Isoperimetric Inequalities and Magnetic Fields at CERN

TL;DR

This paper explores the extension of isoperimetric inequalities to hyperbolic manifolds, linking them to magnetic fields and temperature in heavy ion collisions, and discusses how CERN experiments test these mathematical-physical relationships.

Contribution

It introduces a formulation of isoperimetric inequalities in terms of measurable physical quantities relevant to heavy ion collisions.

Findings

CERN experiments test the proposed isoperimetric inequality.

The inequality relates magnetic fields and temperature in collision systems.

The work connects geometric inequalities with experimental physics.

Abstract

We discuss the generalization of the classical isoperimetric inequality to asymptotically hyperbolic Riemannian manifolds. It has been discovered that the AdS/CFT correspondence in string theory requires that such an inequality hold in order to be internally consistent. In a particular application, to the systems formed in collisions of heavy ions in particle colliders, we show how to formulate this inequality in terms of measurable physical quantities, the magnetic field and the temperature. Experiments under way at CERN in Geneva can thus be said to be testing an isoperimetric inequality.