386 research outputs found
Cosmogenesis and Collapse
Some possible benefits of dynamical collapse for a quantum theory of
cosmogenesis are discussed. These are a possible long wait before creation
begins, creation of energy and space, and choice of a particular universe out
of a superposition.Comment: For a festschrift in Foundations of Physics in honor of Daniel
Greenberger and Helmut Rauch in Foundations of Physics. This updates the
previous version by adding an appendix (Appendix B) which contains the exact
solution of a partial differential equation of importance in the pape
Quasirelativistic quasilocal finite wave-function collapse model
A Markovian wave function collapse model is presented where the
collapse-inducing operator, constructed from quantum fields, is a manifestly
covariant generalization of the mass density operator utilized in the
nonrelativistic Continuous Spontaneous Localization (CSL) wave function
collapse model. However, the model is not Lorentz invariant because two such
operators do not commute at spacelike separation, i.e., the time-ordering
operation in one Lorentz frame, the "preferred" frame, is not the time-ordering
operation in another frame. However, the characteristic spacelike distance over
which the commutator decays is the particle's Compton wavelength so, since the
commutator rapidly gets quite small, the model is "almost" relativistic. This
"QRCSL" model is completely finite: unlike previous, relativistic, models, it
has no (infinite) energy production from the vacuum state.
QRCSL calculations are given of the collapse rate for a single free particle
in a superposition of spatially separated packets, and of the energy production
rate for any number of free particles: these reduce to the CSL rates if the
particle's Compton wavelength is small compared to the model's distance
parameter. One motivation for QRCSL is the realization that previous
relativistic models entail excitation of nuclear states which exceeds that of
experiment, whereas QRCSL does not: an example is given involving quadrupole
excitation of the Ge nucleus.Comment: 10 pages, to be published in Phys. Rev.
How Stands Collapse II
I review ten problems associated with the dynamical wave function collapse
program, which were described in the first of these two papers. Five of these,
the \textit{interaction, preferred basis, trigger, symmetry} and
\textit{superluminal} problems, were discussed as resolved there. In this
volume in honor of Abner Shimony, I discuss the five remaining problems,
\textit{tails, conservation law, experimental, relativity, legitimization}.
Particular emphasis is given to the tails problem, first raised by Abner. The
discussion of legitimization contains a new argument, that the energy density
of the fluctuating field which causes collapse should exert a gravitational
force. This force can be repulsive, since this energy density can be negative.
Speculative illustrations of cosmological implications are offered.Comment: 37 page
Relativistic state reduction model
In order to address the measurement problem of quantum theory we make the
assumption that quantum state reduction should be regarded as a genuine
physical process deserving of a dynamical description. Generalizing the
nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and
Pearle, a relativistic state reduction mechanism is proposed. The mechanism
involves nonlinear stochastic modifications to the standard description of
unitary state evolution and the introduction of a mediating field to facilitate
smearing of quantum field interactions.Comment: 7 pages, prepared for DICE2010 conference proceeding
Relativistic formulation of quantum state diffusion?
The recently reported relativistic formulation of the well-known
non-relativistic quantum state diffusion is seriously mistaken. It predicts,
for instance, inconsistent measurement outcomes for the same system when seen
by two different inertial observers.Comment: 5 pages LaTeX, submitted to J. Phys.
Comment on "Finite Size Corrections to the Radiation Reaction Force in Classical Electrodynamics" [arXiv:1005.2617]
In [1, arXiv:1005.2617] effective field theory methods have been employed to
compute the equations of motion of a spherically symmetric charged shell of
radius R, taking into account the radiation reaction force exerted by the
shell's own electromagnetic field up to O(R^2). The authors of Ref. [1] have
stated that the known result for the self force of the shell as can be found
from Eq. (16.28) of the textbook of Jackson [2] (see also Chap. 4 in the review
of Pearle [3]) is incorrect, in that the term linear in R should be absent. We
claim that this conclusion of Ref. [1] is incorrect, and that the textbook
result, Eq. (1) does hold.Comment: 1 pag
Dynamical state reduction in an EPR experiment
A model is developed to describe state reduction in an EPR experiment as a
continuous, relativistically-invariant, dynamical process. The system under
consideration consists of two entangled isospin particles each of which undergo
isospin measurements at spacelike separated locations. The equations of motion
take the form of stochastic differential equations. These equations are solved
explicitly in terms of random variables with a priori known probability
distribution in the physical probability measure. In the course of solving
these equations a correspondence is made between the state reduction process
and the problem of classical nonlinear filtering. It is shown that the solution
is covariant, violates Bell inequalities, and does not permit superluminal
signaling. It is demonstrated that the model is not governed by the Free Will
Theorem and it is argued that the claims of Conway and Kochen, that there can
be no relativistic theory providing a mechanism for state reduction, are false.Comment: 19 pages, 3 figure
Problems and Aspects of Energy-Driven Wavefunction Collapse Models
Four problematic circumstances are considered, involving models which
describe dynamical wavefunction collapse toward energy eigenstates, for which
it is shown that wavefunction collapse of macroscopic objects does not work
properly. In one case, a common particle position measuring situation, the
apparatus evolves to a superposition of macroscopically distinguishable states
(does not collapse to one of them as it should) because each such
particle/apparatus/environment state has precisely the same energy spectrum.
Second, assuming an experiment takes place involving collapse to one of two
possible outcomes which is permanently recorded, it is shown in general that
this can only happen in the unlikely case that the two apparatus states
corresponding to the two outcomes have disjoint energy spectra. Next, the
progressive narrowing of the energy spectrum due to the collapse mechanism is
considered. This has the effect of broadening the time evolution of objects as
the universe evolves. Two examples, one involving a precessing spin, the other
involving creation of an excited state followed by its decay, are presented in
the form of paradoxes. In both examples, the microscopic behavior predicted by
standard quantum theory is significantly altered under energy-driven collapse,
but this alteration is not observed by an apparatus when it is included in the
quantum description. The resolution involves recognition that the statevector
describing the apparatus does not collapse, but evolves to a superposition of
macroscopically different states.Comment: 17 page
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509
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