85 research outputs found
A new pilot-wave model for quantum field theory
We present a way to construct a pilot-wave model for quantum field theory.
The idea is to introduce beables corresponding only to the bosonic degrees of
freedom and not to the fermionic degrees of freedom of the quantum state. We
illustrate this idea for quantum electrodynamics. The beables will be field
beables corresponding to the electromagnetic field and they will be introduced
in a similar way to that of Bohm's model for the free electromagnetic field.
Our approach is analogous to the situation in non-relativistic quantum theory,
where Bell treated spin not as a beable but only as a property of the
wavefunction.Comment: 21 pages, no figures, LaTex, talk given at the conference "On the
present status of quantum mechanics", 7-9 September, 2005, Mali Losinj,
Croati
On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics
In Bohmian mechanics the distribution is regarded as the
equilibrium distribution. We consider its uniqueness, finding that it is the
unique equivariant distribution that is also a local functional of the wave
function .Comment: 15 pages, no figures, LaTe
A minimalist pilot-wave model for quantum electrodynamics
We present a way to construct a pilot-wave model for quantum electrodynamics.
The idea is to introduce beables corresponding only to the bosonic degrees of
freedom and not to the fermionic degrees of freedom of the quantum state. We
show that this is sufficient to reproduce the quantum predictions. The beables
will be field beables corresponding to the electromagnetic field and they will
be introduced in a similar way to that of Bohm's model for the free
electromagnetic field. Our approach is analogous to the situation in
non-relativistic quantum theory, where Bell treated spin not as a beable but
only as a property of the wavefunction. After presenting this model we also
discuss a simple way for introducing additional beables that represent the
fermionic degrees of freedom.Comment: LaTex, 17 pages, no figures; v2 minor corrections, journal versio
On Peres' statement "opposite momenta lead to opposite directions", decaying systems and optical imaging
We re-examine Peres' statement ``opposite momenta lead to opposite
directions''. It will be shown that Peres' statement is only valid in the large
distance or large time limit. In the short distance or short time limit an
additional deviation from perfect alignment occurs due to the uncertainty of
the location of the source. This error contribution plays a major role in
Popper's orginal experimental proposal. Peres' statement applies rather to the
phenomenon of optical imaging, which was regarded by him as a verification of
his statement. This is because this experiment can in a certain sense be seen
as occurring in the large distance limit. We will also reconsider both
experiments from the viewpoint of Bohmian mechanics. In Bohmian mechanics
particles with exactly opposite momenta will move in opposite directions. In
addition it will prove particularly usefull to use Bohmian mechanics because
the Bohmian trajectories coincide with the conceptual trajectories drawn by
Pittman et al. In this way Bohmian mechanics provides a theoretical basis for
these conceptual trajectories.Comment: 20 pages, 3 figures, LaTex, to be published in Found. Phy
On the zig-zag pilot-wave approach for fermions
We consider a pilot-wave approach for the Dirac theory that was recently
proposed by Colin and Wiseman. In this approach, the particles perform a
zig-zag motion, due to stochastic jumps of their velocity. We respectively
discuss the one-particle theory, the many-particle theory and possible
extensions to quantum field theory. We also discuss the non-relativistic limit
of the one-particle theory. For a single particle, the motion is always
luminal, a feature that persists in the non-relativistic limit. For more than
one particle the motion is in general subluminal.Comment: 23 pages, no figures, LaTe
Two-particle interference in standard and Bohmian quantum mechanics
The compatibility of standard and Bohmian quantum mechanics has recently been
challenged in the context of two-particle interference, both from a theoretical
and an experimental point of view. We analyze different setups proposed and
derive corresponding exact forms for Bohmian equations of motion. The equations
are then solved numerically, and shown to reproduce standard quantum-mechanical
results.Comment: Minor corrections, 2 references added, version to appear in J. Phys.
A Dirac sea pilot-wave model for quantum field theory
We present a pilot-wave model for quantum field theory in which the Dirac sea
is taken seriously. The model ascribes particle trajectories to all the
fermions, including the fermions filling the Dirac sea. The model is
deterministic and applies to the regime in which fermion number is
superselected. This work is a further elaboration of work by Colin, in which a
Dirac sea pilot-wave model is presented for quantum electrodynamics. We extend
his work to non-electromagnetic interactions, we discuss a cut-off
regularization of the pilot-wave model and study how it reproduces the standard
quantum predictions. The Dirac sea pilot-wave model can be seen as a possible
continuum generalization of a lattice model by Bell. It can also be seen as a
development and generalization of the ideas by Bohm, Hiley and Kaloyerou, who
also suggested the use of the Dirac sea for the development of a pilot-wave
model for quantum electrodynamics.Comment: 41 pages, no figures, LaTex, v2 minor improvements and addition
On Epstein's trajectory model of non-relativistic quantum mechanics
In 1952 Bohm presented a theory about non-relativistic point-particles moving
along deterministic trajectories and showed how it reproduces the predictions
of standard quantum theory. This theory was actually presented before by de
Broglie in 1926, but Bohm's particular formulation of the theory inspired
Epstein to come up with a different trajectory model. The aim of this paper is
to examine the empirical predictions of this model. It is found that the
trajectories in this model are in general very different from those in the de
Broglie-Bohm theory. In certain cases they even seem bizarre and rather
unphysical. Nevertheless, it is argued that the model seems to reproduce the
predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement
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