457 research outputs found
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 dynamics
A mechanism describing state reduction dynamics in relativistic quantum field
theory is outlined. The mechanism involves nonlinear stochastic modifications
to the standard description of unitary state evolution and the introduction of
a relativistic field in which a quantized degree of freedom is associated to
each point in spacetime. The purpose of this field is to mediate in the
interaction between classical stochastic influences and conventional quantum
fields. The equations of motion are Lorentz covariant, frame independent, and
do not result in divergent behavior. It is shown that the mathematical
framework permits the specification of unambiguous local properties providing a
connection between the model and evidence of real world phenomena. The collapse
process is demonstrated for an idealized example.Comment: 20 pages, 2 figures, replacement with minor correction
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
Collapse Models
This is a review of formalisms and models (nonrelativistic and relativistic)
which modify Schrodinger's equation so that it describes wavefunction collapse
as a dynamical physical process.Comment: 40 pages, to be published in "Open Systems and Measurement in
Relativistic Quantum Theory," F. Petruccione and H. P. Breuer eds. (Springer
Verlag, 1999
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
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
Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\"odinger Equation
We generalize the Weisskopf-Wigner theory for the line shape and transition
rates of decaying states to the case of the energy-driven stochastic
Schr\"odinger equation that has been used as a phenomenology for state vector
reduction. Within the standard approximations used in the Weisskopf-Wigner
analysis, and assuming that the perturbing potential inducing the decay has
vanishing matrix elements within the degenerate manifold containing the
decaying state, the stochastic Schr\"odinger equation linearizes. Solving the
linearized equations, we find no change from the standard analysis in the line
shape or the transition rate per unit time. The only effect of the stochastic
terms is to alter the early time transient behavior of the decay, in a way that
eliminates the quantum Zeno effect. We apply our results to estimate
experimental bounds on the parameter governing the stochastic effects.Comment: 29 pages in RevTeX, Added Note, references adde
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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