Londinium, England, United Kingdom
