La thèse vise à montrer que la cohérence de l’interprétation instrumentaliste de la mécaniquequantique (sur laquelle les reconstructions logiques de la théorie, d’inspiration pragmatiste, s’appuient) ne peut pas être défendue sans remettre en cause la sémantique extensionnelle utilisée en logique classique. J’examine en particulier les arguments misen avant par Niels Bohr, en montrant que son analyse physique du processus de mesureest insuffisante pour assurer la cohérence de l’interprétation conditionnelle des probabilités quantiques qu’il adopte. Au lieu d’essayer de ‘compléter’ l’approche de Bohrpar un compte rendu plus exhaustif des processus physiques (telle la décohérence) quijouent un rôle dans l’observation, je suggère que le problème de la mesure découle d’unethéorie de la signification inadéquate. Je discute l’intérêt et les limites de la critiquebohrienne des présupposés représentationalistes inhérents à la description classique desphénomènes, et je conclus en formulant l’hypothèse que l’adoption d’une sémantiqueinférentialiste permettrait d’envisager à la fois la dissolution du problème de la mesureet la justification a priori des traits structuraux des probabilités quantiques (comme étantl’expression des relations conceptuelles présupposées par tout langage qui doit incluredes énoncés objectifs). / The dissertation purports to show that the consistency of the instrumentalist interpretationof quantum mechanics (upon which the logico-operational reconstructions of thetheory rest) cannot be defended without relinquishing the extensional semantic frameworkof classical logic. I examine in particular Niels Bohr’s argument, arguing that hisphysical analysis of measurement is insufficient to establish the coherence of the conditionalconstrual of quantum probabilities that he advocates. Rather than attemptingto ‘complete’ Bohr’s approach by means of a more sophisticated and comprehensiveaccount of the physical processes involved in the act of observation (e.g., decoherence),I suggest that the measurement problem should be viewed as the outgrowth of an inadequatetheory of meaning. I discuss, and point out some limitations of, Bohr’s ownpioneering critique of the representational assumptions inherent to the classical accountof phenomena, and I conclude by suggesting that the endorsement of an inferentialistsemantic approach would not only contribute to defusing the measurement problem, butmight also enable the a priori justification of the structural features of quantum probability(in terms of the conceptual relations presupposed by any language which allowsfor objective assertions).

Quantum mechanics stands unmatched in its experimental success. However, significant gaps remain in the quantum description of nature, notably the absence of a satisfactory integration of gravity and an unresolved measurement problem. This thesis investigates a potential approach to resolving these issues known as superdeterminism. A superdeterministic theory is one which violates an assumption called Statistical Independence. Although this approach has historically been readily dismissed as harmful to science, superdeterminism has recently gained traction as researchers address these criticisms and explore its implications more deeply. This thesis aims to provide a unified resource on superdeterminism, compiling progress, identifying current gaps, and suggesting future research directions. We establish criteria for evaluating superdeterministic theories and apply these to existing models. Our analysis focuses on two main approaches: the Donadi-Hossenfelder path integral approach and Palmer's Invariant Set Theory. The path integral approach appears promising, particularly if a suitable measure for the "quantumness" of states can be developed. Invariant Set Theory provides a unique, geometric framework but is still too early in its development to show clear potential. Our findings underscore the early stage of superdeterminism research and the need for further theoretical development and empirical testing. By providing a structured framework for future work, this thesis seeks to advance the understanding and application of superdeterminism in addressing the foundational issues in quantum mechanics.

