Abstract

Symmetry: Culture and Science
Volume 29, Number 4, pages 453-474 (2018)
https://doi.org/10.26830/symmetry_2018_4_453

VARIATION PRINCIPLES, INVARIANCE PRINCIPLES, SYMMETRY PRINCIPLES, LAWS OF NATURE

Introduction to the issue on the centenary of the Noether theorems

György Darvas

Physicist, philosopher (b. Budapest, 1948).
Address: Symmetrion, 29 Eötvös St., Budapest, H-1067
E-mail: symmetrion@symmetry.hu
orcid.org/0000-0002-1652-4138

Abstract: This paper is an introduction to the thematic, centenary issue dedicated to the 100th anniversary of the publication of E. Noether’s milestone paper on Invariant variation problems. After formulating the aim of this issue, the author gives a short exposition of the two theorems formulated and proven in Noether’s 1918 paper. He tries to bring them closer to non-mathematician and non-physicist readers by examples of their applications. The paper emphasizes the less realised difference between the two theorems, and discusses their history and development during the past century. It gives a few insights into the mathematical opportunities that the theorems present but that are still less exploited in physics. It also discusses how did the two theorems influenced the classification of physical symmetries. It contains a few words on their generalisation. Finally the author gives a short evaluation on Noether’s contribution to science, and on the importance and actuality of the theorems for contemporary mathematics and physics.

Keywords: symmetry, invariance, variation, laws of nature, events.