Four forms of physical determination are presently known in physics: classical or mechanical determination, related to classical mechanics; dynamical determination, related to the relativistic theories of electromagnetism and gravitation; classical statistical determination, related to classical statistical theories; and quantum statistical determination, related to modern microphysics. The concept of interaction is a fundamental on-tological category, a moment of which is the causal relation; interaction is also local, taking place at finite velocities. Following the evolution of physical theories, it is possible to attest to the historicity of the concept of interaction and, accordingly, of the categories of interaction and determination. According to the Copenhagen School, causality and locality are incompatible with quantum mechanics. On the contrary, according to the point of view developed here, realism, causality and locality are simultaneously compatible in the domain of microphysics.
Four forms of physical determination are presently known in physics: classical or mechanical determination, related to classical mechanics; dynamical determination, related to the relativistic theories of electromagnetism and gravitation; classical statistical determination, related to classical statistical theories; and quantum statistical determination, related to modern microphysics. The concept of interaction is a fundamental on-tological category, a moment of which is the causal relation; interaction is also local, taking place at finite velocities. Following the evolution of physical theories, it is possible to attest to the historicity of the concept of interaction and, accordingly, of the categories of interaction and determination. According to the Copenhagen School, causality and locality are incompatible with quantum mechanics. On the contrary, according to the point of view developed here, realism, causality and locality are simultaneously compatible in the domain of microphysics.
Understanding the concept of causality is fundamental in physics, as it conditions the very possibility of any exchange of information between physical systems. This article examines and compares three main interpretations of the correlative operational concept of "causal separation" that have been respectively proposed in special relativity, quantum theory, and according to the statistical "non-signalling" condition. These interpretations, which can be classified regarding the range of CHSH correlation degrees they allow, lead to radically different results regarding the exchange of information between physical systems. Namely, it can be shown that, in opposition with the non-communication theorem of quantum theory, non-local communication can be established between the two entangled parts of a physical system when the relativistic criterium of causal separation is satisfied but not the quantum one.
In a physical theory we typically describe a system in terms of its state . We specify the relevant physical quantities or variables and then use dynamical laws to find the time evolution of these variables to predict their values in the future. For example, in classical particle mechanics, the state of a system is specified by the positions and velocities (or, equivalently for us, the momenta) of all of the particles in the system (that is, r ( t ) and v ( t ) for each particle). Newton's second law, F = ma , then determines the time evolution of the variables, or of the state, of the system. For electrodynamics, the state variables are the electric and magnetic fields, E and B , and Maxwell's equations govern the time evolution of these. In classical physics (including relativity here), the state variables that are the central entities of the dynamical equations (typically the positions and momenta of the particles) are also the directly observable physical quantities. That is, the state itself is specified in terms of the observables of the theory. The essential features of the classical world view (as modified by relativity) are that the present state of a system in principle determines its future state (as in the flight of a baseball under the influence of gravity) and that the agency responsible for this event-by-event causal structure must propagate from the cause to the effect at some rate no greater than the speed of light.
Fundamentals of quantum mechanics Quantum mechanics remains one of the most successful, yet enigmatic, formulations of physics. Uncertainty and measurement constraints are incorporated at the core of this fundamental description of micro-physical dynamics. Quantum mechanics successfully describes the observed structures in chemistry and materials science. In particular, the impenetrability of matter due to Pauli exclusion is a consequence of incorporating special relativity into quantum mechanics. Microscopic causality , or the requirement that communications cannot propagate at greater than the speed of light, relates a particle's spin to its quantum statistics but does not exclude the space-like correlations associated with a coherent quantum state. This section will examine some of the foundations of quantum physics. An emphasis will be placed upon how the microscopic fundamentals of quantum mechanics relate to the geometric fundamentals of gravitational mechanics. Quantum formalism There are several interpretations of quantum mechanics offering models of the underlying (often hidden) dynamics that generate the observed quantum phenomenology (for example, the Copenhagen interpretation, or the many-worlds interpretation). Since any interpretation consistent with quantum physics cannot be proved or disproved by experiment, only those aspects of quantum formalism directly connected to experimental observables will be developed, with minimal interpretation imposed. To establish the conventions utilized in what follows, a brief overview of the formalism that describes those calculable observables modeled by quantum physics will be given.
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.
Causalism is the traditional attitude of disowning all noncausal categories of determination, holding dogmatically that every connection in the world is causal. The entirely negative attitude taken by indeterminism and by empiricism toward the principle of causation is inconsistent with the very goal of science, which is the search for the objective forms of determination and interconnection. This chapter deals with the question concerning the range of validity of the causal principle. The notion of causal range of the laws of nature will be clarified and illustrated, by analyzing in some detail a typical physical law with which every student of electricity is familiar. Science seems to show neither an enlargement nor a progressive shrinking of the domain of validity of the causal principle. Most scientists and philosophers of science believed that quantum mechanics had given causality the death blow, by showing that quantum phenomena are inherently random, hence only statistically predictable.