Models of spontaneous wave function collapse predict a small heating rate for a bulk solid, as a result of coupling to the noise field that causes collapse. This rate is small enough that ambient radioactivity and cosmic ray flux on the surface of the earth can mask the heating due to spontaneous collapse. In this paper we estimate the background noise due to gamma-radiation and cosmic ray muon flux, at different depths. We demonstrate that a low-temperature underground experiment at a depth of about 6.5 km.w.e. would have a low enough background to allow detection of bulk heating for a collapse rate $λ$ of $10^{-16}$ s$^{-1}$ using presently available technology.
Spontaneous wavefunction collapse models, like the Continuous Spontaneous Localization, are designed to suppress macroscopic superpositions, while preserving microscopic quantum phenomena. An observable consequence of collapse models is spontaneous heating of massive objects. Here we calculate the collapse-induced heating rate of astrophysical objects, and the corresponding equilibrium temperature. We apply these results to neutron stars, the densest phase of baryonic matter in the universe. Stronger collapse model parameters imply greater heating, allowing us to derive competitive bounds on m…
Mainstream literature on spontaneous wave function collapse never reflects on or profit from the formal coincidence and conceptual relationship with standard collapse under time-continuous quantum measurement (monitoring). I propose some easy lessons of standard monitoring theory which would make spontaneous collapse models revise some of their claims. In particular, the objective detection of spontaneous collapse remains impossible as long as the correct identification of what corresponds to the signal in standard monitoring is missing from spontaneous collapse models, the physical detectabil…
Currently there is not a satisfactory relativistic spontaneous collapse model. Here we show the impossibility of a simple generalization of the continuous spontaneous collapse (CSL) model to the relativistic framework. We consider a mass coupled model as in the non-relativistic limit this gives the CSL model. We show that a Lorentz covariant collapse equation cannot simultaneously satisfy the following conditions: i) To avoid a divergent rate of energy, ii) To prevent superluminal signaling.
We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the centre-of-mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilising a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoherence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show…
The argument for an objective wave function collapse: Why spontaneous localization collapse or no-collapse decoherence cannot solve the measurement problem in a subjective fashion
We calculate the rate of heating through phonon excitation implied by the noise postulated in mass-proportional-coupled collapse models, for a general noise power spectrum. For white noise with reduction rate $λ$, the phonon heating rate reduces to the standard formula, but for non-white noise with power spectrum $λ(ω)$, the rate $λ$ is replaced by $λ_{\rm eff}=\frac{2}{3 π^{3/2}} \int d^3w e^{-\vec w^2} \vec w^2 λ(ω_L(\vec w/r_c))$, with $ω_L(\vec q)$ the longitudinal acoustic phonon frequency as a function of wave number $\vec q$, and with $r_C$ the noise correlation length. Hence if the noi…
A simple and natural introduction to the concept and formalism of spontaneous wave function collapse can and should be based on textbook knowledge of standard quantum state collapse and monitoring. This approach explains the origin of noise driving the paradigmatic stochastic Schrödinger equations of spontaneous localization of the wave function $Ψ$. It reveals, on the other hand, that these equations are empirically redundant and the master equations of the noise-averaged state $\hatρ$ are the only empirically testable dynamics in current spontaneous collapse theories.
In this paper, new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models. This study allows the obtainment of the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate $λ$ and the correlation length $r_C$ are mapped, thus allowing the exclusion of a broad range of the parameter spa…
Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength of collapse depends on the mass of the system. Flavor oscillating systems such as neutral mesons feature superpositions of states of different masses and, hence, could be used to test the validity of spontaneous collapse models. Recently, it has been shown that the mass-proportional CSL model causes exponential damping of the neutral meson oscillations whic…
I impose the Newtonian criteria of inertial frames on the c.o.m. trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schrödinger equation eliminates the Brownian motion of the c.o.m., restores the exact inertial motion for free masses. For the collapse of Schrödinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m. ---inevitable in the collap…
{The Continuous Spontaneous Localization (CSL) theory alters the Schrödinger 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 $λ$ 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 predic…
We discuss limits on the noise strength parameter in mass-proportional-coupled wave function collapse models implied by bulk heating effects, and examine the role of the noise power spectrum in comparing experiments of different types. This comparison utilizes a calculation of the rate of heating through phonon excitation implied by a general noise power spectrum $λ(ω)$. We find that in the standard heating formula, the reduction rate $λ$ is replaced by $λ_{\rm eff}=\frac{2}{3 π^{3/2}} \int d^3w e^{-\vec w^2} \vec w^2 λ(ω_L(\vec w/r_c))$, with $ω_L(\vec q)$ the longitudinal acoustic phonon fre…
Collapse models predict a tiny violation of energy conservation, as a consequence of the spontaneous collapse of the wave function. This property allows to set experimental bounds on their parameters. We consider an ultrasoft magnetically tipped nanocantilever cooled to millikelvin temperature. The thermal noise of the cantilever fundamental mode has been accurately estimated in the range $0.03-1$ K, and any other excess noise is found to be negligible within the experimental uncertainty. From the measured data and the cantilever geometry, we estimate the upper bound on the Continuous Spontane…
