Spontaneous photon-emission from a non-relativistic free charged particle in collapse models: A case-study

We study the photon emission rate of a non relativistic charged particle interacting with an external classical noise through its position. Both the particle and the electromagnetic field are quantized. Under only the dipole approximation, the equations of motion can be solved exactly for a free particle, or a particle bounded by an harmonic potential. The physical quantity we will be interested in is the spectrum of the radiation emitted by the particle, due to the interaction with the noise. We will highlight several properties of the spectrum and clarify some issues appeared in the literature, regarding the exact mathematical formula of a spectrum for a free particle.Comment: 15 pages, LaTe

Bohmian Mechanics, Collapse Models and the emergence of Classicality

We discuss the emergence of classical trajectories in Bohmian Mechanics (BM), when a macroscopic object interacts with an external environment. We show that in such a case the conditional wave function of the system follows a dynamics which, under reasonable assumptions, corresponds to that of the Ghirardi-Rimini-Weber (GRW) collapse model. As a consequence, Bohmian trajectories evolve classically. Our analysis also shows how the GRW (istantaneous) collapse process can be derived by an underlying continuous interaction of a quantum system with an external agent, thus throwing a light on how collapses can emerge from a deeper level theory.Comment: 19 pages, 2 figure

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 spontaneous photon emission in collapse models

We reanalyze the problem of spontaneous photon emission in collapse models. We show that the extra term found by Bassi and Duerr is present for non-white (colored) noise, but its coefficient is proportional to the zero frequency Fourier component of the noise. This leads one to suspect that the extra term is an artifact. When the calculation is repeated with the final electron in a wave packet and with the noise confined to a bounded region, the extra term vanishes in the limit of continuum state normalization. The result obtained by Fu and by Adler and Ramazanoglu from application of the Golden Rule is then recovered.Comment: 23 pages, LaTex. Minor changes with respect to previous versio

The Schr\"odinger-Newton equation and its foundations

The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schr\"odinger equation stays linear, in the latter case one ends up with the so-called Schr\"odinger-Newton equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schr\"odinger-Newton equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schr\"odinger-Newton equation.Comment: 17 pages, 3 figures, revised version (some minor changes

Bounds on collapse models from cold-atom experiments

The spontaneous localization mechanism of collapse models induces a Brownian motion in all physical systems. This effect is very weak, but experimental progress in creating ultracold atomic systems can be used to detect it. In this paper, we considered a recent experiment [1], where an atomic ensemble was cooled down to picokelvins. Any Brownian motion induces an extra increase of the position variance of the gas. We study this effect by solving the dynamical equations for the Continuous Spontaneous Localizations (CSL) model, as well as for its non-Markovian and dissipative extensions. The resulting bounds, with a 95% of confidence level, are beaten only by measurements of spontaneous X-ray emission and by experiments with cantilever (in the latter case, only for rC > 10^(-7) m, where rC is one of the two collapse parameters of the CSL model). We show that, contrary to the bounds given by X-ray measurements, non-Markovian effects do not change the bounds, for any reasonable choice of a frequency cutoff in the spectrum of the collapse noise. Therefore the bounds here considered are more robust. We also show that dissipative effects are unimportant for a large spectrum of temperatures of the noise, while for low temperatures the excluded region in the parameter space is the more reduced, the lower the temperature.Comment: 16 pages, 14 figure

Ancora sull’Aldina dell’Encomio di Elena

Il saggio si occupa della trasmissione del testo greco dello Ἑλένης ἐγκώμιον di Gorgia, con particolare riguardo per il rapporto che intercorre tra il manoscritto di mano di Costantino Lascari e la princeps aldina del 1508.The work deals with the transmission of the Greek text of Gorgias’s Ἑλένης ἐγκώμιον, and focuses on the relationship between the manuscript copied by Constantinus Lascaris and the Aldine princeps of the year 1508

A Superdeterministic Toy Model

A superdeterministic toy model for quantum mechanics is introduced and discussed. It is demonstrated that, when averaged over the hidden variables, the model produces the same predictions as quantum mechanics. In the model considered here, the dynamics depends only on the settings of the measurement device at the detection time, not how those settings were chosen. This provides a counter-example to the claim that superdeterminism is fine-tuned and unscientific.Comment: 21 pages, 2 figures, improved discussion and clarified definitions, references adde

KVN: Keypoints Voting Network with Differentiable RANSAC for Stereo Pose Estimation

Object pose estimation is a fundamental computer vision task exploited in several robotics and augmented reality applications. Many established approaches rely on predicting 2D-3D keypoint correspondences using RANSAC (Random sample consensus) and estimating the object pose using the PnP (Perspective-n-Point) algorithm. Being RANSAC non-differentiable, correspondences cannot be directly learned in an end-to-end fashion. In this paper, we address the stereo image-based object pose estimation problem by (i) introducing a differentiable RANSAC layer into a well-known monocular pose estimation network; (ii) exploiting an uncertainty-driven multi-view PnP solver which can fuse information from multiple views. We evaluate our approach on a challenging public stereo object pose estimation dataset, yielding state-of-the-art results against other recent approaches. Furthermore, in our ablation study, we show that the differentiable RANSAC layer plays a significant role in the accuracy of the proposed method. We release with this paper the open-source implementation of our method.Comment: Submitted to IEEE Robotics and Automation Letter