It is often taken for granted that on board a rotating disk it is possible to
operate a \QTR{it}{global}3+1 splitting of space-time, such that both lengths
and time intervals are \QTR{it}{uniquely} defined in terms of measurements
performed by real rods and real clocks at rest on the platform. This paper
shows that this assumption, although widespread and apparently trivial, leads
to an anisotropy of the velocity of two light beams travelling in opposite
directions along the rim of the disk; which in turn implies some recently
pointed out paradoxical consequences undermining the self-consistency of the
Special Theory of Relativity (SRT). A correct application of the SRT solves the
problem and recovers complete internal consistency for the theory. As an
immediate consequence, it is shown that the Sagnac effect only depends on the
non homogeneity of time on the platform and has nothing to do with any
anisotropy of the speed of light along the rim of the disk, contrary to an
incorrect but widely supported idea.Comment: Latex, 2 figure
