Related papers: The measuring principle and the continuum hypothes…
We show that the quadratic measure need not be postulated, but follows from the compatibility of two structural features of physical processes: linear reversible evolution prior to the formation of persistent records, and multiplicative…
We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary…
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an extension of Gamboa, Nagel and Rouault (2016), where we have…
The Two-Measure theory (TMT) has been developing since 1998 and has yielded a number of highly interesting results, including those not realized in traditional field theory models. The most important advantage of TMT as an alternative…
A forcing extension may create new isomorphisms between two models of a first order theory. Certain model theoretic constraints on the theory and other constraints on the forcing can prevent this pathology. A countable first order theory is…
The jiggling lemma of Thurston shows that any triangulation can be jiggled (read: subdivided and then perturbed) to be in general position with respect to a distribution. Our main result is a generalization of Thurston's lemma. It states…
The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a…
Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies; but at the same time the various solutions one encounters must fulfill some rather nontrivial constraints. Most of the freedom comes not…
The result of a physical measurement depends on the timescale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to…
We extend the results presented by Weinstein concerning the measurement of the length of a moving rod by a single observer, without making assumptions concerning the distance between the moving rod and the observer who measures its length.
The aim of this note is to remove an implausible assumption in Moser's theorem \cite{JM} to establish our new theorem 1 which gives a lower estimate for the sum $p+c^2\rho$ on Riemann hypothesis. Corollary 1 gives a rather plausible…
We prove existence of infinite volume Gibbs measures relative to Brownian motion. We require the pair potential W to fulfill a uniform integrability condition, but otherwise our restrictions on the potentials are relatively weak. In…
In Real Analysis, Littlewood's three principles are known as heuristics that help teach the essentials of measure theory and reveal the analogies between the concepts of topological space and continuos function on one side and those of…
We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…
We construct a topos in which the Dedekind reals are countable. The topos arises from a new kind of realizability, which we call parameterized realizability, based on partial combinatory algebras whose application depends on a parameter.…
We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact…