19,578 research outputs found
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 can be considered a deterministic dynamical
system evolving on a causal measure-zero fractal invariant set in its
state space. Symbolic representations of 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
, 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
A simultaneous spin/eject mechanism for aerospace payloads
A simultaneous spin/eject mechanism was developed for aerospace applications requiring a compact, passive device which would accommodate payload support and controlled-release functions, and which would provide a highly accurate spin-ejection motion to the payload. The mechanism satisfied the requirements and is adaptable to other deployment applications
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