Symmetry and Symmetry Breaking in Science and Arts
Klaus Mainzer
Carl Friedrich von Weizsäcker Zentrum, Universität Tübingen, Doblerstraße 33, 72074 Tübingen;
TUM Senior Excellence Faculty, Arcisstr. 21, 80333 München; European Academy of Sciences and Arts,
St.Peter Bezirk 10, 5020 Salzburg
DOI: 10.5281/zenodo.7602077
Abstract
In this review article, symmetry and symmetry breaking are considered as complementary principles in science and arts. It starts with symmetry and symmetry breaking in early world views of nature and art. Then, symmetries are definied as fundamental structures of mathematics. Mathematical models of symmetry and symmetry breaking are used to explain the emergence of space-time and matter in modern physics. Even molecular structures in chemistry are distinguished by mathematical symmetries. Their elegance and beauty seem to realize aesthetical categories in nature. In biological evolution, the question arises how symmetry breaking (e.g. molcular chirality) can be explained. In modern arts, symmetry and symmetry breaking are „hidden“ structures which can be found in music, painting, and architecture. In a philosophical outlook, symmetry and symmetry breaking are highlighted as regulative guiding ideas of research.
Keywords
Platonic bodies, harmony, symmetry groups, automorphism, space-time symmetries, gauge symmetries, cosmological symmetry principle, global and local symmetries, spontaneous symmetry breaking, chirality.
1. Introduction
Symmetries are used in the history of science and culture as fundamental models of order. This raises the question of whether they were merely invented by humans to order the diversity of phenomena, whether they even arise only from an aesthetic need, or whether they are basic structures of nature that exist independently of humans. In antiquity, at any rate, knowledge, art and nature were understood from a common symmetrical basic order. In modern times, this unity of natural and human sciences breaks down. In art, symmetries and symmetry calculations are related to subjective judgements of taste. In mathematics and the natural sciences, symmetries and symmetry breaking remain fundamental principles of describing nature, the application of which ranges from the formation of primordial matter to the evolution of life. In fact, current discoveries and laws in cosmology, physics, chemistry and biology are related to symmetry and symmetry breaking. It is symmetry breaking, according to the thesis in many of the author's books, that gives rise to diversity, complexity and new structures in nature - from physics and chemistry to biology and brain research. Without symmetry breaking, the world would remain invariant and unchanged. Mathematical structures make these interdisciplinary connections in nature and art transparent. (Johnson et al., 2022; Conway et al., 2008; Ball 2016)...read more in pdf
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