Whittaker studied Dirac's equation, using prequantum mathematics, and found oscillating vectors corresponding to Schrödinger'sZitterbewegung. An extension of his study, without added assumptions or speculation, reveals the speedc associated at any instant with a direction that can be defined by specification of the Dirac spinor. This direction is hidden from quantum theory because that theory violates the physical principle that coherent amplitudes of the same kind must be added before quadratic quantities are formed from them. Two-component equations are formed from Dirac's (...) four-component equation and are found to contain information not explicit in Dirac's equation. (shrink)