  In this paper, we discuss two features of the noncommmutative geometry and
spectral action approach to the Standard Model: the fact that the model is
inherently Euclidean, and that it requires a quadrupling of the fermionic
degrees of freedom. We show how the two issues are intimately related. We give
a precise prescription for the Wick rotation from the Euclidean theory to the
Lorentzian one, eliminating the extra degrees of freedom. This requires not
only projecting out mirror fermions, as has been done so far, and which leads
to the correct Pfaffian, but also the elimination of the remaining extra
degrees of freedom. The remaining doubling has to be removed in order to
recover the correct Fock space of the physical (Lorentzian) theory. In order to
get a Spin(1,3) invariant Lorentzian theory from a Spin(4) invariant Euclidean
theory such an elimination must be performed after the Wick rotation.
Differences between the Euclidean and Lorentzian case are described in detail,
in a pedagogical way.
