Related papers: James Clerk Maxwell on quantities and units
We consider the situation of a physical entity that is the compound entity consisting of two 'separated' quantum entities. In earlier work it has been proven by one of the authors that such a physical entity cannot be described by standard…
In the article "The Tale of Two Queens and Two Towering Figures" published in CNJ in 2012 (CNJ vol. 57 No. 5, pp. 304-315), we discussed the contributions of Copernicus and Newton to coin minting and monetary reforms, as well as the…
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
A mathematical proof is given that Maxwell's equations are an {\it artifact} of Hodge theory together with the laws of Gauss and Amp\`ere, taken as axioms. They are thus geometric in nature, independent of any specific physical mechanisms,…
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first…
Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016. These algebras provide the mathematical foundation for…
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
Maxwell's equations comprise both electromagnetic and gravitational fields. The transverse part of the vector potential belongs to magnetism, the longitudinal one is concerned with gravitation. The Coulomb gauge indicates that longitudinal…
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq…
The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as…
This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of…
We presented a model for unification of electricity and gravity. We have found a consistent description of all physical quantities pertaining to the system. We have provided limiting values for all physical values. These values are neither…
This work is an introduction to modern mathematical physics. We begin with Maxwell laws and vector calculus, pass next to consider the action and the Feynman integral in quantum mechanics, next relativity and differential geometry to…
Many quantities are attributed a range of values that can apparently extend to infinity (on one side or both sides). In this respect, the definitions of their measurement units do not place any constraint to the maximum (or minimum) value…
Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…