A Local Deterministic Model of Quantum Spin Measurement

The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrised model, Q, for the state vector evolution of spin 1/2 particles during measurement is developed. Q draws on recent work on so-called riddled basins in dynamical systems theory, and is local, deterministic, nonlinear and time asymmetric. Moreover the evolution of the state vector to one of two chaotic attractors (taken to represent observed spin states) is effectively uncomputable. Motivation for this model arises from Penrose's speculations about the nature and role of quantum gravity. Although the evolution of Q's state vector is uncomputable, the probability that the system will evolve to one of the two attractors is computable. These probabilities correspond quantitatively to the statistics of spin 1/2 particles. In an ensemble sense the evolution of the state vector towards an attractor can be described by a diffusive random walk. Bell's theorem and a version of the Bell-Kochen_specker quantum entanglement paradox are discussed. It is shown that proving an inconsistency with locality demands the existence of definite truth values to certain counterfactual propositions. In Q these deterministic propositions are physically uncomputable and no non-algorithmic solution is either known or suspected. Adapting the mathematical formalist approach, the non-existence of definite truth values to such counterfactual propositions is posited. No inconsistency with experiment is found. Hence Q is not necessarily constrained by Bell's inequality.Comment: This paper has been accepted for publication in the Proceedings of the Royal Society of London (Proc.Roy.Soc.A) I will mail the paper's figures on request (write to [email protected]

Lorenz, G\"{o}del and Penrose: New perspectives on determinism and causality in fundamental physics

Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of Lorenz's fractal invariant set relate space-time calculus to deep areas of mathematics such as G\"{o}del's Incompleteness Theorem. These properties, combined with some recent developments in theoretical and observational cosmology, motivate what is referred to as the `cosmological invariant set postulate': that the universe $U$ can be considered a deterministic dynamical system evolving on a causal measure-zero fractal invariant set $I_U$ in its state space. Symbolic representations of $I_U$ are constructed explicitly based on permutation representations of quaternions. The resulting `invariant set theory' provides some new perspectives on determinism and causality in fundamental physics. For example, whilst the cosmological invariant set appears to have a rich enough structure to allow a description of quantum probability, its measure-zero character ensures it is sparse enough to prevent invariant set theory being constrained by the Bell inequality (consistent with a partial violation of the so-called measurement independence postulate). The primacy of geometry as embodied in the proposed theory extends the principles underpinning general relativity. As a result, the physical basis for contemporary programmes which apply standard field quantisation to some putative gravitational lagrangian is questioned. Consistent with Penrose's suggestion of a deterministic but non-computable theory of fundamental physics, a `gravitational theory of the quantum' is proposed based on the geometry of $I_U$, with potential observational consequences for the dark universe.Comment: This manuscript has been accepted for publication in Contemporary Physics and is based on the author's 9th Dennis Sciama Lecture, given in Oxford and Triest

Direct-use Values of Non-Timber Forest Products from Two Areas on the Transkei Wild Coast

It is now widely appreciated internationally that rural communities make extensive use of wild resources, and that this use has significant direct use value. The number of case studies in South Africa that have valued the use of such resources are small, albeit growing. Yet none of them have been from coastal sites, which would include use of marine resources, nor have previous studies included the non-biological resources of sand and clay for building purposes. This paper addresses this gap, through examination of the role and value of wild resources in rural livelihoods of households in the Ntubeni and Cwebe areas of the Transkei Wild Coast in the Eastern Cape. Households used a wide range of resources collected from the surrounding communal lands and the Dwesa Cwebe Nature Reserve. Major differences between the sites were the widespread use of bushmeat, shellfish and building sand at Ntubeni compared with relatively small use of these three resources at Cwebe. These differences resulted in a markedly higher, gross, annual, direct-use value at Ntubeni than at Cwebe. The gross, annual, direct-use value averaged across all resources (excluding medicinal plants) and all households (user and non-users) was over R12 000 at Ntubeni, compared to R4 858 at Cwebe. At Ntubeni over half of the total annual direct-use value was contributed by fish and shellfish, indicating the need for more studies in coastal areas. A similar pattern was not evident at Cwebe, because residents did not have access to a rocky shoreline outside of the marine reserve. Local trade was highly variable, both between resources and between households. Averaging the value of trade across all households (i.e. traders and non-traders), gave a total gross, annual value of R1 660 and R600 at Ntubeni and Cwebe, respectively.Resource /Energy Economics and Policy,