Pauli term exactly as before, because the spatial Dirac matrices multiplied by , have the same squaring and commutation properties as the Pauli matrices. What is more, the value of the gyromagnetic ratio of the electron, standing in front of Pauli's new term, is explained from first principles. This was a major achievement of the Dirac equation and gave physicists great faith in its overall correctness. There is more however. The Pauli theory may be seen as the low energy limit of the Dirac theory in the following manner. First the equation is written in the form of coupled equations for 2-spinors with the SI units restored: so Assuming the field is weak and the motion of the electron non-relativistic, the total energy of the electron is approximately equal to its rest energy, and the momentum going over to the classical value, and so the second equation may be written which is of order – thus at typical energies and velocities, the bottom components of the Dirac spinor in the standard representation are much suppressed in comparison to the top components. Substituting this expression into the first equation gives after some rearrangement The operator on the left represents the particle energy reduced by its rest energy, which is just the classical energy, so one can recover Pauli's theory upon identifying his 2-spinor with the top components of the Dirac spinor in the non-relativistic approximation. A further approximation gives the Schrödinger equation as the limit of the Pauli theory. Thus, the Schrödinger equation may be seen as the far non-relativistic approximation of the Dirac equation when one may neglect spin and work only at low energies and velocities. This also was a great triumph for the new equation, as it traced the mysterious that appears in it, and the necessity of a complex wave function, back to the geometry of spacetime through the Dirac algebra. It also highlights why the Schrödinger equation, although superficially in the form of a diffusion equation, actually represents the propagation of waves. It should be strongly emphasized that this separation of the Dirac spinor into large and small components depends explicitly on a low-energy approximation. The entire Dirac spinor represents an irreducible whole, and the components just neglected here to arrive at the Pauli theory will bring in new phenomena in the relativistic regime – antimatter and the idea of creation and annihilation of particles. Weyl