Cette thèse est consacrée à l’étude des trajectoires quantiques issues de la théorie desmesures continues en mécanique quantique non relativiste. On y présente de nouveaux résultatsthéoriques ainsi que des exemples d’applications. Sur le front théorique, on étudie principalementla limite de mesure «forte» dans laquelle on met en évidence l’émergence de sauts quantiques etd’échardes quantiques, deux phénomènes dont on précise la statistique. Hors de la limite forte, onpropose une méthode d’extraction optimale d’information pour un registre de qubits. Sur le frontdes applications, on introduit une méthode originale de contrôle utilisant l’intensité de la mesurecomme unique variable et on explique la transition balistique-diffusif dans les marches aléatoiresquantiques ouvertes; deux sous produits de l’étude théorique préalable des situations de mesureforte. On s’intéresse aussi au problème de la gravité semi-classique et montre que la théorie desmesures continues peut permettre d’en construire un modèle cohérent à la limite newtonienne. Onsuggère enfin quelques extensions possibles de la théorie à l’estimation a posteriori et d’éventuellesgénéralisations des résultats théoriques à des situations de mesures répétées discrètes. Dans laprésentation des résultats, l’accent est mis davantage sur l’explicitation des liens entre les multiplespoints de vue possibles sur les trajectoires quantiques (parallèles avec la théorie classique du filtrageet les modèles de collapse objectif utilisés dans les fondements) que sur la rigueur mathématique. / This thesis is devoted to the study of the quantum trajectories obtained from thetheory of continuous measurement in non relativistic quantum mechanics. New theoretical resultsas well as examples of applications are presented. On the theoretical front, we study mostly thelimit of «strong» measurement where we put forward the emergence of quantum jumps and quantumspikes, two phenomena we characterize in detail. Out of the strong measurement limit, weinvestigate a method to extract information from a register of qubits optimally. On the applicationfront, we introduce an original method to control quantum systems exploiting only the freedomof changing the measurement intensity and we explain the transition between a ballistic and adiffusive behavior in open quantum random walks; two byproduct of the theoretical study of thestrong measurement regime. We further study the problem of semi-classical gravity and show thatcontinuous measurement theory allows to construct a consistent model in the Newtonian regime.We eventually suggest possible extensions of the formalism to a posteriori estimation and hint atgeneralizations of the results for the strong measurement limit in the wider context of discreterepeated measurements. In the course of our presentation, we emphasize the link with other approachesto the theory of continuous measurement (parallels with stochastic filtering and collapsemodels in foundations) rather than aim for mathematical rigor.

I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level (purportedly more accurate and encompassing) model to that of the high-level (purportedly less accurate and encompassing) model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.

We focus on the Tensor Product Structure (TPS) of the Hilbert space and the fact that a choice in the TPS has an impact on the representation of the studied quantum system. We define the measurement problem in quantum mechanics and present some theories about quantum mechanics, each of them highlighting a different approach to quantum measurements. Then, a new approach to quantum measurement is presented by considering it as a change in the Tensor Product Structure of the Hilbert space associated with the description of a system. The system is made of a physical quantum system entangled with a measurement device. The description of the system changes to a new one where there is no entanglement anymore between the physical system and the measurement apparatus. The change in the TPS is performed using a global unitary transformation and more precisely by diagonalizing the density matrix of the system using unitary matrices. Four sets of matrices are obtained, each of them diagonalizing the density matrix in a different way for our toy model made of 2 qubits. Then, we want to recover Born’s rule directly from the diagonalizing matrices by measuring the size of their sets using Haar measure. We have not been able to conclude this program, but we outline what is expected to happen such that standard probabilities can be recovered.

In this review study, we ask ourselves if decoherence theory can solve the problems of measurement in quantum mechanics. After an introduction to decoherence theory, we present the problem of preferred basis, the problem of non-observability of interference and the problem of definite outcomes. We present Zurek's theory of environment induced superselection rules and find that the problem of preferred basis and the problem of non-observability of interference can be solved through decoherence theory, but not the problem of outcomes, if we accept the eigenstate-eigenvalue link and the Born statistical interpretation. We reveal that these two concepts are essential in the Copenhagen interpretations of quantum mechanics, and give an account for von Neumann's and Wigner's conscious collapse interpretation as well as a detailed description of Bohr's and Heisenberg's interpretation. We discuss how Bohr's and Heisenberg's interpretation relates to decoherence with a special emphasis on the irreducibility of classical concepts as interpreted by Don Howard. During the discussion, we critique Wigner's use of the word "consciousness" as opposed to von Neumann's use, as well as Howard's decisively ontological approach to Bohr through an antithetical Kantian approach. We conclude by stating that decoherence theory cannot decisively solve the problem of definite outcomes of quantum mechanics, even when considering it in relation to the Copenhagen interpretation.