Unit GEOMETRIC METHODS IN THE THEORY OF RELATIVITY
- Course
- Mathematics
- Study-unit Code
- 55A00094
- Curriculum
- Didattico-generale
- Teacher
- Marco Mamone Capria
- Teachers
-
- Marco Mamone Capria
- Hours
- 42 ore - Marco Mamone Capria
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2020/21
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/03
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The theory of relativity as an application of pseudo-Euclidean geometry, differential geometry, and group theory to physics. Attention is paid to the historical and critical development of formalism and theories, and it is stressed how advanced mathematical tools help to clarify conceptual issues.
- Reference texts
- R. D’Inverno, Introducing Einstein’s Relativity, Cambridge University Press, 1992; M. Mamone Capria (ed.), Physics Before and After Einstein, IOS, 2005; B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press, 1983; Lecture notes by the teacher.
- Educational objectives
- The main objectives of the course are: 1) a rigorous understanding of special relativity, as compared to classical physics and to some aspects of quantum mechanics and general relativity; 2) getting acquainted with the notion of space-time, including a working knowledge of space-time diagrams, both for their importance in physics and as a valuable example of applied differential geometry and topology; 3) an introduction to the historical issues concerning such momentous changes in the foundations of physics as that occurred with the relativity revolution.The course is also suitable for would-be high-school mathematics and physics teachers.
- Prerequisites
- A working knowledge of basic linear algebra, multivariate calculus, and differential geometry. Elements of classical physics.
- Teaching methods
- Classes -- Office hours -- Lecture notes.
- Other information
- Please check the office hours at the web-site http://www.dmi.unipg.it/mamone/, or just contact the teacher to arrange a meeting.
- Learning verification modality
- Oral examination (in any language previously agreed upon with the teacher), including some simple written problems. The examination starts with an in-depth treatment on a topic selected by the student from the program, followed by a number of questions on the rest of the program.
- Extended program
- General outline of the foundations of physics in its historical and critical development. The universe from a topological and geometrical point of view. The principle of relativity in classical physics. Newtonian space-time. The origins of special relativity. Derivations of the Lorentz transformations. Affine pseudo-Euclidean geometry. The Poincaré group and its subgroups. Minkowski space-time. Proper time. Relativistic dynamics. Mass-energy equivalence. About the pedagogy of special relativity for high school. About the relationship of special relativity with quantum mechanics. Relativistic electromagnetism. Relativity and non-Euclidean geometries. Basic concepts of general relativity. An outline of standard cosmological relativity. Friedmann's equation.