= Solution
The <relativity of simultaneity> creates a serious difficulty for an observer-independent global present, but a conclusion about what exists requires an additional metaphysical premise. <Eternalism> regards past, present and future events as equally real. <Presentism> restricts existence to the present. These are ontological claims; the coordinate dependence of distant simultaneity is a physical claim.
A useful argument can be made mathematically explicit. In units $c=1$, consider <spacetime events> $O=(0,0)$, $C=(1,2)$ and $D=(1,0)$ in coordinates $(t,x)$. The <Lorentz boost> of <velocity> $v=1/2$ makes $O,C$ simultaneous, since $t'_C=\gamma(1-\tfrac12\cdot2)=0$. The original <inertial frame> makes $C,D$ simultaneous. Yet $D$ is in the <timelike> future of $O$. Suppose one assumes that simultaneity in every <inertial frame> equally warrants co-reality, and that this co-reality is transitive. From the reality of $O$ one then obtains the reality of the future event $D$. Applying the construction repeatedly puts pressure on a presentist ontology.
\Image[/past-exam-of-the-philosophy-of-space-time-course-of-the-university-of-oxford/2022-mixed-frame-simultaneity.png]
{title=Two different inertial simultaneity slices connect O to its timelike future D through a distant event C; no single inertial frame makes O and D simultaneous}
The extra premise does real work. There is a <failure of transitivity for mixed-frame simultaneity>: $O$ is simultaneous with $C$ in one <inertial frame>, and $C$ with $D$ in another, but $O,D$ are not simultaneous in any <inertial frame>. The physical relation therefore cannot itself be identified with a transitive relation of co-reality. <Special relativity> supplies the geometry in this argument, not the ontological bridge. Writing an entire history as a four-dimensional mathematical solution also does not, by itself, prove that every represented event exists in the same sense.
A presentist could postulate an additional preferred <foliation>. That recovers an absolute present but adds <background structure> absent from ordinary <Minkowski spacetime>, and must explain its physical role or its empirical unobservability. Alternatively, one might give a local account of becoming along a <world line>, rather than a single simultaneous becoming throughout the universe. The latter does not automatically vindicate global <presentism>, but shows why lack of a universal present is not identical to a denial of all temporal passage.
<General relativity> further weakens any universal identification of time with a single inertial <foliation>. Some cosmological solutions have a useful matter-selected time slicing; this is a property of those solutions and matter distributions. It is not an absolute simultaneity structure in every relativistic spacetime. The defensible conclusion is that relativity gives strong reasons against a fundamental observer-independent global present in its minimal structure. It does not entail <eternalism> without further premises about existence and the interpretation of that structure.
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