Collapse models are posited as a resolution to the measurement problem. On one level, they offer a clear, simple and testable resolution to an age-old problem. Yet at the same time, they raise many new questions of their own - what is the origin of the putative noise field? What are its properties, and why ought it couple to wavefunctions in this particular way, inducing collapse in some analogue of the position basis? How might these models be extended to the realm of relativity without incurring catastrophe? What sort of image of the world do they deliver? In this thesis we begin with a philosophical exploration of collapse theories. We examine, in detail, the relationship between stochastic noise fields and the evolution of the wavefunction - shedding light both on the solutions offered by collapse models and the new issues which they raise. We discuss the possibilities for constructing an ontology based on these theories, and look at possible implications for the arrow of time and the meaning of causation. This in turn motivates the development of protocols for experiments which might be capable of probing these models; to new degrees in some senses, and in new forms in others. We develop a comprehensive theoretical model of a levitated nanosphere held in an electric quadrupole trap, and find the limits to which this can probe the characteristic collapse rate $\lambda$ and correlation length $r$ of collapse models. Further, we develop a novel treatment of this scenario in the style of open quantum systems, and show that such an apparatus can constitute a general quantum spectrometer, capable of characterising arbitrary correlation functions for a noise source coupled to the oscillator - whether that noise be invoked by collapse models or other, more mundane sources. Finally, we utilise numerical simulations of trap dynamics to demonstrate the capabilities of electronic feedback cooling - showing that quantum states ought to be achievable without the use of optics. This work is motivated by a desire to understand the world, and specifically to address some of the paradoxes which arise when we try to use quantum mechanics to do so. We have aimed to follow what we see as best practice in physics - from a motivation within philosophy, to the development of theory capable of meeting that philosophy, to the design of experiments which would be able to speak to the relationship between that theory and the world.
Collapse models are posited as a resolution to the measurement problem. On one level, they offer a clear, simple and testable resolution to an age-old problem. Yet at the same time, they raise many new questions of their own - what is the origin of the putative noise field? What are its properties, and why ought it couple to wavefunctions in this particular way, inducing collapse in some analogue of the position basis? How might these models be extended to the realm of relativity without incurring catastrophe? What sort of image of the world do they deliver? In this thesis we begin with a philosophical exploration of collapse theories. We examine, in detail, the relationship between stochastic noise fields and the evolution of the wavefunction - shedding light both on the solutions offered by collapse models and the new issues which they raise. We discuss the possibilities for constructing an ontology based on these theories, and look at possible implications for the arrow of time and the meaning of causation. This in turn motivates the development of protocols for experiments which might be capable of probing these models; to new degrees in some senses, and in new forms in others. We develop a comprehensive theoretical model of a levitated nanosphere held in an electric quadrupole trap, and find the limits to which this can probe the characteristic collapse rate λ and correlation length r of collapse models. Further, we develop a novel treatment of this scenario in the style of open quantum systems, and show that such an apparatus can constitute a general quantum spectrometer, capable of characterising arbitrary correlation functions for a noise source coupled to the oscillator - whether that noise be invoked by collapse models or other, more mundane sources. Finally, we utilise numerical simulations of trap dynamics to demonstrate the capabilities of electronic feedback cooling - showing that quantum states ought to be achievable without the use of optics. This work is motivated by a desire to understand the world, and specifically to address some of the paradoxes which arise when we try to use quantum mechanics to do so. We have aimed to follow what we see as best practice in physics - from a motivation within philosophy, to the development of theory capable of meeting that philosophy, to the design of experiments which would be able to speak to the relationship between that theory and the world.
This is the first single volume about the collapse theories of quantum mechanics, which is becoming a very active field of research in both physics and philosophy. In standard quantum mechanics, it is postulated that when the wave function of a quantum system is measured, it no longer follows the Schrödinger equation, but instantaneously and randomly collapses to one of the wave functions that correspond to definite measurement results. However, why and how a definite measurement result appears is unknown. A promising solution to this problem are collapse theories in which the collapse of the wave function is spontaneous and dynamical. Chapters written by distinguished physicists and philosophers of physics discuss the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse. This is an invaluable resource for students and researchers interested in the philosophy of physics and foundations of quantum mechanics.
