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Diagnosing the Trouble With Quantum Mechanics
We discuss an article by Steven Weinberg expressing his discontent with the
usual ways to understand quantum mechanics. We examine the two solutions that
he considers and criticizes and propose another one, which he does not discuss,
the pilot wave theory or Bohmian mechanics, for which his criticisms do not
apply.Comment: 23 pages, 4 figure
On quantum potential dynamics
Non-relativistic de Broglie-Bohm theory describes particles moving under the
guidance of the wave function. In de Broglie's original formulation, the
particle dynamics is given by a first-order differential equation. In Bohm's
reformulation, it is given by Newton's law of motion with an extra potential
that depends on the wave function--the quantum potential--together with a
constraint on the possible velocities. It was recently argued, mainly by
numerical simulations, that relaxing this velocity constraint leads to a
physically untenable theory. We provide further evidence for this by showing
that for various wave functions the particles tend to escape the wave packet.
In particular, we show that for a central classical potential and bound energy
eigenstates the particle motion is often unbounded. This work seems
particularly relevant for ways of simulating wave function evolution based on
Bohm's formulation of the de Broglie-Bohm theory. Namely, the simulations may
become unstable due to deviations from the velocity constraint.Comment: 10 pages, 4 figures, LaTex; v2 minor additions; v3 figures adde
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
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