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arXiv:1302.0171 · The Ninth Marcel Grossmann Meeting

BOUNDS ON SPONTANEOUS COLLAPSE MODEL OF QUANTUM MECHANICS FROM FORMATION OF CMBR AND STANDARD COSMOLOGY

Suratna Das, Kinjalk Lochan, Angelo Bassi

Published Jan 29, 2015• 1 citation
arXivHTMLPDF

Abstract

Continuous Spontaneous Localization (CSL) model of Quantum Mechanics modifies Schrödinger equation by adding non-linear stochastic terms due to which the total energy of a system increases with a constant rate which is proportional to the collapse rate $λ$. Thus applying CSL model to cosmological scenarios can change the thermal behaviour of the particles during evolution and we will put constraints on $λ$ by considering several cosmological scenarios.

DOI
10.1142/9789814623995_0244

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Continuous Spontaneous Localization (CSL) model of Quantum Mechanics modifies Schrödinger equation by adding non-linear stochastic terms due to which the total energy of a system increases with a constant rate which is proportional to the collapse rate λλλ. Thus applying CSL model to cosmological scenarios can change the thermal behaviour of the particles during evolution and we will put constraints on λλλ by considering several cosmological scenarios.
Models of spontaneous wave function collapse modify the linear Schr\"odinger equation of standard quantum mechanics by adding stochastic nonlinear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such nonlinear terms in the Schr\"odinger equation leads to nonconservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat nonrelativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the well-understood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms, according to the continuous spontaneous localization model, on the standard evolution of nonrelativistic matter and on the formation of cosmic microwave background radiation. We will also put constraints on the continuous spontaneous localization collapse rate $\ensuremath{\lambda}$ by considering that the standard evolution of nonrelativistic matter is not hampered and the observed precise blackbody spectrum of cosmic microwave background radiation would not get distorted (in the form of $\ensuremath{\mu}$-type and yyy-type distortions) so as to violate the observed bounds.
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrodinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schr\"odinger equation, thus (slightly) modifying the dynamics of quantum systems. Experimental bounds on the collapse parameters have been derived from various experiments involving a plethora of different systems, from single atoms to gravitational wave detectors. Here, we give a comprehensive treatment of the continuous spontaneous localization (CSL) model, the most studied among collapse models, for Fermi liquids. We consider both the white and non-white noise case. Application to various astrophysical sources is presented.
Abstract Models of spontaneous wave function collapse describe the quantum-to-classical transition by assuming a progressive breakdown of the superposition principle when the mass of the system increases, providing a well-defined phenomenology in terms of a non-linearly and stochastically modified Schrödinger equation, which can be tested experimentally. The most popular of such models is the continuous spontaneous localization (CSL) model: in its original version, the collapse is driven by a white noise, and more recently, generalizations in terms of colored noises, which are more realistic, have been formulated. We will analyze how current non-interferometric tests bound the model, depending on the spectrum of the noise. We will find that low frequency purely mechanical experiments provide the most stable and strongest bounds. Graphical abstract
Spontaneous collapse models provide a possible solution to the measurement problem by modifying standard quantum dynamics. The modification consists of adding non-linear and stochastic terms inducing wavefunction collapse in space. Non-Markovian versions of these models are motivated by physical reasons, phenomenological consistency, and potential for relativistic extensions. Here, we investigate a non-Markovian version of the Poissonian Spontaneous Localization (PSL) model, i.e., a model characterized by instantaneous and localized collapse events. We assume that our model is characterized by a typical time scale τCτ_CτC​ so that, given an initial state ρ0ρ_0ρ0​ of standard quantum matter at time t=0t=0t=0, we derive an effective long-time (t≫τCt\gg τ_Ct≫τC​) statistical dynamics in terms of a CPTP map ΦtΦ_tΦt​. We then show how ΦtΦ_tΦt​ can be made equal to that obtained by non-Markovian CSL models. Moreover, given ΦtΦ_tΦt​, we obtain the associated time-convolutionless master equation by means of a supercumulant expansion. Finally, we characterize the collapse events process (for events with t≫τCt \gg τ_Ct≫τC​) given an initial quantum state ρ0ρ_0ρ0​ at t=0t=0t=0.