Electron as Spatiotemporal Complexity due to Self-Organized Criticality

The electron, which has been pictured as an elementary particle ever since J.J. Thomson’s e/m-measurement in 1897, and the relativistic motion of which is described by the Dirac equation, is discussed in the light of the recent progress made in Science of Complex Systems. Theoretical arguments and experimental evidences are presented which show that such an electron exhibits characteristic properties of spatiotemporal complexities due to Self-Organized Criticality (SOC). This implies in particular that, conceptually and logically, it is neither possible nor meaningful to identify such an object with an ordinary particle, which by definition is something that has a fixed mass (size), a fixed lifetime, and a fixed structure. The electron has been pictured as a particle, and as one of the elementary building blocks of nature, ever since J.J. Thomson published the result of his e/m-measurement in 1897. The Dirac equation2–4, originally designed as an one-particle equation, which describes the relativistic motion of such an electron (e) in the framework of Quantum Theory, is undoubtedly one of the greatest achievements in physics — although the original goal failed. This is because, it is Dirac’s equation which predicted the existence of positron and thus led to the discovery of one of the general fundamental symmetries (the charge-conjugation symmetry) in nature; and because, it is also this equation which describes in general the relativistic motion of all the known (electrically charged) spin-1/2 objects, in particular, that of the heavier leptons (μ, τ), as well as that of the quarks (u, d, s, etc) which are