This work addresses the problem of causation in physics, as for quantum fields, the fundamental theory describing elementary particle physics. Three basic elements are used as methodological concepts: a) the notion of mass-point and the notion of a field (as quantum field) describing a physical system (both concepts are used in physics to characterize elementary particles); b) the notion of state of a mass-point and of a field; c) the notion of causality among states, which are defined by symmetries. Then time and space changes include a space-like causality. These elements are discussed by using the definition of measurement, associated with the notion of symmetry. The derived results give rise to a generalization of the concept of causality, since a mechanical system includes mass-points, fields, and systems composed of mass-points and fields, together. In addition, conserved quantities, founding some causality theories, are generalized due to the notion of symmetry associated with causality.
This work addresses the problem of causation in physics, as for quantum fields, the fundamental theory describing elementary particle physics. Three basic elements are used as methodological concepts: a) the notion of mass-point and the notion of a field (as quantum field) describing a physical system (both concepts are used in physics to characterize elementary particles); b) the notion of state of a mass-point and of a field; c) the notion of causality among states, which are defined by symmetries. Then time and space changes include a space-like causality. These elements are discussed by using the definition of measurement, associated with the notion of symmetry. The derived results give rise to a generalization of the concept of causality, since a mechanical system includes mass-points, fields, and systems composed of mass-points and fields, together. In addition, conserved quantities, founding some causality theories, are generalized due to the notion of symmetry associated with causality.
In this dissertation, I will argue that quantum field theory can be interpreted as a description of causal interactions. I will first discuss previous theories of physical causation, and come to the conclusion that they are inapplicable in quantum field theory. As a consequence, I will start to develop a new theory of causation by first analysing the concept ‘causation’ into the most basic and widely shared intuitions, in order to find out later whether these intuitions can be reduced to physics. I will then have a closer look on the intuition that causation is a directed relation, which is commonly regarded as incompatible with the symmetries of physics. I will present a new argument to the effect that causation and quantum field theory are compatible with respect to the directionality of causation. After that, I will analyse the theoretical description of interactions in quantum field theory, and in particular group structure, locality and local conservation laws will crystallise as the central concepts that a causal interpretation might be based on. Subsequently, I will discuss and present replies to what I believe are the most relevant objections to a causal interpretation of physics, namely, Haag’s theorem, the measurement problem and entanglement. In the final chapter of this dissertation, I will conjoin the results of the previous chapters to a new theory of causation for quantum field theory. The main result will be that a causal process is a quantum field theoretical interaction, i.e., the exchange of energy from an initial to a final state via a force.
Philosophical analyses of causation take many forms but one major difficulty they all aim to address is that of the spatiotemporal continuity between causes and their effects. Bertrand Russell in 1913 brought the problem to its most transparent form and made it a case against the notion of causation in physics. The issue highlighted in Russell's argument is that of temporal contiguity between cause and effect. This tension arises from the imposition of a spectrum of discrete events occupying spacetime points upon a background of spacetime continuum. An immediate and natural solution is to superpose instead spatiotemporally continuous entities, or processes, on the spacetime continuum. This is indeed the process view of physical causation advocated by Wesley Salmon and Phil Dowe. This view takes the continuous trajectories of physical objects (worldlines) as the causal connection whereby causal influences in the form of conserved quantities are transported amongst events. Because of their reliance on spatiotemporal continuity, these theories have difficulty when confronted with the discontinuous processes in the quantum domain. This thesis is concerned with process theories. It has two parts. The first part introduces and criticizes these theories, which leads to my proposal of the History Conserved Quantity Theory with Transmission. The second part considers the extension of the idea of causal processes to quantum physics. I show how a probability distribution generated by the Schrodinger wavefunction can be regarded as a conserved quantity that makes the spacetime evolution of the wavefunction a quantum causal process. However, there are conceptual problems in the interpretation of the wavefunction, chiefly to do, as I shall argue, with the difference in the behaviours of probabilistic potentials between quantum and classical physics. I propose in the final chapter, the Feynman Path Integral formulation of quantum mechanics (with the Feynman histories) as an alternative approach to incorporating the probabilistic potentials in quantum physics. This account of how to introduce causal processes in quantum mechanics fares better, I claim, than the previous one in dealing with the situational aspect of quantum phenomena that requires the consideration of events at more than one time.
