From Quasars to Extraordinary N-body Problems

We outline reasoning that led to the current theory of quasars and look at George Contopoulos's place in the long history of the N-body problem. Following Newton we find new exactly soluble N-body problems with multibody forces and give a strange eternally pulsating system that in its other degrees of freedom reaches statistical equilibrium.Comment: 13 pages, LaTeX with 1 postscript figure included. To appear in Proceedings of New York Academy of Sciences, 13th Florida Workshop in Nonlinear Astronomy and Physic

Sea-level change and storm surges in the context of climate change

This paper reviews the latest research in New Zealand surrounding the issues of sea-level rise and extreme sea levels in the context of global warming and variability in the Pacific-wide El Nino– Southern Oscillation (ENSO). Past records of climate, sea level (excluding tides) and sea and air temperatures have shown that they are continuously fluctuating over various long-term timescales of years, decades and centuries. This has made it very difficult to determine whether the anthropogenic effects such as increased levels of “greenhouse” gases are having an accelerating effect on global sea levels or an increased incidence of extreme storms. Over the past century, global sea level has risen by 10–25 cm, and is in line with the rise in relative sea level at New Zealand’s main ports of +1.7 mm yr –1. What has become very clear is the need to better understand interannual (year-to-year) and decadal variability in sea-level, as these larger signals of the order of 5–15 cm in annual-mean sea level have a significant “flow-on” effect on the long-term trend in sea level. The paper describes sea level variability in northern New Zealand—both long- and short-term—involved in assessing the regional trends in sea level. The paper also discusses the relative contributions of tides, barometric pressure and wind set-up in causing extreme sea levels during storm surges. Some recent research also looked at a related question—Is there any sign of increased storminess, and hence storm surge, in northern New Zealand due to climate change? The paper concludes that, while no one can be completely sure how sea-level and the degree of storminess will respond in the near future, what is clear is that interannual and decadal variability in sea level is inextricably linked with Pacific-wide ENSO response and longer inter-decadal shifts in the Pacific climate regime, such as the latest shift in 1976

Loophole-free Bell's experiment and two-photon all-versus-nothing violation of local realism

We introduce an all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom, which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this proof gives eta > 0.69. This efficiency is lower than that required for previous proposals.Comment: REVTeX4, 4 page

Criteria for generalized macroscopic and mesoscopic quantum coherence

We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalized $S$-scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing. We also discuss how the signatures enable a new type of Einstein-Podolsky-Rosen gedanken experiment.Comment: 15 pages, accepted for publication in Phys. Rev.

Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other -- it is possible to reproduce quantum mechanics with deterministic models that violate locality as well as indeterministic models that satisfy locality. On the other hand, the operational assumption of signal locality is an empirically testable (and well-tested) consequence of relativity. Thus Bell inequality violations imply that we can trust that some events are fundamentally \emph{unpredictable}, even if we cannot trust that they are indeterministic. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the assumption of no superluminal signalling, regardless of any postulates of quantum mechanics. It also sheds a new light on an early stage of the historical debate between Einstein and Bohr.Comment: Substantially modified version; added HMW as co-autho

Hardy's proof of nonlocality in the presence of noise

We extend the validity of Hardy's nonlocality without inequalities proof to cover the case of special one-parameter classes of non-pure statistical operators. These mixed states are obtained by mixing the Hardy states with a completely chaotic noise or with a colored noise and they represent a realistic description of imperfect preparation processes of (pure) Hardy states in nonlocality experiments. Within such a framework we are able to exhibit a precise range of values of the parameter measuring the noise affecting the non-optimal preparation of an arbitrary Hardy state, for which it is still possible to put into evidence genuine nonlocal effects. Equivalently, our work exhibits particular classes of bipartite mixed states whose constituents do not admit any local and deterministic hidden variable model reproducing the quantum mechanical predictions.Comment: 9 pages, 2 figures, RevTex, revised versio

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.Comment: V2: corrected image display; V3: substantial changes including new proofs, arguments, and result

Greenberger-Horne-Zeilinger argument of nonlocality without inequalities for mixed states

We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball (in the trace distance topology) surrounding the pure GHZ state and containing arbitrary mixed statistical operators which cannot be described by any local and realistic hidden variable model and which are, as a consequence, noncompletely separable. As a practical application, we focus on certain one-parameter classes of mixed states which are commonly considered in the experimental realization of the original GHZ argument and which result from imperfect preparations of the pure GHZ state. In these cases we determine for which values of the parameter controlling the noise a nonlocality argument can still be exhibited, despite the mixedness of the considered states. Moreover, the effect of the imperfect nature of measurement processes is discussed.Comment: 8 pages, RevTex; added references, corrected typo