4 Ottobre, 2012 17:00

Seminario Matematico e Fisico di Milano

PHYSICS AND MATHEMATICS WITHOUT COORDINATES

WALTER NOLL, Carnegie Mellon University

Politecnico di Milano, Dipartimento di Matematica, Sala del Consiglio VII piano

I will start with a quote from the most famous scientist of the first half of the 20th century:Why were another seven years required for the construction of the general theory of relativity. The main reason is the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.

The following quote is from a far less famous scientist:
The approach of this treatise is conceptual, geometric, and uncompromisingly coordinate-free. In some of the literature tensors are still defined in terms of coordinates and their transformations. To me, this is like looking at shadows dancing on the wall rather than at reality itself.

The first quote is, of course, by Albert Einstein, and is cited in Section 1.2, (entitled spacetime with and without coordinates) of the book Gravitation by Misner, Thorne, and Wheeler. The second quote is by a far less famous scientist, namely me (Walter Noll) in part F of the Introduction to the Book entitled Finite-Dimensional Spaces, Algebra, Geometry, and Analysis.

I will discuss specific examples of coordinate-free treatments of the following topics:

1. Continuum Mechanics

2. Geometry

3. Special Relativity

4. General Relativity

5 Lineons versus Matrices