= Minkowski simultaneity relative to an inertial observer
{c}
{title2=$\eta(u,Q-P)=0$}
In <Minkowski spacetime> of <metric signature> $(-,+,+,+)$, let $u$ be a constant future-directed <four-velocity> with $\eta(u,u)=-c^2$. The time difference assigned to two <spacetime events> is $\Delta t_u=-\eta(u,Q-P)/c^2$. Thus the observer's simultaneous events form an affine <hyperplane> orthogonal to $u$. This is an invariant relation of the three arguments $u,P,Q$; the <Minkowski metric> alone does not single out one $u$. For fixed $u$, it defines an <equivalence relation> and the hyperplanes form a <foliation>. Changing $u$ changes this <foliation>.
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