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.
Operatoric Research CorpusStudies in World-Formation Section I Ontology and Physics Volume 2 The Ontological Limits of Physical ExplanationMeasurement, Collapse and Boundary Phenomena in Quantum Physics This volume brings together a series of contributions on the ontology of fundamental problems in physics, in particular the measurement problem of quantum mechanics, the collapse of the wave function, the relationship between quantum mechanics and relativity theory, as well as boundary phenomena such as black holes, renormalization, and vacuum energy. The point of departure of these investigations is the thesis that numerous paradoxes of modern physics do not primarily result from insufficient physical theories, but from a categorical misaddressing. Transitions that concern the very conditions of world stability—especially the transition from possibility to facticity—are often interpreted as dynamical processes within an already stabilized world. This gives rise to explanatory programs that attempt to bridge this boundary by means of additional mechanisms, ontologies, or informational structures. The texts collected in this volume pursue an alternative strategy. They understand the so-called collapse of the wave function not as a physical process, but as an irreversible constriction of a space of possibility through which objectivity and the direction of time first emerge at all. The concept of indimergence designates the boundary act in which possibility passes into facticity without itself being describable as an event within the world. On the basis of this determination, central approaches in the foundations of quantum mechanics—particularly dynamical collapse models, Many-Worlds interpretations, and information-theoretic ontologies—are comparatively analyzed. It becomes evident that, despite their differences, they share a common presupposition: the assumption that the transition from possibility to facticity must itself be explicable within physical description. The contributions in this volume instead propose to read the measurement problem and related paradoxes as indications of structural limits of physical description. From this perspective, other fundamental problems—such as the tension between quantum mechanics and relativity theory, the information paradoxes of black holes, or divergences in field theory—no longer appear primarily as unsolved technical puzzles, but as boundary phenomena of world formation itself. The volume therefore does not present itself as an alternative physical theory, but as an ontological clarification of the conditions under which physical theories are able to describe a world at all.
We present the quantum measurement problem as a serious physics problem. Serious because without a resolution, quantum theory is not complete, as it does not tell how one should - in principle - perform measurements. It is physical in the sense that the solution will bring new physics, i.e. new testable predictions, hence it is not merely a matter of interpretation of a frozen formalism. I argue that the two popular ways around the measurement problem, many-worlds and Bohmian-like mechanics, do, de facto, introduce effective collapses when "I" interact with the quantum system. Hence, surprisingly, in many-worlds and Bohmian mechanics, the "I" plays a more active role than in alternative models, like e.g. collapse models. Finally, I argue that either there are several kinds of stuffs out there, i.e. physical dualism, some stuff that respects the superposition principle and some that doesn't, or there are special configurations of atoms and photons for which the superposition principle breaks down. Or, and this I argue is the most promising, the dynamics has to be modified, i.e. in the form of a stochastic Schrödinger equation.
Wave-function collapse models are considered to be the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models (different from standard quantum mechanics) predict 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 these kinds of experiments are greatly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-P\'erot cavity. We show that the collapse noise results in a large reduction of the steady-state entanglement, and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to determine unambiguously the effect of these models.
This paper is an in depth implementation of the proposal (Ellis 2012 Ann. Phys. NY 327 1890–932) that the quantum measurement issue can be resolved by carefully looking at top-down contextual effects within realistic measurement contexts. The specific setup of the measurement apparatus determines the possible events that can take place. The interaction of local heat baths with a quantum system plays a key role in the process. In contrast to the usual attempts to explain quantum measurement by decoherence, we argue that the heat bath follows unitary time evolution only over limited length and time scales (Drossel 2017 His. Phil. Sci. B 58 12–21) and thus leads to localization and stochastic dynamics of quantum particles that interact with it. We show furthermore that a theory that describes all the steps from the initial arrival of the quantum particle to the final pointer deflection must use elements from classical physics. This proposal also provides a contextual answer to the puzzle of the origin of the arrow of time when quantum measurements take place: it derives from the cosmological direction of time. Overall, our proposal is for contextual wavefunction collapse.