Quantum Causality, Stochastics, Trajectories and Information

A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within event enhanced quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent histories with the statistically predictable future. The application of this rule in the form of the nondemolition principle leads to the statistical inference of the von Neumann projection postulate, and also to the more general quantum information dynamics for instantaneous events, spontaneous localizations (i.e. quantum jumps), and state diffusions (i.e. continuous trajectories). This gives a dynamical solution, in the form of a Dirac boundary value problem and reduced filtering equations, of the notorious decoherence and measurement problems which was tackled unsuccessfully by many famous mathematicians and physicists starting with von Neumann, Schroedinger and Bohr.Comment: 67 pages, 120 references. In celebration of the 100th anniversary of the discovery of quant

Physical Logic

In R.D. Sorkin's framework for logic in physics a clear separation is made between the collection of unasserted propositions about the physical world and the affirmation or denial of these propositions by the physical world. The unasserted propositions form a Boolean algebra because they correspond to subsets of an underlying set of spacetime histories. Physical rules of inference, apply not to the propositions in themselves but to the affirmation and denial of these propositions by the actual world. This physical logic may or may not respect the propositions' underlying Boolean structure. We prove that this logic is Boolean if and only if the following three axioms hold: (i) The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied then its negation, or complement, is affirmed. When a physical system is governed by a dynamical law in the form of a quantum measure with the rule that events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid and need to be modified. One promising scheme for quantum mechanics as quantum measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other minor change

Quantum Measure Theory and its Interpretation

We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its behavior. We associate a "quantum measure" |S| to the set S of histories, and point out that |S| fulfills a sum rule generalizing that of classical probability theory. We interpret |S| as a "propensity", making this precise by stating a criterion for |S|=0 to imply "preclusion" (meaning that the true history will not lie in S). The criterion involves triads of correlated events, and in application to electron-electron scattering, for example, it yields definite predictions about the electron trajectories themselves, independently of any measuring devices which might or might not be present. (So we can give an objective account of measurements.) Two unfinished aspects of the interpretation involve *conditonal* preclusion (which apparently requires a notion of coarse-graining for its formulation) and the need to "locate spacetime regions in advance" without the aid of a fixed background metric (which can be achieved in the context of conditional preclusion via a construction which makes sense both in continuum gravity and in the discrete setting of causal set theory).Comment: Changes to original version: correction to the description of the quantum measure in the non relativistic case; some rewording in other places; a few typos corrected. 23 pages, plaintex with 7 eps figure

Learning and Discovery

We formulate a dynamic framework for an individual decision-maker within which discovery of previously unconsidered propositions is possible. Using a standard game-theoretic representation of the state space as a tree structure generated by the actions of agents (including acts of nature), we show how unawareness of propositions can be represented by a coarsening of the state space. Furthermore we develop a semantics rich enough to describe the individual's awareness that currently undiscovered propositions may be discovered in the future. Introducing probability concepts, we derive a representation of ambiguity in terms of multiple priors, reflecting implicit beliefs about undiscovered proposition, and derive conditions for the special case in which standard Bayesian learning may be applied to a subset of unambiguous propositions. Finally, we consider exploration strategies appropriate to the context of discovery, comparing and contrasting them with learning strategies appropriate to the context of justification, and sketch applications to scientific research and entrepreneurship.

Spenser and the Historical Revolution: Briton Moniments and the Problem of Roman Britain

Curran argues that, since Roman Britain is a key to understanding the historiographical debates of Edmund Spenser\u27s time, the Roman Britain section of Briton Moniments in The Faerie Queene needs to be examined. It is here that Spenser acknowledged the direction historiography was taking, and saw how this new trend altered the relation between history and glory