  Suppose physical spacetime corresponds to a Weyl geometry. Then two  identical clocks \(A\) and \(B\) at an event \(p\) with a  common unit of time, that is, a timelike vector of given length  \(l_{p}\), which are separated and moved along  different world lines to an event \(q\), will not only differ with respect to the elapsed time (first clock effect (i.e., relativistic  effect)), but in general the clocks will differ with respect to their common unit of time (rate of ticking) at \(q\) (second clock  effect). That is, congruent time displacement in a Weyl geometry is  such that two congruent time intervals at \(p\) will not in  general be congruent at \(q\), when congruently displaced in  parallel along different world lines from \(p\) to \(q\), that  is, \(l^{A}_{q} \ne l^{B}_{q}\).  This means that a twin who travels to a distant star and then returns to earth would not only discover that the other twin on earth had  aged much more, but also that all the clocks on earth tick at a  different rate. Hence, in the presence of a non-vanishing  electromagnetic field \(F_{jk}(x)\) the  clock rates will not in general be the same; that is, there will be a second clock effect in addition to the relativistic effect (first  clock effect). Thus, \(l^{A}_{q} = l^{B}_{q}\) if  and only if the curl of \(A_{j}(x)\)  vanishes, that is, if and only if the electromagnetic field tensor  \(F_{jk}(x)\) vanishes, namely, 