We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In practice, since photons and gravitons are ubiquitous and scatter from massive particles, dynamical collapses of the former will effectively induce collapses of the latter. In non-relativistic models in which particle number is conserved and interactions are modelled by classical potentials, massive systems can be modelled as collections of elementary massive particles bound by potentials, interacting with an environment of photons and gravitons. In this picture, although the photon and/or graviton collapse dynamics effectively localize massive systems, these collapses take the effective form of approximate measurements on the environment whose effect on the massive systems is indirect. We argue that these environmental collapse models, like standard mass-dependent spontaneous localisation models, may be consistent with quantum experiments on microscopic systems while predicting very rapid effective collapse of macroscopic massive systems, and hence a potential solution to the quantum measurement problem. However, the models considered here have different experimental signatures from standard mass-dependent spontaneous localisation models. For example, they predict no deviations from standard quantum interferometry for mesoscopic systems of massive particles isolated from a decohering environment, nor do they predict anomalous spontaneous emission of radiation from isolated matter of the type prediction by standard mass-dependent spontaneous localization models. New experiments and analyses are required to obtain empirical bounds on the decoherence rate in our models.
We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In practice, since photons and gravitons are ubiquitous and scatter from massive particles, dynamical collapses of the former will effectively induce collapses of the latter. In non-relativistic models in which particle number is conserved and interactions are modelled by classical potentials, massive systems can be modelled as collections of elementary massive particles bound by potentials, interacting with an environment of photons and gravitons. In this picture, although the photon and/or graviton collapse dynamics effectively localize massive systems, these collapses take the effective form of approximate measurements on the environment whose effect on the massive systems is indirect. We argue that these environmental collapse models, like standard mass-dependent spontaneous localisation models, may be consistent with quantum experiments on microscopic systems while predicting very rapid effective collapse of macroscopic massive systems, and hence a potential solution to the quantum measurement problem. However, the models considered here have different experimental signatures from standard mass-dependent spontaneous localisation models. For example, they predict no deviations from standard quantum interferometry for mesoscopic systems of massive particles isolated from a decohering environment, nor do they predict anomalous spontaneous emission of radiation from isolated matter of the type prediction by standard mass-dependent spontaneous localization models. New experiments and analyses are required to obtain empirical bounds on the decoherence rate in our models.
The basic strategy underlying models of spontaneous wave function collapse (collapse models) is to modify the Schrödinger equation by including nonlinear stochastic terms, which tend to localize wave functions in space in a dynamical manner. These terms have negligible effects on microscopic systems—therefore their quantum behaviour is practically preserved. On the other end, since the strength of these new terms scales with the mass of the system, they become dominant at the macroscopic level, making sure that wave functions of macro-objects are always well-localized in space. We will review these basic features. By changing the dynamics of quantum systems, collapse models make predictions, which are different from standard quantum mechanical predictions. Although they are difficult to detect, we discuss the most relevant scenarios, where such deviations can be observed.
An open problem in modern physics is why microscopic quantum objects can be at two places at once (i.e. a superposed quantum state) while macroscpoic classical object never show such a behaviour. Collapse models provides a quantitative answer for this problem and explain how macroscopic classical world emerges out of microscopic quantum world. A universal noise field is postulated in collapse models, inducing appropriate Brownian- motion corrections to standard quantum dynamics. The strength of collapse-driven Brownian fluctuations depend on: (i) the parameters characterizing the system (e.g., mass, size, density), and (ii) two phenomenological parameters defining the statistical properties of the collapse noise. The collapse-driven Brownian motion works such that microscopic systems behave quantum mechanically, while macroscopic objects are classical. At the intermediate mesocopic scale, collapse models predict deviations from standard quantum predictions. This issue has been subject of experimental tests. All experiments to date have been at the scales where collapse effects are negligible for all practical purposes. However, recent experimental progress in revealing quantum features of larger objects, increases the hope for testing at unprecedented scales where collapse models can be falsified. Current experiments are mainly focused on the preparation of macroscopic systems in a spatial quantum superposition state. The collapse effects would then manifest as loss of visibility in the observed inference pattern. However, one needs a quantum interference with single particles of mass ∼ 10 10 amu for a decisive test of collapse models. Creating such massive superpositionsis quite challenging, and beyond currectstate-of-the-art. Quite recently, an alternative approach has been proposed where the collapse manifests in the fluctuating properties of light interacting with the quantum system. The great advantage of this new approach is that here there is no need for the preparation of a quantum superposed state. It has been discussed that promising results can be revealed in the spectrum of light interacting with a radiation pressure-driven mechanical oscillator in a cavity optomechanics setting. Here, we review the theoretical modelling of the above optomechenical proposal. We discuss how collapse-driven Brownian motion modifies the spectrum. We quantify the collapse effect and explain how it depends on the parameters of the mechanical oscillator (e.g., mass, density, geometry).
