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

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 Reduction Models: present status and future developments

We review the major achievements of the dynamical reduction program, showing why and how it provides a unified, consistent description of physical phenomena, from the microscopic quantum domain to the macroscopic classical one. We discuss the difficulties in generalizing the existing models in order to comprise also relativistic quantum field theories. We point out possible future lines of research, ranging from mathematical physics to phenomenology.Comment: 12 pages. Contribution to the Proceedings of the "Third International Workshop DICE2006", Castello di Piombino (Tuscany), September 11-15, 2006. Minor changes mad

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

The Hilbert space operator formalism within dynamical reduction models

Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the postulates defining these models. In this paper, we show why and how the Hilbert-space operator formalism, which standard quantum mechanics postulates, can be derived from the fundamental evolution equation of dynamical reduction models. Far from having any special ontological meaning, we show that within the dynamical reduction context the operator formalism is just a compact and convenient way to express the statistical properties of the outcomes of experiments.Comment: 25 pages, RevTeX. Changes made and two figures adde

On the Electromagnetic Properties of Matter in Collapse Models

We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and under only the dipole approximation, we are able to solve the equation of motion exactly. In this way, both the finite time and large time behavior can be analyzed accurately. We discovered new features, which did not appear in previous works on the same subject. Since, so far, the spontaneous photon emission process places the strongest upper bounds on the collapse parameters, our results call for a further analysis of this process for those atomic systems which can be employed in experimental tests of collapse models, as well as of quantum mechanics.Comment: 17 pages, LaTeX, updated version with minor change

The quantum theory of measurement within dynamical reduction models

We analyze in mathematical detail, within the framework of the QMUPL model of spontaneous wave function collapse, the von Neumann measurement scheme for the measurement of a 1/2 spin particle. We prove that, according to the equation of the model: i) throughout the whole measurement process, the pointer of the measuring device is always perfectly well localized in space; ii) the probabilities for the possible outcomes are distributed in agreement with the Born probability rule; iii) at the end of the measurement the state of the microscopic system has collapsed to the eigenstate corresponding to the measured eigenvalue. This analysis shows rigorously how dynamical reduction models provide a consistent solution to the measurement problem of quantum mechanics.Comment: 24 pages, RevTeX. Minor changes mad

Local Fields without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. Such fields can exist as part of a hidden matter in the Universe if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT- invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT- invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particulary needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed.Comment: Latex 23 pages, sent to "Foundations of Physics

Numerical analysis of a spontaneous collapse model for a two-level system

We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at which the collapse of the state vector occurs, the reduction and delocalization times, and the reduction probabilities; it also allows to quantify the effect that an Hamiltonian which does not commute with the reducing terms has on the collapse mechanism. We also give a clear picture of the transition from the "microscopic" regime (when the noise terms are weak and the Hamiltonian prevents the state vector to collapse) to the "macroscopic" regime (when the noise terms are dominant and the collapse becomes effective for very long times). Finally, we clarify the distinction between decoherence and collapse.Comment: 7 pages, RevTeX. Significative improvements made. To appear on Phys. Rev.

Stochastic Schroedinger Equations with General Complex Gaussian Noises

Within the framework of stochastic Schroedinger equations, we show that the correspondence between statevector equations and ensemble equations is infinitely many to one, and we discuss the consequences. We also generalize the results of [Phys. Lett. A 224, p. 25 (1996)] to the case of more general complex Gaussian noises and analyze the two important cases of purely real and purely imaginary stochastic processes.Comment: 5 pages, LaTeX. To appear on Phys. Rev.