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We reanalyze from a modern perspective the bold idea of G. Helm, W. Ostwald, P. Duhem and others that energy is the fundamental entity composing the physical world. We start from a broad perspective reminding the search for a fundamental…
The idea of atoms is old but X-rays provided the first probe into the physical atom. Photographs of X-ray scattering from crystals -Laue spots- were the first visual proof for the physical existence of atoms arranged in a perfect geometric…
The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of…
According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of indistinguishable objects?". This is the aim of quasi-set…
A system's apparent simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and…
A method for quantization of the proton mass is here addressed, which provides a plausible explanation for the origin of mass and leads to the unification of mass and electric charge through their coupling. By means of an electromagnetic…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
We propose a system of information-theoretic axioms from which we derive the formalism of quantum theory. Part I is devoted to the conceptual foundations of the information-theoretic approach. We argue that this approach belongs to the…
The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what…
We prove that for every nonempty set $\Sigma$ of integers bigger than $1$, which has at most three elements, there exists a numerical semigroup $T$ and an element $x$ of $T$ such that a natural number $n$ is the number of atoms in a…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…
In this paper we put forward a new solution of the well-known problem of relevant logics, i.e. we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
Here, we show that the first isomorphism theorem, the orbit-stabilizer theorem, and the non-uniqueness of solutions of underdetermined linear systems are all manifestations of the same underlying algebraic property. We will call this…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
A physical theory consists of the mathematical formalism and an interpretation, which contains the definition of symbols, measurement assignments, concepts and principles, and an ontology. We present a scheme to classify these different…
The problem of representing the atomic elements of language in modern neural learning systems is one of the central challenges of the field of natural language processing. I present a survey of the distributional, compositional, and…