178 research outputs found
Detection Time Distribution for Several Quantum Particles
We address the question of how to compute the probability distribution of the
time at which a detector clicks, in the situation of non-relativistic
quantum particles in a volume in physical space
and detectors placed along the boundary of . We have
recently [http://arxiv.org/abs/1601.03715] argued in favor of a rule for the
1-particle case that involves a Schr\"odinger equation with an absorbing
boundary condition on introduced by Werner; we call this rule
the "absorbing boundary rule." Here, we describe the natural extension of the
absorbing boundary rule to the -particle case. A key element of this
extension is that, upon a detection event, the wave function gets collapsed by
inserting the detected position, at the time of detection, into the wave
function, thus yielding a wave function of particles. We also describe an
extension of the absorbing boundary rule to the case of moving detectors.Comment: 15 pages LaTeX, no figure
Bohmian Mechanics at Space-Time Singularities. I. Timelike Singularities
We develop an extension of Bohmian mechanics to a curved background
space-time containing a singularity. The present paper focuses on timelike
singularities. We use the naked timelike singularity of the super-critical
Reissner-Nordstrom geometry as an example. While one could impose boundary
conditions at the singularity that would prevent the particles from falling
into the singularity, we are interested here in the case in which particles
have positive probability to hit the singularity and get annihilated. The wish
for reversibility, equivariance, and the Markov property then dictates that
particles must also be created by the singularity, and indeed dictates the rate
at which this must occur. That is, a stochastic law prescribes what comes out
of the singularity. We specify explicit equations of a non-rigorous model
involving an interior-boundary condition on the wave function at the
singularity, which can be used also in other versions of quantum theory besides
Bohmian mechanics. As the resulting theory involves particle creation and
annihilation, it can be regarded as a quantum field theory, and the stochastic
process for the Bohmian particles is analogous to Bell-type quantum field
theories.Comment: 26 pages LaTeX, 2 figures (no separate figure files); v2 major
revisio
Comment on "The Free Will Theorem"
In a recent paper [quant-ph/0604079], Conway and Kochen claim to have
established that theories of the GRW type, i.e., of spontaneous wave function
collapse, cannot be made relativistic. On the other hand, relativistic GRW-type
theories have already been presented, in my recent paper [quant-ph/0406094] and
by Dowker and Henson [J. Statist. Phys. 115: 1327 (2004), quant-ph/0209051].
Here, I elucidate why these are not excluded by the arguments of Conway and
Kochen.Comment: 10 pages LaTeX, no figures; v2 minor improvement
Paradoxes and Primitive Ontology in Collapse Theories of Quantum Mechanics
Collapse theories are versions of quantum mechanics according to which the
collapse of the wave function is a real physical process. They propose precise
mathematical laws to govern this process and to replace the vague conventional
prescription that a collapse occurs whenever an "observer" makes a
"measurement." The "primitive ontology" of a theory (more or less what Bell
called the "local beables") are the variables in the theory that represent
matter in space-time. There is no consensus about whether collapse theories
need to introduce a primitive ontology as part of their definition. I make some
remarks on this question and point out that certain paradoxes about collapse
theories are absent if a primitive ontology is introduced.Comment: 21 pages LaTeX, no figures; v2 major extension and revisio
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