Related papers: Physics in Riemann's mathematical papers
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…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
This monograph discusses dualities in physics: what dualities are, their main examples--from quantum mechanics and electrodynamics to statistical mechanics, quantum field theory and string theory--and the philosophical questions they raise.…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
Causality is one of the most fundamental -- and yet elusive -- concepts in physics. From its intuitive role in everyday experience to its formal and often implicit role in scientific theories, causality has challenged philosophers and…
The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of…
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as…
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual…
In their study of physics beyond the first year of University -- termed upper-division in the US, many of students' primary learning opportunities come from working long, complex back-of-the-book style problems, and from trying to develop…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
The textbook contains the problems in mechanics and special relativity for physics departments of universities. Many original problems were proposed by active scientists from the institutes of the Siberian Branch of Russian Academy of…
The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
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…
Recent developments in foundations of physics have given rise to a class of views suggesting that physically meaningful descriptions must always be relativized to a physical perspective. In this article I distinguish between strong physical…
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…
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.