The Logic of Experimental Tests, Particularly of Everettian Quantum Theory

Claims that the standard methodology of scientific testing is inapplicable to Everettian quantum theory, and hence that the theory is untestable, are due to misconceptions about probability and about the logic of experimental testing. Refuting those claims by correcting those misconceptions leads to various simplifications, notably the elimination of everything probabilistic from fundamental physics (stochastic processes) and from the methodology of testing ('Bayesian' credences)

The Run Transform

We consider the transform from sequences to triangular arrays defined in terms of generating functions by f(x) -> (1-x)/(1-xy) f(x(1-x)/(1-xy)). We establish a criterion for the transform of a nonnegative sequence to be nonnegative, and we show that the transform counts certain classes of lattice paths by number of "pyramid ascents", as well as certain classes of ordered partitions by number of blocks that consist of increasing consecutive integers.Comment: 18 page

Machines, Logic and Quantum Physics

Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.Comment: 19 pages, 8 figure

Quantum Theory of Probability and Decisions

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory