Related papers: On Measurements, Numbers and p-Adic Mathematical P…
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts…
The laws of physics have a set of fundamental constants, and it is generally admitted that only dimensionless combinations of constants have physical significance. These combinations include the electromagnetic and gravitational fine…
The significance of the quantum feature of entanglement between physical systems is investigated in the context of quantum measurements. It is shown that, while there are measurement couplings that leave the object and probe systems…
In these notes, based on lectures given as part of the Les Houches summer school on Quantum Optics and Nanophotonics in August, 2013, I have tried to give a brief survey of some important approaches and modern tendencies in quantum…
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The…
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based…
The philosophy of science is a discipline concerning the metaphysical aspect of science. Recently, I proposed measurement theory, which is characterized as the metaphysical and linguistic interpretation of quantum mechanics. I assert that…
This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…
In this paper we introduce the concepts of p-logarithmic and Alpha-power divergence measures and point out a number of basic results.
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
A pedagogical and reasonably self-contained introduction to the measurement problems in quantum mechanics and their partial solution by environment-induced decoherence (plus some other important aspects of dcoherence) is given. The point…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
In this paper we have discussed convergence of power series both in p-adic norm as well as real norm. We have investigated rational summability of power series with respect to both p-adic norm and real norm under certain conditions. Then we…
We will discuss the link between scientific explanations and probabilities, specially in relationship with statistical mechanics and the derivation of macroscopic laws from microscopic ones.
Power-meter measurements are used to study a model that accounts for the use of power by a cyclist. The focus is on relations between rates of change of model quantities, such as power and speed, both in the context of partial derivatives,…
This paper has been withdrawn by the author. In this short paper I present a new approach to the problem of measurement, based on the difference between language (reality) and meta-language (meta-reality). This way, it will be shown as the…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
The phenomenon of concentration of measure on high dimensional structures is usually stated in terms of a metric space with a Borel measure, also called an mm-space. We extend some of the mm-space concepts to the setting of a quasi-metric…