Quantum mechanics has achieved unparalleled success as an operational theory, describing a wide range of experiments to remarkable accuracy. However, the physical foundations on which it rests remain as puzzling as they were a century ago, and a concise statement of the physical principles that underlie quantum mechanics is still outstanding. One promising approach holds that these principles should be formulated in terms of information, since many of the counter-intuitive effects in quantum theory concern questions such as what one can know about a quantum system and how the information encoded therein can be processed and distributed between parties. Another challenging feature of quantum theory is its incompatibility with the other cornerstone of modern physics, general relativity. In order to reconcile the two, one must identify and retain only the essential concepts and principles of each theory, and in the case of general relativity, causality has been identified as such a concept. This raises the question of how our classical understanding of causality must change when quantum theory is taken into account. In order to address these questions about information, knowledge and causality, I turn to the framework of causal models. In classical statistics, causal models explain the relations among a set of variables in terms of causal influences, which makes them a powerful tool for structuring our knowledge about complex systems and developing strategies for interacting with them. More importantly, the framework provides the conceptual underpinnings and mathematical methods for addressing questions about causation, information and knowledge in a rigorous manner. In this thesis, I develop a version of the classical causal models framework that is compatible with quantum theory and explore its physical implications. \n \n \nA first step is to define quantum versions of fundamental elements such as variables, conditionals and belief propagation rules. This allows one to consider the question of what one can come to know about a quantum variable from the point of view of causal modelling. The conditionals relating quantum variables are found to have a richer structure than their classical counterparts, which can be exploited for the task of discerning causal relations given limited data -- a central problem in classical causal modelling. The mathematical properties of quantum conditionals also establish a correspondence between various classes of two-party correlations, such as bound and distillable entanglement, and the types of causal structures that can give rise to them, which may become a useful tool for entanglement theory and quantum information processing. In the context of open quantum systems dynamics, quantum causal models provide a clear physical explanation of not completely positive maps and, more broadly, of non-Markovian quantum dynamics. Finally, I consider the possibility of non-classical effects in the way that different causal mechanisms are combined -- that is, non-classical causal structures. For the simple case of two causally ordered variables, I propose indicators that witness different classes of combinations of causal mechanisms, including a non-classical mixture, and describe an experiment realizing examples of the different classes. \n \n \nAs these results illustrate, the framework of quantum causal models provides both greater conceptual clarity and a comprehensive mathematical formalism for studying a diverse set of problems, ranging from foundational questions to applications in open systems dynamics and the exploration of non-classical causal structures, which are likely to feature in a future theory of quantum gravity. The material presented in this thesis is intended as a foundation and inspiration for further applications of quantum causal models.
This chapter focuses specifically on the notion of causation. Unless a causal interpretation can be given of quantum mechanics, there is a fundamental discontinuity between the quantum realm and everything else in the world. The quantum-theoretical dualism of waves and particles makes the same entity appear both as matter and as force. There are of course challenges to other basic ontological categories that come from quantum physics, such as to notions of continuity and identity. Both in philosophy and physics, there is a frequent assumption that causation is the provider or vehicle of determinism, via causal necessitation. The indeterminism of quantum physics leaves people with a more practical concern about causation. A feature of causation that makes predictions fallible is that causal processes are extremely sensitive to a change in context. The genuine interaction of multiple factors should therefore be seen as a symptom of causation rather than as something that needs to be analysed away by theoretical abstraction.
The author's attempt to construct a local causal model of quantum theory (QT) that includes quantum field theory (QFT) resulted in the identification of "quantum objects" as the elementary units of causality and locality. Quantum objects are collections of particles (including single particles) whose collective dynamics and measurement results can only be described by the laws of QT and QFT. Local causal models of quantum objects' internal dynamics are not possible if a locality is understood as a space-point locality. Within quantum objects, state transitions may occur which instantly affect the whole quantum object. The identification of quantum objects as the elementary units of causality and locality has two primary implications for a causal model of quantum objects: (1) quantum objects run autonomously with system-state update frequencies based on their local proper times and with either no or minimal dependency on external parameters. (2) The laws of physics that describe global (but relativistic) interrelationships must be translated to a causal model of interactions between quantum objects and interactions between quantum objects and the space.
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is represented by a pure state wavefunction contained in a factorisable Hilbert space of enormous dimension, and where this statevector is developed by successive applications of operators that correspond to unitary rotations and Hermitian tests. Moreover, because by definition the Universe contains everything, it is argued that these operators must be chosen self-referentially; the overall dynamics of the system is envisaged to be analogous to a gigantic, self-governing, quantum computation. The issue of how the Universe could choose these operators without requiring or referring to a fictitious external observer is addressed. The processes by which conventional physics might be recovered from this fundamental, mathematical and global description of reality are particularly investigated. Specifically, it is demonstrated that by considering the changing properties, separabilities and factorisations of both the state and the operators as the Universe proceeds though a sequence of discrete computations, familiar notions such as classical distinguishability, particle physics, space, time, special relativity and endo-physical experiments can all begin to emerge from the proposed picture. A pregeometric vision of cosmology is therefore discussed, with all of physics ultimately arising from the relationships occurring between the elements of the underlying mathematical structure.