Favorite Prefaces IV

Classical Mathematical Physics: Dynamical Systems and Field Theories
by Walter Thirring [son of Hans Thirring, who was the co-discoverer of the Lense-Thirring frame effect in general relativity]
(Preface to the second edition).

Since the first edition already contained plenty of material for a one-semester course, new material was added only when some of the original could be dropped or simplified. (…) This involved not only the use of more refined mathematical tools, but also a reevaluation of the word fundamental. What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler’s laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order. These irrational numbers are precisely the ones that are the least well approximated by rationals, and orbits with radii having these ratios are the most robust against each other’s perturbations, since they are the least affected by resonance effects.

Click-the-Links!

Dear Readers,

Forgive my long delay in writing here. I spent the last few months wondering whether I would shutdown this blog or not. Well, I have decided that I will not, at least, not yet. So here are a few interesting links that I came across recently:

1) From the [PhilPhys] e-mail list, a talk by Stephen Summers (University of Florida).

“Yet More Ado About Nothing: The Remarkable Relativistic Vacuum State”

Abstract: An overview is given of what mathematical physics can currently say about the vacuum state for relativistic quantum field theories on Minkowski space. Along with a review of classical results such as the Reeh-Schlieder Theorem and its immediate and controversial consequences, more recent results are discussed. These include the nature of vacuum correlations and the degree of entanglement of the vacuum, as well as the striking fact that the modular objects determined by the vacuum state and algebras of observables localized in certain regions of Minkowski space encode a remarkable range of physical information, from the dynamics and scattering behavior of the theory to the external symmetries and even the space-time itself. In addition, an intrinsic characterization of the vacuum state provided by the modular objects is discussed. [Foundations of Physics in Greater Paris]

2) A new issue of Philosophia Mathematica is available online [June 2009; Vol. 17, No. 2], in special:

- Mark Balaguer, Fictionalism, Theft, and the Story of Mathematics

- Francesco Berto, The Gödel Paradox and Wittgenstein’s Reasons

3) New edition of Edge:

What’s Next? Dispatches on the Future of Science (Edited by Max Brockman): “A preview of the ideas you’re going to be reading about in ten years.”