88 research outputs found
Bohmian Mechanics and Quantum Information
Many recent results suggest that quantum theory is about information, and
that quantum theory is best understood as arising from principles concerning
information and information processing. At the same time, by far the simplest
version of quantum mechanics, Bohmian mechanics, is concerned, not with
information but with the behavior of an objective microscopic reality given by
particles and their positions. What I would like to do here is to examine
whether, and to what extent, the importance of information, observation, and
the like in quantum theory can be understood from a Bohmian perspective. I
would like to explore the hypothesis that the idea that information plays a
special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure
Can Everett be Interpreted Without Extravaganza?
Everett's relative states interpretation of quantum mechanics has met with
problems related to probability, the preferred basis, and multiplicity. The
third theme, I argue, is the most important one. It has led to developments of
the original approach into many-worlds, many-minds, and decoherence-based
approaches. The latter especially have been advocated in recent years, in an
effort to understand multiplicity without resorting to what is often perceived
as extravagant constructions. Drawing from and adding to arguments of others, I
show that proponents of decoherence-based approaches have not yet succeeded in
making their ontology clear.Comment: Succinct analysis forthcoming in Found. Phy
Typicality vs. probability in trajectory-based formulations of quantum mechanics
Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.Comment: 24 pages, no figures. To appear in Foundation of Physic
Realism about the Wave Function
A century after the discovery of quantum mechanics, the meaning of quantum
mechanics still remains elusive. This is largely due to the puzzling nature of
the wave function, the central object in quantum mechanics. If we are realists
about quantum mechanics, how should we understand the wave function? What does
it represent? What is its physical meaning? Answering these questions would
improve our understanding of what it means to be a realist about quantum
mechanics. In this survey article, I review and compare several realist
interpretations of the wave function. They fall into three categories:
ontological interpretations, nomological interpretations, and the \emph{sui
generis} interpretation. For simplicity, I will focus on non-relativistic
quantum mechanics.Comment: Penultimate version for Philosophy Compas
Seven Steps Towards the Classical World
Classical physics is about real objects, like apples falling from trees,
whose motion is governed by Newtonian laws. In standard Quantum Mechanics only
the wave function or the results of measurements exist, and to answer the
question of how the classical world can be part of the quantum world is a
rather formidable task. However, this is not the case for Bohmian mechanics,
which, like classical mechanics, is a theory about real objects. In Bohmian
terms, the problem of the classical limit becomes very simple: when do the
Bohmian trajectories look Newtonian?Comment: 16 pages, LaTeX, uses latexsy
Classical and Non-Relativistic Limits of a Lorentz-Invariant Bohmian Model for a System of Spinless Particles
A completely Lorentz-invariant Bohmian model has been proposed recently for
the case of a system of non-interacting spinless particles, obeying
Klein-Gordon equations. It is based on a multi-temporal formalism and on the
idea of treating the squared norm of the wave function as a space-time
probability density. The particle's configurations evolve in space-time in
terms of a parameter {\sigma}, with dimensions of time. In this work this model
is further analyzed and extended to the case of an interaction with an external
electromagnetic field. The physical meaning of {\sigma} is explored. Two
special situations are studied in depth: (1) the classical limit, where the
Einsteinian Mechanics of Special Relativity is recovered and the parameter
{\sigma} is shown to tend to the particle's proper time; and (2) the
non-relativistic limit, where it is obtained a model very similar to the usual
non-relativistic Bohmian Mechanics but with the time of the frame of reference
replaced by {\sigma} as the dynamical temporal parameter
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
Does quantum nonlocality irremediably conflict with Special Relativity?
We reconsider the problem of the compatibility of quantum nonlocality and the
requests for a relativistically invariant theoretical scheme. We begin by
discussing a recent important paper by T. Norsen [arXiv:0808.2178] on this
problem and we enlarge our considerations to give a general picture of the
conceptually relevant issue to which this paper is devoted.Comment: 18 pages, 1 figur
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