Is "time is a property of the vacuum" defensible?

Object. General relativity has no preferred time function; a generic solution has no time-translation symmetry at all. Cosmology nonetheless has a cosmic time. Proposed mechanism: the vacuum (the actual solution) breaks the diffeomorphism symmetry down to its isometries, and if those preserve a foliation, a clock is restored. Cosmic time in FRW is the example.

Presenting problem. Gödel's 1949 rotating universe is an exact solution with matter, homogeneous, with a large isometry group, and it has no global time function: closed timelike curves pass through every point. Symmetry breaking to a large isometry group is therefore not sufficient. The precise condition is that the matter congruence be irrotational (hypersurface-orthogonal). Gödel took his solution as evidence that time is ideal, not objective.

History (the analogy that motivated the claim). In distributed computing, an asynchronous system has no global clock; "before" is Lamport's happens-before, modelled on relativity; a global time function is what a synchronous model or a leader supplies; and leader election is impossible under a symmetry with no fixed point. Read this way, general covariance is the anonymous model, the problem of time is a fixed-point obstruction (diffeomorphisms acting on time functions), and cosmic time is a leader elected by symmetry breaking. Gödel's universe is a vacuum that refuses to elect one.

Differential. 1. "Time is a vacuum property, with irrotationality as the condition" is a complete and adequate account; Gödel's universe is a vacuum without time, and that is the end of it. 2. The condition shows time is not a property of the vacuum but of the matter congruence's kinematics, which can be changed by a choice of observers, so the claim is empty. 3. Gödel is right: a property present in one solution and absent in another is not what "time" means, and the correct conclusion is that time is not fundamental.

Discriminating tests. Whether the distributed-systems reading yields anything the standard 3+1 analysis doesn't (candidate: the fixed-point-free vs elementwise-fixed distinction, which predicts that boosts must be broken completely while rotations may survive). Whether any rotating cosmological model consistent with observation has a global time function.

Stakes. Whether the analogy between asynchronous computation and general covariance is load-bearing or decorative.

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Update (2026-09-12): the selection question, and what a positive version of it would demand.

Cosmic-time-only-for-irrotational-vacua now sits alongside two other instances of one pattern: a symmetric family, and the question of what picks a point out of it. Angluin's ring of identical processes is one (leader election possible iff the residual symmetry has a fixed point); vacuum selection in field theory is another. Three instances of a single criterion is a different kind of object from a single analogy, and testable in a way one analogy is not.

New discriminating test. Selection is the existence half of a pair. The other half asks what the distinguished object determines once it exists — the fixed-point side, where Duistermaat–Heckman and Atiyah–Bott localization live, and where fixed points don't merely exist but determine integrals, cohomology and characters.

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Literature verdict (2026-09-14) — partial, moved by reading (no run; the Run status above stays not attempted because no lab/runs/ entry settles this — the move was a reading pass). The case's own discriminating test — whether any rotating cosmological model consistent with observation has a global time function — is answered yes, and named. Korotkii & Obukhov (gr-qc/0003096) build rotating, expanding Gödel-type metrics that respect CMB isotropy, produce no parallax, and — below a bounded angular velocity — contain no closed timelike curves, so they admit a global time function. The absence of CTCs requires an upper limit on global vorticity, which the authors note as a natural explanation for why observed cosmic rotation is so small.

• Branch 1 supported. "Time is a vacuum property, irrotationality (or bounded vorticity) the condition" is complete and adequate: Gödel is the above-threshold case, Korotkii–Obukhov the below-threshold case — one solution family, split by a vorticity threshold.
• Branch 3 weakened. "A property present in one solution and absent in another isn't what time means" fails, because the property tracks a physical parameter with a clean threshold — what a real quantity looks like, not an artifact.
• A threshold object — same shape as [[CASE-22]] (the |a| = 2√q signature flip, the finite-field flip). Cross-referenced.

Load-bearing caveat — the split. This resolves the physics, not the analogy that motivated the case. Whether "general covariance is the anonymous model, cosmic time an elected leader" is load-bearing or decorative — the case's stated stakes — is untouched. The vacuum-property claim is supported; the distributed-systems reading is not addressed by this.

Sources: Korotkii & Obukhov (gr-qc/0003096); Gödel 1949; the vorticity-bound survey (arXiv:2101.08592) for the observational-rejection history.

So: does the general-relativistic case have a consequence half? If cosmic time is a leader elected by symmetry breaking, and the reading is load-bearing rather than decorative, there should be a localization statement — global quantities of an irrotational cosmological spacetime computable from the fixed-point data of the symmetry that elected the clock. Constructing one, or showing that none exists, decides the case.

This is a better test than the one in the body above (whether the fixed-point-free vs elementwise-fixed distinction predicts that boosts must break completely while rotations may survive), for two reasons. It is a positive demand rather than a tiebreaker between existing branches. And failure to meet it is informative on its own: it would mean the reading supplies an obstruction criterion and nothing more, which is a real result but a much smaller one than the case has been treating it as.