Related papers: On Measurements, Numbers and p-Adic Mathematical P…
Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
The dynamics of a system, made of a particle interacting with a field mode, thwarted by the action of repeated projective measurements on the particle, is examined. The effect of the partial measurements is discussed by comparing it with…
What science does, what science could do, and how to make science work? If we want to know the answers to these questions, we need to be able to uncover the mechanisms of science, going beyond metrics that are easily collectible and…
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
No consensus seems to exist as to what constitutes a measurement which is still considered somewhat mysterious in many respects in quantum mechanics. At successive stages mathematical theory of measure, metrology and measurement theory…
A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…
Parametric downconversion (PDC) is a technique of ubiquitous experimental significance in the production of non-classical, photon-number correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne…
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe…
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances…
We clarified the connection between measurements and partitions, and discussed the meaning of semiotics for measurements based on functions. The terms of property and relation quantity were defined by our understanding of partitions and…
Peptide strings have been developed as a concept for the past fourteen years. They are proposed to basically entail various quantum states engendered by the physical interactions of proteins containing peptide portions that are similar to…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…