One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schroedinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini, and Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focussing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.
In the DP-model, gravity-related spontaneous wave function collapses suppress undesirable Schrödinger Cat states. We derive the equations of the model for the hydrodynamic-elastic (acoustic) modes in a bulk. Two particular features are discussed: the universal dominance of spontaneous collapses at large wavelengths, and the reduction of spontaneous heating by a slight refinement of the DP-model.
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.
On the basis of a proposed model of wave function collapse, we investigate spontaneous localization of a quantum state. The model is similar to the Ghirardi-Rimini-Weber model, while we postulate the localization functions to depend on the quantum state to suffer collapse. According to the model, dual dynamics in quantum mechanics, deterministic and stochastic time evolution, are algorithmically implemented in tandem. After discussing the physical implications of the model qualitatively, we present numerical results for one-dimensional systems by way of example.
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…
A brief review is given of the Continuous Spontaneous Localization (CSL) model in which a classical field interacts with quantized particles to cause dynamical wavefunction collapse. One of the model's predictions is that particles "spontaneously" gain energy at a slow rate. When applied to the excitation of a nucleon in a Ge nucleus, it is shown how a limit on the relative collapse rates of neutron and proton could be obtained, and a rough estimate is made from data. When applied to the spontaneous excitation of 1s electrons in Ge, by a more detailed analysis of more accurate data than previo…
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 propose a modified dynamics of quantum mechanics, in which classical mechanics of a point mass derives intrinsically in a massive limit of a single-particle model. On the premise that a position basis plays a special role in wavefunction collapse, we deduce to formalize spontaneous localization of wavefunction on the analogy drawn from thermodynamics, in which a characteristic energy scale and a time scale are introduced to separate quantum and classical regimes.
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…
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 Gold…
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 …
We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (free particle case). We compute the explicit expression of the Green's function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time evolution of average quantities, such as the mean position, momentum and energy. We eventually specializ…
A more detailed analysis of the measurement problem continues to support the position taken by Shimony and the author that collapse of the wave function takes place in an objective manner in the rhodopsin molecule of the retina. This casts further doubts on the theories involving a spontaneous localization collapse process or a no-collapse decoherence process taking place in the visual cortex in a subjective fashion. The possibility is then raised, as per Anandan, as to whether the solution of the measurement problem in quantum theory allows one to address the problem of quantizing gravitation…
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…
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.
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…
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…
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…
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…
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）
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.
The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.
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 literatu…
Some versions of quantum theory treat wave function collapse as a fundamental physical phenomenon to be described by explicit laws. One motivation is to find a consistent unification of quantum theory and gravity, in which collapse prevents superpositions of space-times from developing. Another is to invoke collapse to explain our perception of definite measurement outcomes. Combining these motivations while avoiding two different collapse postulates seems to require that perceptibly different physical states necessarily create significantly different mass distributions in our organs of percep…
We present a spontaneous collapse model of a field theory on a 1+1 null lattice, in which the causal structure of the lattice plays a central role. Issues such as ``locality,'' ``non-locality'' and superluminal signaling are addressed in the context of the model which has the virtue of extreme simplicity. The formalism of the model is related to that of the consistent histories approach to quantum mechanics.
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…
We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at which the collapse of the state vector occurs, the reduction and delocalization times, and the reduction probabilities; it also allows to quantify the effect that an Hamiltonian which does not commute with the reducing terms has on the collapse mechanism. We also give a clear picture of the transition from the "microscopic" regime (when the noise terms are weak …
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…
We compute the effect of collapse models on neutrino oscillations. The effect of the collapse is to modify the evolution of the `spatial' part of the wave function, which indirectly amounts to a change on the flavor components. In many respects, this phenomenon is similar to neutrino propagation through matter. For the analysis we use the mass proportional CSL model, and perform the calculation to second order perturbation theory. As we will show, the CSL prediction is very small - mainly due to the very small mass of neutrinos - and practically undetectable.
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.
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 collap…
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…
The Continuous Spontaneous Localization (CSL) model predicts a tiny break of energy conservation via a weak stochastic force acting on physical systems, which triggers the collapse of the wave function. Mechanical oscillators are a natural way to test such a force; in particular levitated micro-mechanical oscillator has been recently proposed to be an ideal system. We report a proof-of-principle experiment with a micro-oscillator generated by a micro-sphere diamagnetically levitated in a magneto-gravitational trap under high vacuum. Due to the ultra-low mechanical dissipation, the oscillator p…
Selected issues of the concept of spontaneous collapse are discussed, with the emphasis on the gravity-related model. We point out that without spontaneous collapses the Schrödinger cat states would macroscopically violate the standard conservation laws even in the presence of environmental noise. We prove that the collapse time of condensed matter c.o.m. superpositions is not sensitive to the natural uncertainty of the nuclear locations whereas we formulate the conjecture that superfluid He may show an anomalous low rate of spontaneous collapse compared to common condensed matter.
Quantum experiments with nanomechanical oscillators are regarded as a testbed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macro-scale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes f…
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 Schrodinger 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…
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…
