[Show abstract][Hide abstract] ABSTRACT: Quantum mechanics allows only certain sets of experimental results (or "probabilistic models") for Bell-type 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), 533-628 (2015) 10.1007/s00220-014-2260-1], 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 "almost-quantum" 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 almost-quantum set from a simple physical principle.
Physical Review A 01/2015; 91(4). DOI:10.1103/PhysRevA.91.042114 · 2.81 Impact Factor
[Show abstract][Hide abstract] 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 Horava-Lifshitz gravity.
[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 non-locality and contextuality experiments, as compared to
more general theories. Approaching from considerations of quantum gravity,
Sorkin has proposed lack of irreducible third-order 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 third-order interference (along
with the condition that several independent copies of any realisable behaviour
should again be realisable) rules out the existence of the Popescu-Rorlich 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.
[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 non-classical 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,
Popescu-Rohrlich 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
theory-independent 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
general-probabilistic correlations.
New Journal of Physics 05/2014; 16(11). DOI:10.1088/1367-2630/16/11/113043 · 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 non-classical 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, Popescu-Rohrlich 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 theory-independent 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 general-probabilistic correlations.
[Show abstract][Hide abstract] ABSTRACT: 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
$Q^{1+AB}$.
New Journal of Physics 11/2013; 16(3). DOI:10.1088/1367-2630/16/3/033033 · 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 non-separability, 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/s10701-013-9730-8 · 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 PR-box
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 non-contextuality in many scenarios.
[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 better-known 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 added
[Show abstract][Hide abstract] 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 sum-over-histories, 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 three-dimensional 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 three-dimensional causal dynamical triangulations. In this case, the value for the short-scale 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 Horava-Lifshitz gravity, among other approaches to quantum gravity. Comment: 25 pages, 6 figures. Version 2: references to figures added, acknowledgment added.
[Show abstract][Hide abstract] ABSTRACT: A new procedure for coarse-graining 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 coarse-graining scheme is an extension of this idea, using random simplicial complexes produced from a dynamical triangulation. In order for a coarse-graining 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. Grav
[Show abstract][Hide abstract] 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 multi-matrix models, and can be studied by the method of character expansion.
Physics Letters B 07/2009; 678(2-678):222-226. 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
continuum-inspired 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:10.1088/1742-6596/174/1/012049
[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 figures
Journal of Physics Conference Series 01/2009; 174(1). DOI:10.1088/1742-6596/174/1/012020
[Show abstract][Hide abstract] ABSTRACT: Non-perturbative 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; DOI:10.1088/0264-9381/25/10/105025 · 3.17 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 sum-over-histories 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.
[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 finite-valency graph to a sprinkling consistently with Lorentz invariance. Comment: 7 pages, laTeX
Modern Physics Letters A 05/2006; 24(32). DOI:10.1142/S0217732309031958 · 1.20 Impact Factor