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment $ΔT$ of equilibrium temperature in a mechanical oscillator. The obtained form $ΔT$ is linear in the oscillator's relaxation time $τ$ and independent of the mass. The oscillator can be in a classical thermal state, the effect $ΔT$ is classical for a wide range of frequencies and quality factors. We note that the test of $ΔT$ does not necessitate quantum state monitoring but tomography. In both gravity-related (DP) and continuous spontaneous localization (CSL) models the s…
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is governed by a phenomenological non-Hermitian Hamiltonian. In turn, we apply two popular collapse models, the Quantum Mechanics with Universal Position Localization and the Continuous Spontaneous Localization models, to a neutral meson system. By using the equivalence between the approaches to the time evolution of decaying systems with a non-Hermitian Hamilt…
The Continuous Spontaneous Localisation (CSL) theory in the cosmological context is subject to uncertainties related to the choice of the collapse operator. In this paper, we constrain its form based on generic arguments. We show that, if the collapse operator is even in the field variables, it is unable to induce the collapse of the wavefunction. Instead, if it is odd, we find that only linear operators are such that the outcomes are distributed according to Gaussian statistics, as required by measurements of the cosmic microwave background. We discuss implications of these results for previo…
Collapse models describe phenomenologically the quantum-to-classical transition by adding suitable nonlinear and stochastic terms to the Schroedinger 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 n…
We have analyzed recently published XENONnT data for the spontaneous X-ray emission signature predicted by the objective wave function collapse model of quantum mechanics. With extremely low background and large exposure, XENONnT data can be used to completely exclude the theoretically predicted collapse parameters of continuous spontaneous localization~(CSL) model suggested by Ghirardi, Rhimini and Weber. Our result strongly suggests that the simplest version of the CSL model with the white-noise assumption is unlikely to provide answers to the long-standing measurement problem of quantum mec…
In a recent article [Phys. Rev. A 94, 052128 (2016)], the authors compute the predictions of two collapse models on the transition probabilities of neutral mesons. Notably, they claim to find an influence on the decay rates and attempt to prove that a new parameter $θ(0)$ is required to fully characterize the noise of standard collapse models. These two claims are incorrect and motivated by flawed computations. This comment derives the correct transition probabilities exactly from the master equation, explains how they could be computed perturbatively in a safe way and finally shows where the …
Why do we never see a table in a superposition of here and there? This problem gets a solution by so called collapse models assuming the collapse as a genuinely physical process. Here we consider two specific collapse models and apply them to systems at high energies, i.e. flavour oscillating neutral meson systems. We find on one hand a potentially new interpretation of the decay rates introduced by hand in the standard formalism and on the other hand that these systems at high energies constrain by experimental data the possible collapse scenarios.
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…
We study how matter-wave interferometry with Bose-Einstein condensates is affected by hypothetical collapse models and by environmental decoherence processes. Motivated by recent atom fountain experiments with macroscopic arm separations, we focus on the observable signatures of first-order and higher-order coherence for different two-mode superposition states, and on their scaling with particle number. This can be used not only to assess the impact of environmental decoherence on many-body coherence, but also to quantify the extent to which macrorealistic collapse models are ruled out by such…
Wigner functions, allowing for a reformulation of quantum mechanics in phase space, are of central importance for the study of the quantum-classical transition. A full understanding of the quantum-classical transition, however, also requires an explanation for the absence of macroscopic superpositions to solve the quantum measurement problem. Stochastic reformulations of quantum mechanics based on spontaneous collapses of the wavefunction are a popular approach to this issue. In this article, we derive the dynamic equations for the four most important spontaneous collapse models - Ghirardi-Rim…
Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor--oscillating neutral mesons for the two most promising collapse models, the QMUPL (Quantum Mechanics with Universal Position Localization) model and the mass-proportional CSL (Continuous Sponta…
Atomic correlation effects in collapse-induced spontaneous radiation
Laboratori Nazionali di Frascati INFN（INFN 弗拉斯卡蒂国家实验室）；Centro Ricerche Enrico Fermi, Museo Storico della Fisica e Centro Studi e Ricerche ”Enrico Fermi”（恩里科·费米研究中心、物理历史博物馆及恩里科·费米研究与研究中心）；Wigner Research Center for Physics（维格纳物理学研究中心）；Eötvös Loránd University（罗兰大学）；IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei（霍里亚·胡利贝伊国家核物理与核工程研究所）
Wave function collapse models are considered as the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schrödinger equation, these models make predictions, differently from those of standard quantum mechanics, that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments and hence efficient protocols for this kind of experiments are highly needed. Here we provide a protocol that is able to probe the postulated collapse effe…
We propose a model to identify the quantum/classical boundary. The model introduces a spontaneous collapse of state superposition: $\frac{d}{dt} ρ_{ij} =-\frac{i}{\hbar}[H,ρ]_{ij}-ρ_{ij}/τ_{ij}$. Different from other collapse models, the collapsing scale $τ_{ij}$ here does not contain a universal parameter, but is specified by the two states $| i\rangle $ and $ | j\rangle$: If each state is {\em in principle} repeatedly readable (typically by a QND measurement), then $τ_{ij}$ is the {\em potentially} needed measuring time to discriminate the two states, and the collapse occurs spontaneously {\…
We present a concise outlook on future experimental tests of spontaneous wave function collapse models. We discuss tests based on force noise measurements in ultrasensitive mechanical systems, spontaneous heating in ultracold solid matter and atoms, matter-wave interferometry, and ultrahigh precision measurements.
