89 research outputs found
Arrival Time Distributions of Spin-1/2 Particles
The arrival time statistics of spin-1/2 particles governed by Pauli's
equation, and defined by their Bohmian trajectories, show unexpected and very
well articulated features. Comparison with other proposed statistics of arrival
times that arise from either the usual (convective) quantum flux or from
semiclassical considerations suggest testing the notable deviations in an
arrival time experiment, thereby probing the predictive power of Bohmian
trajectories. The suggested experiment, including the preparation of the wave
functions, could be done with present-day experimental technology.Comment: 9 pages, 5 figure
The role of the probability current for time measurements
Time measurements are routinely preformed in laboratories, nevertheless their
theoretical account presents some difficulties and for actual experiments an
approximate, semiclassical expression is always used. Here, we will discuss
their quantum description with particular emphasis on the role of the
probability current.Comment: Chapter of the book "The Message of Quantum Science - Attempts
Towards a Synthesis", Springer (2014). P. Blanchard, and J. Fr\"ohlich (Eds.
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
Bohmian mechnaics is the most naively obvious embedding imaginable of
Schr\"odingers's equation into a completely coherent physical theory. It
describes a world in which particles move in a highly non-Newtonian sort of
way, one which may at first appear to have little to do with the spectrum of
predictions of quantum mechanics. It turns out, however, that as a consequence
of the defining dynamical equations of Bohmian mechanics, when a system has
wave function its configuration is typically random, with probability
density given by , the quantum equilibrium distribution. It
also turns out that the entire quantum formalism, operators as observables and
all the rest, naturally emerges in Bohmian mechanics from the analysis of
``measurements.'' This analysis reveals the status of operators as observables
in the description of quantum phenomena, and facilitates a clear view of the
range of applicability of the usual quantum mechanical formulas.Comment: 77 page
Bohmian Mechanics and the Meaning of the Wave Function
We outline how Bohmian mechanics works: how it deals with various issues in
the foundations of quantum mechanics and how it is related to the usual quantum
formalism. We then turn to some objections to Bohmian mechanics, for example
the fact that in Bohmian mechanics there is no back action of particle
configurations upon wave functions. These lead us to our main concern: a more
careful consideration of the meaning of the wave function in quantum mechanics,
as suggested by a Bohmian perspective. We propose that the reason, on the
universal level, that there is no action of configurations upon wave functions,
as there seems to be between all other elements of physical reality, is that
the wave function of the universe is not an element of physical reality. We
propose that the wave function belongs to an altogether different category of
existence than that of substantive physical entities, and that its existence is
nomological rather than material. We propose, in other words, that the wave
function is a component of physical law rather than of the reality described by
the law.Comment: 15 pages, LaTeX, 1 figure, contribution to ``Experimental
Metaphysics---Quantum Mechanical Studies in Honor of Abner Shimony,'' edited
by R.S.Cohen, M. Horne, and J. Stachel, Boston Studies in the Philosophy of
Science (Kluwer, 1996
On the classical limit of Bohmian mechanics for Hagedorn wave packets
We consider the classical limit of quantum mechanics in terms of Bohmian
trajectories. For wave packets as defined by Hagedorn we show that the Bohmian
trajectories converge to Newtonian trajectories in probability.Comment: some minor changes; published versio
Bohmian Mechanics and Quantum Field Theory
We discuss a recently proposed extension of Bohmian mechanics to quantum
field theory. For more or less any regularized quantum field theory there is a
corresponding theory of particle motion, which in particular ascribes
trajectories to the electrons or whatever sort of particles the quantum field
theory is about. Corresponding to the nonconservation of the particle number
operator in the quantum field theory, the theory describes explicit creation
and annihilation events: the world lines for the particles can begin and end.Comment: 4 pages, uses RevTeX4, 2 figures; v2: shortened and with minor
addition
The ontology of Bohmian mechanics
The paper points out that the modern formulation of Bohm's quantum theory
known as Bohmian mechanics is committed only to particles' positions and a law
of motion. We explain how this view can avoid the open questions that the
traditional view faces according to which Bohm's theory is committed to a
wave-function that is a physical entity over and above the particles, although
it is defined on configuration space instead of three-dimensional space. We
then enquire into the status of the law of motion, elaborating on how the main
philosophical options to ground a law of motion, namely Humeanism and
dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch
out how these options apply to primitive ontology approaches to quantum
mechanics in general
Naive Realism about Operators
A source of much difficulty and confusion in the interpretation of quantum
mechanics is a ``naive realism about operators.'' By this we refer to various
ways of taking too seriously the notion of operator-as-observable, and in
particular to the all too casual talk about ``measuring operators'' that occurs
when the subject is quantum mechanics. Without a specification of what should
be meant by ``measuring'' a quantum observable, such an expression can have no
clear meaning. A definite specification is provided by Bohmian mechanics, a
theory that emerges from Sch\"rodinger's equation for a system of particles
when we merely insist that ``particles'' means particles. Bohmian mechanics
clarifies the status and the role of operators as observables in quantum
mechanics by providing the operational details absent from standard quantum
mechanics. It thereby allows us to readily dismiss all the radical claims
traditionally enveloping the transition from the classical to the quantum
realm---for example, that we must abandon classical logic or classical
probability. The moral is rather simple: Beware naive realism, especially about
operators!Comment: 18 pages, LaTex2e with AMS-LaTeX, to appear in Erkenntnis, 1996 (the
proceedings of the international conference ``Probability, Dynamics and
Causality,'' Luino, Italy, 15-17 June 1995, a special issue edited by D.
Costantini and M.C. Gallavotti and dedicated to Prof. R. Jeffrey
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