On the spontaneous emission of electromagnetic radiation in the CSL model

Spontaneous photon emission in the Continuous Spontaneous Localization (CSL) model is studied one more time. In the CSL model each particle interacts with a noise field that induces the collapse of its wave function. As a consequence of this interaction, when the particle is electrically charged, it radiates. As discussed in [1], the formula for the emission rate, to first perturbative order, contains two terms: One is proportional to the Fourier component of the noise field at the same frequency as that of the emitted photon and one is proportional to the zero Fourier component of the noise field. As discussed in previous works, this second term seems unphysical. In [1], it was shown that the unphysical term disappears when the noises is confined to a bounded region and the final particle's state is a wave packet. Here we investigate the origin of the unphysical term and why it vanishes according to the previous prescription. For this purpose, the electrodynamic part of the equation of motion is solved exactly while the part due to the noise is treated perturbatively. We show that the unphysical term is connected to exponentially decaying function of time which dies out in the large time limit, however, approximates to 1 in the first perturbative order in the electromagnetic field.Comment: 10 pages, 1 figure, LaTe

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

Reply to Comments of Bassi, Ghirardi, and Tumulka on the Free Will Theorem

We show that the authors in the title have erred in claiming that our axiom FIN is false by conflating it with Bell locality. We also argue that the predictions of quantum mechanics, and in particular EPR, are fully Lorentz invariant, whereas the Free Will Theorem shows that theories with a mechanism of reduction, such as GRW, cannot be made fully invariant.Comment: We sharpen our theorem by replacing axiom FIN by a weaker axiom MIN to answer the above authors' objection

Kinin-B1 receptors in ischaemia-induced pancreatitis: Functional importance and cellular localisation

In this study we compare the role of kininB1 and B2 receptors during ischaemia/reperfusion of rat pancreas. Our investigations were prompted by the observation that infusion of a kininB2 receptor antagonist produced significant improvement in acute experimental pancreatitis. In an acute model with two hours of ischaemia/two hours of reperfusion, application of the kininB1 receptor antagonist (CP-0298) alone, or in combination with kininB2 receptor antagonist (CP-0597), significantly reduced the number of adherent leukocytes in postcapillary venules. In a chronic model with five days of reperfusion, the continuous application of kininB1 receptor antagonist or a combination of kininB1 and B2 receptor antagonists markedly reduced the survival rate. In kininreceptor binding studies kininB1 receptor showed a 22-fold increase in expression during the time of ischaemia/ reperfusion. Carboxypeptidase M activity was upregulated 10-fold following two hours of ischaemia and two hours of reperfusion, provided the appropriate specific ligand, desArg10-kallidin and/or desArg9-bradykinin, was used. The occurrence of kininB1 receptor binding sites on acinar cell membranes was demonstrated by microautoradiography. With a specific antibody, the localisation of kininB1 receptor protein was confirmed at the same sites. In conclusion, we have demonstrated the upregulation of the pancreatic acinar cell kininB1 receptors during ischaemia/reperfusion. The novel functional finding was that antagonism of the kininB1 receptors decreased the survival rate in an experimental model of pancreatitis

On the long time behavior of Hilbert space diffusion

Stochastic differential equations in Hilbert space as random nonlinear modified Schroedinger equations have achieved great attention in recent years; of particular interest is the long time behavior of their solutions. In this note we discuss the long time behavior of the solutions of the stochastic differential equation describing the time evolution of a free quantum particle subject to spontaneous collapses in space. We explain why the problem is subtle and report on a recent rigorous result, which asserts that any initial state converges almost surely to a Gaussian state having a fixed spread both in position and momentum.Comment: 6 pages, EPL2-Te

Spectral triples on the Jiang-Su algebra

We construct spectral triples on a class of particular inductive limits of matrix-valued function algebras. In the special case of the Jiang-Su algebra we employ a particular $AF$-embedding

Consciousness and the Wigner's friend problem

It is generally agreed that decoherence theory is, if not a complete answer, at least a great step forward towards a solution of the quantum measurement problem. It is shown here however that in the cases in which a sentient being is explicitly assumed to take cognizance of the outcome the reasons we have for judging this way are not totally consistent, so that the question has to be considered anew. It is pointed out that the way the Broglie-Bohm model solves the riddle suggests a possible clue, consisting in assuming that even very simple systems may have some sort of a proto-consciousness, but that their ``internal states of consciousness'' are not predictive. It is, next, easily shown that if we imagine the systems get larger, in virtue of decoherence their internal states of consciousness progressively gain in predictive value. So that, for macro-systems, they may be identified (in practice) with the predictive states of consciousness on which we ground our observational predictions. The possibilities of carrying over this idea to standard quantum mechanics are then investigated. Conditions of conceptual consistency are considered and found rather strict, and, finally, two solutions emerge, differing conceptually very much from one another but in both of which the, possibly non-predictive, generalized internal states of consciousness play a crucial role

On the uniqueness of the equation for state-vector collapse

The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question, whether such models are in some sense unique, i.e. whether the nonlinear equations replacing Schroedinger's equation, are uniquely determined as collapse equations. Various people worked on identifying the class of nonlinear modifications of the Schroedinger equation, compatible with general physical requirements. Here we identify the most general class of continuous wavefunction evolutions under the assumption of no-faster-than-light signalling.Comment: 7 pages, LaTeX. Major changes performe

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

Exact solution for a non-Markovian dissipative quantum dynamics

We provide the exact analytic solution of the stochastic Schr\"odinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models, for infinite dimensional systems. We compute the Green's function; in the case of a free particle, and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.Comment: to appear in Phys. Rev. Let