Related papers: Physics in Riemann's mathematical papers
Feyerabend frequently discussed physics. He also referred to the history of the subject when motivating his philosophy of science. Alas, as some examples show, his understanding of physics remained superficial. In this respect, Feyerabend…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
These notes were written from a series of lectures given in March 2010 at the Universidad Complutense of Madrid and then in Barcelona for the centennial anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
In this paper we present some results obtained in a previous paper about the Cartan's approach to Riemannian normal coordinates and our conformal transformations among pseudo-Riemannian manifolds. We also review the classical and the…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
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 aim of this paper is to introduce a mathematical logic based approach investigating why-type questions in physics.
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the…
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous…
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
Without a doubt many problems in physics arise as a consequence of our philosophical conception of the world. In this contribution however we endeavor to alleviate this scenario by putting forward a philosophical approach under which some…
The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and…
We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.
A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…
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…
A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
The appearance of two geometries in one and the same gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between…