Quantum mechanics exhibits a broad collection of theoretical results in complete agreement with experimental evidence. Besides showing unquestionable success in the description of isolated systems, it can be also successfully used to characterize non-isolated quantum system. In such a case, phenomena like dissipation, diffusion or decoherence. The theory of open quantum systems provides the framework where such features can be conveniently explained. \nThis thesis is about decoherence and collapse models. Albeit conceptually they are very far from each other, they both belong the framework of open quantum systems. Indeed, they consider systems interacting with an external entity: an environment for decoherence models, a noise for collapse models. Although the external influence has different origin, they can be described by similar dynamical equations and, to confirm or falsify them, the same experimental tests can be performed. \nThe quantum Brownian motion model can be considered the paradigm of decoherence models. We provide an exact and analytic equation for the time evolution of the operators and we show that the corresponding equation for the states is equivalent to well-known results in the literature. Our derivation allows to compute the time evolution of physically relevant quantities in a much easier way than previous formulations. Moreover, we are not bound to compute the time evolution of the state of the system, which in general is a complicated task. The explicit dependence on the initial state appears only in the initial expectation values and not in the dynamics. This makes possible the derivation of expectation values also for nontrivial states. \nAnother decoherence model we considered is a recently proposed model, based on the mass-energy equivalence. The model describes a decoherence source acting universally on every system whose superposition is extended on positions experiencing different gravitational potentials. We studied the conditions under which this mechanism becomes the dominant decoherence effect in typical interferometric experiments. We show that current experiments are off by several orders of magnitude. New ideas are needed to achieve the necessary requirements. \nThe second part of this thesis concerns collapse models, in particular the Continuous Spontaneous Localization (CSL) model. We focus on experimental tests that can probe it. In this respect, experiments can be grouped in two classes: interferometric tests and non-interferometric ones. The first class includes those experiments, which directly create and detect quantum superpositions of the center of mass of massive systems. The strongest bounds on the CSL parameters come from the second class of non-interferometric experiments, which are sensitive to small position displacements and detect CSL-induced diffusion in position. \nWe investigate how we can benefit from the non-interferometric perspective given by optomechanical setups, which have reached high sensitivities as force and position sensors. Three examples are considered.\nFirst, we compute the upper bounds on the CSL parameters, which can be inferred by the gravitational wave detectors LIGO, LISA Pathfinder and AURIGA.\nSecond, we report new results from an experiment based on a high-quality cantilever cooled to millikelvin temperature. High accuracy measurements of the cantilever thermal fluctuations reveal a nonthermal force noise of unknown origin. This excess noise is compatible with the CSL heating predicted by Adler. Several physical mechanisms able to explain the observed noise have been ruled out.\nThird, we propose an unattempted non-interferometric test aimed to investigate the still unexplored region of the CSL parameter space. Our proposal relies on torsional degrees of freedom rather than the usual vibrational ones. We believe that the test that has been put forward here, will eventually probe the unexplored CSL parameter space.
Spontaneous collapse models have been proposed as a possible realist solution of the quantum measurement problem. They assume that the standard unitary evolution is valid only in the microscopic limit, with stochastic corrections leading to a dynamical reduction of the wave function at macroscopic level. A remarkable feature of collapse models is that, unlike interpretations of quantum mechanics, they predict departures from standard theory that can be experimentally tested. A common prediction is a violation of energy conservation, which manifests as an universal force noise acting on mechanical systems. Here, we will discuss recent bounds on collapse models set by mechanical experiments, focusing on ultracold cantilevers and gravitational wave detectors. First notable results are a partial exclusion of the CSL parameters proposed by Adler and a full exclusion of an early model based on quantum gravity arguments.
Some collapse models proposed that gravitational effects cause the instability of mass distribution superpositions, leading to wave function collapse. In this paper, we utilize the quantum Boltzmann equation (QBE) to analyze the behavior of a fermion in a spatial superposition under graviton emission. We introduce a quantitative measure that links the stability of the superposition to the spatial separation, particle mass, and gravitational coupling. By examining the collision term in the QBE, we derive the decoherence rate and show how it depends on these parameters. Our results provide a detailed framework for understanding gravity induced decoherence, bridging the gap between quantum field theory and collapse models. We also discuss the implications of these findings for experimental tests of gravitationally induced wave function collapse and the broader class of collapse models known as dissipative continuous spontaneous localization (CSL) model.
Spontaneous collapse models aim to solve the long-standing measurement problem in quantum mechanics by modifying the theory's dynamics to include objective wave function collapses. These collapses occur randomly in space, bridging the gap between quantum and classical behavior. A central feature of these models is their dependence on mass density, which directly influences how and when collapse events occur. In this work, we explore a generalized framework in which the collapse dynamics depend on arbitrary functions of the mass density, extending previous models. We analyze the theoretical consistency of these generalizations, investigate their predictions, and compare them with experimental data. Our findings show that only a limited range of mass-dependence functions are viable, with significant implications for the future development and empirical testability of collapse-based models. Importantly, they also indicate that a well-justified model denoted here as PSL shows much more resilience to experimental falsification than standard collapse models.