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 $^{74}$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 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

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.

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

On Spontaneous Wave Function Collapse and Quantum Field Theory

One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schroedinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini, and Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focussing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.Comment: 14 pages LaTeX, no figures; v2 minor improvement

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