The neutral pion experiment and the two-slit experiments pose difficulties for the thesis that causality implies explanation. There are various options available. One option is to hold that the "causality implies explanation" thesis does hold for relations between quantum phenomena, provided that quantum phenomena are identified with the results of measurements. A second option is to retain the "causality implies explanation" thesis by locating causal relatedness at a deeper level of interaction. In third option, causal relatedness is regularity between states of a physical system. A fourth option is to reevaluate the "causality implies explanation" thesis on some alternative theory about causal relatedness. A fifth option is to follow the lead of Niels Bohr and examine the limitations placed on causal explanation by investigations of the quantum realm. Bohr declared that all knowledge presents itself within a conceptual framework adapted to account for previous experience and any such frame may prove to be too narrow to comprehend new experience.
The neutral pion experiment and the two-slit experiments pose difficulties for the thesis that causality implies explanation. There are various options available. One option is to hold that the "causality implies explanation" thesis does hold for relations between quantum phenomena, provided that quantum phenomena are identified with the results of measurements. A second option is to retain the "causality implies explanation" thesis by locating causal relatedness at a deeper level of interaction. In third option, causal relatedness is regularity between states of a physical system. A fourth option is to reevaluate the "causality implies explanation" thesis on some alternative theory about causal relatedness. A fifth option is to follow the lead of Niels Bohr and examine the limitations placed on causal explanation by investigations of the quantum realm. Bohr declared that all knowledge presents itself within a conceptual framework adapted to account for previous experience and any such frame may prove to be too narrow to comprehend new experience.
In 1935, Einstein, Podolsky, and Rosen (EPR) argued that the Copenhagen interpretation of the quantum realm is incomplete. Moreover, they maintained that it is based on an unacceptable interpretation of physical reality. David Bohm revised the EPR thought experiment by focusing on spin determination as a state variable. Consider the creation of a pair of electrons by the spontaneous decay of a neutral pion. This is a physical process whose existence has been established. The spin of the pion before decay is zero. Consequently, the sum of the spins of the electrons also must be zero, given that spin is conserved in nuclear reactions. Analysis of the two-slit experiments reveals a failure of the causality-explanation relationship. The interference effect produced when no detecting devices are present at the two slits is no longer present. It would seem that detecting the passage of individual electrons through the slits destroys the wave-like behavior of the electrons.
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.
The framework of causal models is ideally suited to formalizing certain conceptual problems in quantum the-ory, and conversely, a variety of tools developed by physicists studying the foundations of quantum theory have applications for causal inference. This talk reviews some of the connections between the two fields. In partic-ular, it is shown that certain correlations predicted by quantum theory and observed experimentally cannot be explained by any causal model while respecting the core principles of causal discovery algorithms. Nonetheless, it is argued that by understanding quantum theory as an innovation to the theory of Bayesian inference, one can introduce a quantum generalization of the notion of a causal model and salvage a causal explanation of these cor-relations without fine-tuning. Furthermore, experiments exhibiting certain quantum features, namely, coherence and entanglement, enable solutions to causal inference problems that are intractable classically. In particular, while passive observation of a pair of variables cannot determine the causal relation that holds between them according to classical physics, this is not the case in quantum physics. In other words, according to quantum theory, certain kinds of correlation do imply causation. The results of a quantum-optical experiment confirming these predictions will be presented. This talk is based on the work described in Refs. [1] and [2].
The regularity-between-states view is a viable interpretation of causal relatedness for systems discussed in classical physics. Ambiguities arose, however, upon application of this view to quantum mechanical systems. The sketch of this theory is based primarily on the work of Niels Bohr and Werner Heisenberg. Heisenberg pointed out that applications of the quantum theory involve translations from a level of language in which observations are recorded, into a theoretical level, and back again. A quantum mechanical interpretation of an experiment typically is a three-stage process: translation of an initial experimental situation into a probability function, mathematical analysis of the variation of this function with time, and translation of the results of calculation into a prediction of the results of a new measurement to be made of the system. The principle of complementarity stipulates that pictorial-level interpretations of quantum phenomena in wave language and particle language are of equivalent importance.
Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a reimagining of what fundamental reality, or “ontology”, could look like. This thesis examines different ontological features in light of the success of quantum theory, what it requires, and what it rules out. While these investigations are primarily foundational, they also have relevance to quantum information, quantum communication, and experiments on quantum systems. The way that quantum theory describes the state of a system is one of its most unintuitive features. It is natural, therefore, to ask whether a similarly strange description of states is required on an ontological level. This thesis proves that almost all quantum superposition states for d > 3 dimensions must be real—that is, present in the ontology in a well-defined sense. This is a strong requirement which prevents intuitive explanations of the many quantum phenomena which are based on superpositions. A new theorem is also presented showing that quantum theory is incompatible with macro-realist ontologies, where certain physical quantities must always have definite values. This improves on the Leggett-Garg argument, which also aims to prove incompatibility with macro-realism but contains loopholes. Variations on both of these results that are error-tolerant (and therefore amenable to experimentation) are presented, as well as numerous related theorems showing that the ontology of quantum states must be somewhat similar to the quantum states themselves in various specific ways. Extending these same methods to quantum communication, a simple proof is found showing that an exponential number of classical bits are required to communicate a linear number of qubits. That is, classical systems are exponentially bad at storing quantum data. Causal influences are another part of ontology where quantum theory demands a revision of our classical notions. This follows from the outcomes of Bell experiments, as rigorously shown in recent analyses. Here, the task of constructing a native quantum framework for reasoning about causal influences is tackled. This is done by first analysing the simple example of a common cause, from which a quantum version of Reichenbach’s principle is identified. This quantum principle relies on an identification of quantum conditional independence which can be defined in four ways, each naturally generalising a corresponding definition for classical conditional independence. Not only does this allow one to reason about common causes in a quantum experiments, but it can also be generalised to a full framework of quantum causal models (mirroring how classical causal models generalise Reichenbach’s principle). This new definition of quantum causal models is illustrated by examples and strengthened by it’s foundation on a robust quantum Reichenbach’s principle. An unusual, but surprisingly fruitful, setting for considering quantum ontology is found by considering time travel to the past. This provides a testbed for different ontological concepts in quantum theory and new ways to compare classical and quantum frameworks. It is especially useful for comparing computational properties. In particular, time travel introduces non-linearity to quantum theory, which brings (sometimes implicit) ontological assumptions to the fore while introducing strange new abilities. Here, a model for quantum time travel is presented which arguably has fewer objectionable features than previous attempts, while remaining similarly well-motivated. This model is discussed and compared with previous quantum models, as well as with the classical case. Together, these threads of investigation develop a better understanding of how quantum theory affects possible ontologies and how ontological prejudices influence quantum theory.
It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.