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Shattered Symmetry: Group Theory From the Eightfold Way to the Periodic Table
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.
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.
521 pages, Kindle Edition
Published January 2, 2017
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July 15, 2020
I've been in the habit recently of trying to understand the nature of reality and after reading this book I'm convinced that the answer is in higher dimensional symmetry. I've probably only understood 40-50% of what I read, but the tidbits of wisdom were explosively mind blowing. For example the shell structure of the S2 and Px, Py, Pz orbitals although different shapes are the same energy level and are related to each other by a rotation in 4D space, an introduction to Noether's theorom where linear and rotational momentum were productions of symmetry, and more. This has been a detour on my completion of "The Road to Reality ~ Penrose" that I'm glad I took.
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