3,698 research outputs found
Beables for Quantum Electrodynamics
We show that it is possible to obtain a realistic and deterministic model,
based on a previous work of John Bell, which reproduces the experimental
predictions of the orthodox interpretation of quantum electrodynamics.Comment: To appear in the proceedings of the Peyresq conference on
electromagnetism (September 2002). Annales de la Fondation de Brogli
The continuum limit of the Bell model
In a paper entitled Beables for Quantum Field Theory, John Bell has shown
that it was possible to build a realistic interpretation of any hamiltonian
lattice quantum field theory involving Fermi fields. His model is stochastic
but Bell thought that it would become deterministic in the continuum limit. We
show that it is indeed the case, under an assumption about the state of the
universe, namely that the universe is in a state obtained from the positronic
sea (all positron states occupied) by creating a finite number of negative
charges. Moreover, the continuum model can be established directly. The
physical interpretation is the following: the negative charges are in motion in
the positronic sea and their positions are the beables of the Bell model.Comment: 26 page
Long-time relaxation in pilot-wave theory
We initiate the study of relaxation to quantum equilibrium over long
timescales in pilot-wave theory. We simulate the time evolution of the
coarse-grained H-function Hbar(t) for a two-dimensional harmonic oscillator.
For a (periodic) wave function that is a superposition of the first 25 energy
states we confirm an approximately exponential decay of Hbar over five periods.
For a superposition of only the first four energy states we are able to
calculate Hbar(t) over 50 periods. We find that, depending on the set of phases
in the initial wave function, Hbar can decay to a large nonequilibrium residue
exceeding 10% of its initial value or it can become indistinguishable from zero
(the equilibrium value). We show that a large residue in Hbar is caused by a
tendency for the trajectories to be confined to sub-regions of configuration
space for some wave functions, and that this is less likely to occur for larger
numbers of energy states (if the initial phases are chosen randomly). Possible
cosmological implications are briefly discussed.Comment: 23 pages, 11 figures. Significant improvements in v2; new section on
confinement of trajectories. Accepted by J. Phys. A: Math. Theo
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