This open access book explores the nature of events that occur spontaneously and with no known cause, and asks whether they are truly, i.e. "irreducibly" random.
The aim of this paper is to give a review of the known results and open problems concerning causal completeness (closedness) of classical and non-classical (quantum) probability spaces. Causal closedness of a probabilistic theory means that the theory is causally rich enough to be able to explain causally all the correlations it predicts. It is natural to ask whether probabilistic theories are causally closed if one assumes that Reichenbach’s Common Cause Principle holds: this principle states that if two events A and B are probabilistically correlated then either the correlation is due to a causal interaction between A and B, or, if A and B are causally independent, Rind(A,B), then there exists a third event C, a so-called common cause that explains the correlation by being related to A and B probabilistically in a specific way (see Definition 1). Causal closedness of a probabilistic theory is intended to express that the theory complies with the Common Cause Principle; accordingly, and more precisely, a probability theory is defined to be causally closed with respect to a causal independence relation
The prevailing ontological framework of contemporary science posits "randomness" as a fundamental, irreducible property of the physical universe. This paper challenges that assumption, contending that randomness is an epistemic placeholder—a linguistic and mathematical heuristic for unresolved causal complexity. I introduce the Causal Vacuum Postulate, asserting that for an event to be truly stochastic (ontically random), it must occur in a state of absolute suspension from all universal fields—a state physically prohibited by the ubiquity of the Higgs, Gravitational, and Zero-Point fields. By synthesizing evidence from the Large Hadron Collider (LHC), Evolutionary Biology, and Algorithmic Information Theory, I argue for the Principle of Scalar Inheritance: the mechanism by which deterministic subatomic laws scale up to dictate macroscopic outcomes in complex systems. Finally, I argue that ontological randomness raises conceptual difficulties when examined under causal closure—a state that is unavoidable within the manifest universe. Furthermore, I apply this framework to the epistemology of artificial intelligence and macroeconomic market dynamics, illustrating how probabilistic smoothing destroys causal data. Finally, I address the biological paradox of measurement independence, arguing that human cognition itself is deterministically channelled by evolutionary constraints.
This book proposes a way of thinking about computation the way physicists think about quantum mechanics. In that picture, a computation is the dynamics of a wave-like field. Events happen at random. If one happens at a given tick, the chance that it happens at each place is the squared amplitude of the field there. The book doesn’t claim that computation is quantum mechanics. Nor does it claim that physical quantum mechanics gives rise to computation. It treats computation as a domain in its own right, e.g., formal systems, cellular automata, neural networks, brains and distributed systems. Each concrete system that carries out a computation, such as a cellular automaton or a brain, is called a substrate. The claim is that this domain has a wave-mechanical description of its own. Its structure runs parallel to the wave mechanics of physical particles, but it is a distinct theory. The framework introduces a substrate-relative quantum of action ℏ𝑐, which plays the role of Planck’s ℏ. It also introduces a substrate-relative speed limit 𝑐𝑐, the analog of the speed of light. Both depend on the substrate, and across the substrates the book considers they span many orders of magnitude. TheframeworkiscalledComputational Wave Field Theory, abbreviatedCWF.Initscurrent form it has two levels, and the key to reading it is to keep them apart. The first level is operational. CWFdefinesasubstrate-relativewavemodelforcomputationalevents. Thesecond level is explanatory. It asks why such a wave is the right object, and the present answer comes in layers. First, computational irreducibility conjecturally explains the wave’s epistemic part, the part that encodes what an observer can know. (Irreducibility means there is no shortcut, so the only way to learn the outcome is to run the computation. How far the epistemic part compresses tracks the causal structure.) Second, in the book’s model theorems, self-reference explains the wave’s genuinely complex phase. Third, holographic encoding, which stores information redundantly on a boundary, explains a substrate’s gravity-like structure. These three sources are distinct and separable. Irreducibility and encoding are two of the book’s three substrate axes, and the remaining axis is dynamical disorder. Self-reference sits off those axes. The book’s long-range target is that nature sits where all three sources meet. The operational postulate lets the framework run.