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This book is open access under a CC BY 4.0 license. This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un-)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe. .

Physics. --- Epistemology. --- Philosophy and science. --- Probabilities. --- History and Philosophical Foundations of Physics. --- Theoretical, Mathematical and Computational Physics. --- Probability Theory and Stochastic Processes. --- Philosophy of Science. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Science and philosophy --- Science --- Epistemology --- Theory of knowledge --- Philosophy --- Psychology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Genetic epistemology. --- Distribution (Probability theory. --- Philosophy. --- Normal science --- Philosophy of science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Developmental psychology --- Knowledge, Theory of --- Mathematical physics. --- Physical mathematics --- Physics --- Self-reflexive knowledge --- Physical chaos --- Physical random number generators --- Irreducible randomness --- Randomness in physics --- Physical indeterminism --- Acausality in physics --- Ecotoxicology. --- Environmental management. --- Waste management. --- Environmental Management. --- Waste Management/Waste Technology. --- Knowledge, Theory of.

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The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics-in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.

Quantum theory.