The geometric in contemporary physics: philosophical examination of a theme in the history of scientific ideas

• Grant number: 16/26182-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2017
• End date: November 30, 2023
• Field of knowledge: Humanities - Philosophy - Epistemology
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Valter Alnis Bezerra
• Grantee: Taimara Passero
• Host Institution: Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 19/14654-9 - The Geometric in Contemporary Physics: Philosophical examination of a theme in the history of scientific ideas, BE.EP.DR

Abstract

This project aims at analyzing the philosophical program of geometrization in contemporary physics. For this purpose we will investigate the features of the geometric structure of the physical theories towards the end of the 19th century and the early decades of the 20th century. We will look whether, and to what extent, these features constitute a specific form of scientific thought - which could be described either in terms of a style of reasoning, an image of science or a set of heuristics - and whether they point to a new form of rational intelligibility of reality. If so, we wish to investigate their differences in relation to previous stages of the project of geometrization in the history of physics and natural philosophy. One can find, first in natural philosophy and then in physics, different conceptions about the nature of geometry and its role in science. In a first period, we find geometry in a central place in the ancient science, both at the methodological level and at the epistemological one. In the second period, we have a strong implementation of the program of geometrization in natural philosophy of the 17th century, against the background of mechanistic worldview. Galileo was one of the main characters of this period, accompanied in the project of geometrization by other authors of the 17th century, each in his/her own way. In the 18th and 19th centuries, the mathematical tools used by the physicists were predominantly analytical, rather than geometric. After the crisis of mechanism, in the 19th century, a third period of geometrization of contemporary physics begins, represented by the theories of general relativity and by geometric reformulations of quantum mechanics, classical mechanics and field theory. To fulfill our initial goal, therefore, we will take into account the historical process that allows one to view the background of the development of geometry as well as the epistemological reflection about what would constitute "the geometric". Philosophical analysis of the central problem and associated historiographical aspects will allow us to ascribe meaning to the sequence of historical facts and to find links throughout the historical arc, allowing us a view of the movement of a narrative whose plot revolves around a main theme - the geometrization of physics - up to the contemporary era. (AU)