so that the rest-frame spinors can correctly be interpreted as solutions to the Dirac equation. There are four equations here, not eight. Although 4-spinors are written as four complex numbers, thus suggesting 8 real variables, only four of them have dynamical independence; the other four have no significance and can always be parameterized away. That is, one could take each of the four vectors formula_65 formula_66 and multiply each by a distinct global phase formula_76 This phase changes nothing; it can be interpreted as a kind of global gauge freedom. This is not to say that "phases don't matter", as of course they do; the Dirac equation must be written in complex form, and the phases couple to electromagnetism. Phases even have a physical significance, as the Bohm-Aharonov effect implies: the Dirac field, coupled to electromagnetism, is a U(1) fiber bundle (the circle bundle), and the Bohm-Aharonov effect demonstrates the holonomy of that bundle. All this has no direct impact on the counting of the number of distinct components of the Dirac field. In any setting, there are only four real, distinct components.