Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1206.4425 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Constraining continuous spontaneous localization strength parameter λ from standard cosmology and spectral distortions of cosmic microwave background radiation

Kinjalk Lochan, Suratna Das, Angelo Bassi

Published Sep 12, 2012• 28 citations
arXivHTMLPDF

Abstract

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 $y$-type distortions) so as to violate the observed bounds.

DOI
10.1103/physrevd.86.065016

Related papers

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

Suratna Das, Kinjalk Lochan, Angelo Bassi

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.

arXiv:1302.0171•The Ninth Marcel Grossmann Meeting•Jan 29, 2015•1 citation

Cosmological inflation and the quantum measurement problem

Jérôme Martin, Vincent Vennin, Patrick Peter

According to cosmological inflation, the inhomogeneities in our Universe are of quantum-mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum-to-classical transition, it remains to understand how a specific outcome can be produced in the early Universe, in the absence of any observer. The continuous spontaneous localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wave function collapse is caused by adding new nonlinear and stochastic terms to the Schr\"odinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wave function collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schr\"odinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with ${n}_{\mathrm{S}}=4$, a spectral index in obvious contradiction with the cosmic microwave background anisotropy observations. The requirement that the non-scale-invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics. Due to the absence of a CSL amplification mechanism in field theory, this also has the consequence that the collapse mechanism of the inflationary fluctuations is not efficient. Then, we determine the collapse time. On small scales the collapse is almost instantaneous, and we recover exactly the behavior of the CSL harmonic oscillator (a case for which we present new results), whereas, on large scales, we find that the collapse is delayed and can take several e-folds to happen. We conclude that recovering the observational successes of inflation and, at the same time, reaching a satisfactory resolution of the inflationary ``macro-objectification'' issue seems problematic in the framework considered here. This work also provides a complete solution to the CSL parametric oscillator system, a topic we suggest could play a very important role to further constrain the CSL parameters. Our results illustrate the remarkable power of inflation and cosmology to constrain new physics.

arXiv:1207.2086•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Nov 26, 2012•131 citations

Continuous spontaneous localization wave function collapse model as a mechanism for the emergence of cosmological asymmetries in inflation

Pedro Cañate, Philip Pearle, Daniel Sudarsky

The inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the continuous spontaneous localization model of wave function collapse in the context of inflation. This modification of quantum dynamics introduces a stochastic nonunitary component to the evolution of the inflaton field perturbations. This leads to passage from a homogeneous and isotropic stage to another, where the quantum uncertainties in the initial state of inflation transmute into the primordial inhomogeneities and anisotropies. We show, by proper choice of the collapse-generating operator, that it is possible to achieve compatibility with the precise observations of the cosmic microwave background radiation.

arXiv:1211.3463•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 21, 2013•111 citations

Constraining quantum collapse inflationary models with current data: The semiclassical approach

María Pía Piccirilli, Gabriel León, Susana J. Landau +2 more

The hypothesis of the self-induced collapse of the inflaton wave function was introduced as a candidate for the physical process responsible for the emergence of inhomogeneity and anisotropy at all scales. In particular, we consider different proposal for the precise form of the dynamics of the inflaton wave function: (i) the GRW-type collapse schemes proposals based on spontaneous individual collapses which generate nonvanishing expectation values of various physical quantities taken as ansatz modifications of the standard inflationary scenario; (ii) the proposal based on a Continuous Spontaneous Localization (CSL) type modification of the Schrödinger evolution of the inflaton wave function, based on a natural choice of collapse operator. We perform a systematic analysis within the semi-classical gravity approximation, of the standing of those models considering a full quasi-de Sitter expansion scenario. We note that the predictions for the Cosmic Microwave Background (CMB) temperature and polarization spectrum differ slightly from those of the standard cosmological model. We also analyze these proposals with a Bayesian model comparison using recent CMB and Baryonic Acoustic Oscillations (BAO) data. Our results show a moderate preference of the joint CMB and BAO data for one of the studied collapse schemes model over the [Formula: see text]CDM one, while there is no preference when only CMB data are considered. Additionally, analysis using CMB data provide the same Bayesian evidence for both the CSL and Standard Models, i.e. the data have no preference between the simplicity of the LCDM model and the complexity of the collapse scenario.

