Pieter Thyssen

Symmetry is at the heart of our understanding of matter. This book tells the fascinating story of the constituents of matter from a common symmetry perspective. The standard model of elementary particles and the periodic table of chemical elements have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of Shattered Symmetry is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. Along the way the theory of symmetry groups is gradually introduced with special emphasis on its use as a classification tool and its graphical representations. This is applied to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires us to leave the common ground of linear algebras and explore the potential of non-linearity.

Since its inception in 1869, the periodic system — icon of modern chemistry — has suffered from the problematic accommodation of the rare-earth elements. The substance of this paper intends to retrace Mendeleev’s shifting attitudes with regard to the rare-earth crisis during the period 1869–1871. Based on a detailed examination of Mendeleev's research papers from that period, it will be argued that the rare-earth crisis played a key role in inducing a number of important changes in Mendeleev’s philosophical viewpoints with regard to the epistemological concept of a chemical element and the nature of elementary groups. Many of Mendeleev's most cherished beliefs got endangered by the nature of these elements. Their mystifying properties forced him to revise his ideas about primary and secondary groups, the elements as basic and simple substances, and the use of short and long form tables. They made him question the validity and universality of the periodic law, and led him into hypothesizing about the internal structure of matter and constitution of atoms.