Bookmark 1 & 2: Spinning Particle Model of the electron with the Center of Charge (CC, ) moving at speed | | = c and the Center of Mass (CM, ) moving at the speed .
These figures (and GIFs) are modeled in Mathematica with the equations and code provided in the last section and bookmarked in the Manipulate plots with the referred numbers (Bookmarks can be accessed with the menu in the upper right corner of the plot).
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These figures (and GIFs) are modeled in Mathematica with the equations and code provided in the last section and bookmarked in the Manipulate plots with the referred numbers (Bookmarks can be accessed with the
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The Center of Charge r is moving at the speed of light (| | = c) and the Center of Mass q is moving at a speed | | < c. The complete dynamical equations for the evolution of the Center of Mass and Center of Charge can be expressed in terms of dimensionless classical variables. The observables for the free particle (no external forces, so the charge has no role) in this model depend on two intrinsic parameters that are independent of who measures them, they are given by the invariants of the Poincaré group: the mass m (that, as we will see later, is defined mathematically by the “radius”, the separation between the CC and the CM in the CM reference frame) and the absolute value of the spin in the Center of Mass frame. When quantized, the value of the nonvanishing mass m is arbitrary (each elementary particle has a different mass) but the value of || = ℏ/2, and thus it represents a classical model of a fermion. Electrons (or any fermion, any elementary particle with spin ½ (in natural units), like quarks, muons or Tau, but not the proton as, although it has spin ½ it is not an elementary particle, and not a photon that has spin 1) can be mathematically simulated by the Spinning Particle Model : a Center of Charge point (CC, ) spinning around a Center of Mass point (CM, ), allowing to accurately analyze interactions between elementary particles with spin. We will see that the point dynamics are described by a system of fourth order differential equations (instead of the second order systems we are used to in classical mechanics), thus allowing us to describe the torsion (third order derivative) which originates the spin. These equations can be decoupled into a system of second order differential equations for the points and , where satisfies Newton-type dynamical equations in terms of the external force evaluated at the position of the Center of Charge .
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