arXiv:1709.06237•International Journal of Modern Physics D•Oct 24, 2018•16 citations

Colored collapse models from the non-interferometric perspective

Matteo Carlesso, Luca Ferialdi, Angelo Bassi

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

arXiv:1805.10100•The European Physical Journal D•Sep 1, 2018•30 citations

Heating of trapped ultracold atoms by collapse dynamics

Franck Laloë, William J. Mullin, Philip Pearle

The continuous spontaneous localization (CSL) theory alters the Schr\"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\ensuremath{\lambda}$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\ensuremath{\lambda}$. We obtain $\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{s}}^{\ensuremath{-}1}$.

arXiv:1409.5388•Physical Review A•Nov 24, 2014•95 citations
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 \ensuremathλ\ensuremath{\lambda}\ensuremathλ 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 \ensuremathμ\ensuremath{\mu}\ensuremathμ-type and yyy-type distortions) so as to violate the observed bounds.
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.
According to cosmological inflation, the inhomogeneities in our Universe are of quantum-mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum-to-classical transition, it remains to understand how a specific outcome can be produced in the early Universe, in the absence of any observer. The continuous spontaneous localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wave function collapse is caused by adding new nonlinear and stochastic terms to the Schr\"odinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wave function collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schr\"odinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with nS=4{n}_{\mathrm{S}}=4nS​=4, a spectral index in obvious contradiction with the cosmic microwave background anisotropy observations. The requirement that the non-scale-invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics. Due to the absence of a CSL amplification mechanism in field theory, this also has the consequence that the collapse mechanism of the inflationary fluctuations is not efficient. Then, we determine the collapse time. On small scales the collapse is almost instantaneous, and we recover exactly the behavior of the CSL harmonic oscillator (a case for which we present new results), whereas, on large scales, we find that the collapse is delayed and can take several e-folds to happen. We conclude that recovering the observational successes of inflation and, at the same time, reaching a satisfactory resolution of the inflationary ``macro-objectification'' issue seems problematic in the framework considered here. This work also provides a complete solution to the CSL parametric oscillator system, a topic we suggest could play a very important role to further constrain the CSL parameters. Our results illustrate the remarkable power of inflation and cosmology to constrain new physics.
The inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the continuous spontaneous localization model of wave function collapse in the context of inflation. This modification of quantum dynamics introduces a stochastic nonunitary component to the evolution of the inflaton field perturbations. This leads to passage from a homogeneous and isotropic stage to another, where the quantum uncertainties in the initial state of inflation transmute into the primordial inhomogeneities and anisotropies. We show, by proper choice of the collapse-generating operator, that it is possible to achieve compatibility with the precise observations of the cosmic microwave background radiation.
The hypothesis of the self-induced collapse of the inflaton wave function was introduced as a candidate for the physical process responsible for the emergence of inhomogeneity and anisotropy at all scales. In particular, we consider different proposal for the precise form of the dynamics of the inflaton wave function: (i) the GRW-type collapse schemes proposals based on spontaneous individual collapses which generate nonvanishing expectation values of various physical quantities taken as ansatz modifications of the standard inflationary scenario; (ii) the proposal based on a Continuous Spontaneous Localization (CSL) type modification of the Schrödinger evolution of the inflaton wave function, based on a natural choice of collapse operator. We perform a systematic analysis within the semi-classical gravity approximation, of the standing of those models considering a full quasi-de Sitter expansion scenario. We note that the predictions for the Cosmic Microwave Background (CMB) temperature and polarization spectrum differ slightly from those of the standard cosmological model. We also analyze these proposals with a Bayesian model comparison using recent CMB and Baryonic Acoustic Oscillations (BAO) data. Our results show a moderate preference of the joint CMB and BAO data for one of the studied collapse schemes model over the [Formula: see text]CDM one, while there is no preference when only CMB data are considered. Additionally, analysis using CMB data provide the same Bayesian evidence for both the CSL and Standard Models, i.e. the data have no preference between the simplicity of the LCDM model and the complexity of the collapse scenario.
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
The continuous spontaneous localization (CSL) theory alters the Schr\"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\ensuremath{\lambda}$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\ensuremath{\lambda}$. We obtain $\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{s}}^{\ensuremath{-}1}$.