Symmetry in nature

A discussion of symmetry in nature, art, science and mathematics, coupled with a nontechnical discussion of the mathematics of symmetry. Originally prepared as a set of public lectures at the end of a distinguished career hy a master. StiU an interesting read. 

Among the mostly fundamentally assumed symmetries in nature are the Lorentz invariance and the validity of the CPT theorem which demands an invariance of nature under simultaneous charge conjugation (C), parity operation... 

The non-equivalence of enantiomers through the spontaneous breaking of mirror-symmetry in nature is amplified by asymmetric autocatalytic reaction [34], e.g. Frank s spontaneous asymmetric synthesis [35, 36] (Fig. 7-8). Alberts and Wyn-berg have reported in enantioselective autoinduction that chiral lithium alkoxide products may be involved in the reaction to increase the enantioselectivity (Eq. (7.9)) [37]. The product % ee however does not exceed the level of catalyst % ee. In asymmetric hydrocyanation catalyzed by cyclic dipeptides, the (Si-cyanohydrin product complexes with the cyclic peptide to increase the enantioselectivity in the (S)-cyanohydrin product, the reaction going up to 95.8% ee (Eq. (7.10)) [38]. In the presence of achiral amine, (/ )-l-phenylpropan-l-ol catalyzed carbonyl-addition reaction of diethylzinc has been reported to show lower % ee than that of the catalyst employed [39]. 

A. Symmetry in nature receptor and one enzyme different monomers of the... 

Vernadsky knew that a version of this principle was also formulated by F. R. Japp (Vernadsky, 1965, p. 198) in the following form Only asymmetry can beget asymmetry" (Japp, 1898, p. 458). D Arcy Thompson, in his fundamental work about symmetry in nature, remarked concerning this proposition of Japp ln these last words (which, so far as chemist and biologist are concerned, we may acknowledge to be true) lies the crax of the difficulty" (Thompson, 1961, p. 138). Nevertheless, Vernadsky called this principle - the principle of Pasteur - Curie. This is, plausible, because of the widely-spread belief in the vitalistic views of Japp. 

Whereas energy appears to be distributed almost continuously, compared to matter, the distribution of matter presents the more tractable problem. When delving into the nature of matter, in its most elementary state, it is encountered in two antagonistic forms with equal probability. These two forms, called matter and anti-matter are best considered as the complementary forms of elementary stuff in two symmetry-related modes of existence. Symmetry-related units of matter and antimatter have the same mass but opposite electric charges and behave in opposite sense with respect to time. This relationship obeys the dictates of what is probably the most fundamental symmetry in Nature, known as CPT (charge conjugation-parity-time inversion) symmetry. Wherever it has been investigated, all natural phenomena have been found to obey CPT symmetry without exception. 

My assessment is that Oldershaw has identified a major symmetry of the cosmos, but like most symmetries in Nature, it is not perfect. Extrapolation to infinities and singularities is therefore not valid. A major deficiency is the failure to recognize CPT symmetry and the role of antimatter which, in our view, implies a closed universe. 

Thus, by the end of 1977, five flavours of quark (u, d, s, c, b) were known to exist together with six flavours of lepton (e, p, t, Ve, Tp vj. Assuming that quarks and leptons are the fundamental constituents of matter, many of the strong and weak interactions of hadrons and the weak interactions of leptons can be explained. However, anticipating a symmetry in nature s building blocks, it was expected that a sixth quark would eventually reveal itself. This quark, labelled top (t), would be the 2/3 electronic charge partner to the b quark (see table). 

Therefore, it is not arbitrary that the symmetry toward the central point of a structure is a very important symmetry in nature, the inversion symmetry. By extrapolating the inversion concept, the inversion symmetry. 

We can also look for planes of symmetry in nature. The fern frond shown in Figure 1.3 looks perfectly normal at first glance. However, on close inspection it can be seen that the left side of the leaf is just a reflection of the right-hand side on the surface of a pond. The picture is shown with the water surface vertical, which enhances the illusion. From half the leaf and its reflected image we can easily imagine the complete structure. 

The Erench physicist Louis de Broglie proposed in 1924 that not only light but all matter has a dual nature and possesses both wave and corpuscular properties. He reasoned that there should be symmetry in nature If a radiant corpuscle—-that is, a photon—has a frequency and a wavelength and therefore has wave properties, why should not a material particle also have wave properties (p. 429, original italics). .. When de Broglie first published his wave theory of matter, there was no experimental evidence to support his bold hypothesis. Within three years, however, two different experiments had been performed that demonstrated the diffraction of a beam of electrons. Clinton J. Davisson, assisted by L. H. Germer,. .. observed the diffraction of electrons when a beam of electrons was directed at a nickel crystal (Segal 1989, p. 431, underlined added). 

---