Predictability of weather and climate

Abstract:

Atmospheric circulation is often clustered in so‐called circulation regimes, which are persistent and recurrent patterns. For the Euro‐Atlantic sector in winter, most studies identify four regimes: the Atlantic Ridge, Scandinavian Blocking and the two phases of the North Atlantic Oscillation. These results are obtained by applying k‐means clustering to the first several empirical orthogonal functions (EOFs) of geopotential height data. Studying the observed circulation in reanalysis data, it is found that when the full field data are used for the k‐means cluster analysis instead of the EOFs, the optimal number of clusters is no longer four but six. The two extra regimes that are found are the opposites of the Atlantic Ridge and Scandinavian Blocking, meaning they have a low‐pressure area roughly where the original regimes have a high‐pressure area. This introduces an appealing symmetry in the clustering result. Incorporating a weak persistence constraint in the clustering procedure is found to lead to a longer duration of regimes, extending beyond the synoptic time‐scale, without changing their occurrence rates. This is in contrast to the commonly used application of a time‐filter to the data before the clustering is executed, which, while increasing the persistence, changes the occurrence rates of the regimes. We conclude that applying a persistence constraint within the clustering procedure is a better way of stabilizing the clustering results than low‐pass filtering the data.

Abstract:

Quantum mechanics has irked physicists ever since its conception more than 100 years ago. While some of the misgivings, such as it being unintuitive, are merely aesthetic, quantum mechanics has one serious shortcoming: it lacks a physical description of the measurement process. This “measurement problem” indicates that quantum mechanics is at least an incomplete theory—good as far as it goes, but missing a piece—or, more radically, is in need of complete overhaul. Here we describe an approach which may provide this sought-for completion or replacement: Superdeterminism. A superdeterministic theory is one which violates the assumption of Statistical Independence (that distributions of hidden variables are independent of measurement settings). Intuition suggests that Statistical Independence is an essential ingredient of any theory of science (never mind physics), and for this reason Superdeterminism is typically discarded swiftly in any discussion of quantum foundations. The purpose of this paper is to explain why the existing objections to Superdeterminism are based on experience with classical physics and linear systems, but that this experience misleads us. Superdeterminism is a promising approach not only to solve the measurement problem, but also to understand the apparent non-locality of quantum physics. Most importantly, we will discuss how it may be possible to test this hypothesis in an (almost) model independent way.

Abstract:

An arbitrarily dense discretization of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the quantum-theoretic canon) are used to show that this constructive discretized representation incorporates many of the defining characteristics of quantum systems: completementarity, uncertainty relationships and (with a simple Cartesian product of discretized spheres) entanglement. Unlike Meyer's earlier discretization of the Bloch Sphere, there are no orthonormal triples, hence the Kocken-Specker theorem is not nullified. A physical interpretation of points on the discretized Bloch sphere is given in terms of ensembles of trajectories on a dynamically invariant fractal set in state space, where states of physical reality correspond to points on the invariant set. This deterministic construction provides a new way to understand the violation of the Bell inequality without violating statistical independence or factorization, where these conditions are defined solely from states on the invariant set. In this finite representation, there is an upper limit to the number of qubits that can be entangled, a property with potential experimental consequences.