Related papers: Response to comments on ``Theoretical mathematics'…

We discuss some methodological aspects of the relation between physics and metaphysics by dealing specifically with the case of non-relativistic quantum mechanics. Our main claim is that current attempts to productively integrate quantum…

The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as complementarity, gauge invariance, strong interactions, emergence of new theoretical concepts. This…

Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astro-physics, geophysics etc. It is of our hope that some of the problems discussed in this book will find…

The effects of the experiment itself upon the obtained results and, especially, the influence of a large number of experiments are extensively discussed in the literature. We show that the important factor that stands at the basis of these…

This reply contains a brief response to the comment by R. Howl, D. R\"atzel, and I. Fuentes [arXiv:1811.10306]

The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…

The hypothesis concerning the off-site continuum existence is investigated from the point of view of the mathematical theory of sets. The principles and methods of the mathematical description of the physical objects from different off-site…

It is argued that the traditional "realist" methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof…

The problem of time, considered as a problem in the usual physical context, is reflected in relation with the paper by Kauffman and Smolin (gr-qc/9703026). It is shown that the problem is a misposed problem in the sense that it was raised…

Current problems in particle physics are reviewed from the viewpoint of theories possessing extra spatial dimensions.

We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…

We make a number of observations on Conway surreal number theory which may be useful, for further developments, in both in mathematics and theoretical physics. In particular, we argue that the concepts of surreal numbers and matroids can be…

We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…

Even though quantum mechanics has existed for almost 100 years, questions concerning the foundation and interpretation of the theory still remain. These issues have gathered more attention in recent years, but does this mean that physicists…

We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

We review an emerging body of work by physicists addressing questions of economic organization and function. We suggest that, beyond simply employing models familiar from physics to economic observables, remarkable regularities in economic…

I contrast the profound differences in the ways in which algebra and analysis are used in physics. In particular I discuss the fascinating phenomenon that theoretical physicists devote almost all their efforts to algebraic problems even…

We discuss possible relationships between geometric and topological interactions on one side and physical interactions on the other side.

In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…