How is quantum evolution defined when no global clock exists?
In plain words
Physical clocks in gravitating systems can stop or run backward, and in chaotic systems no variable may serve as a good clock everywhere. The usual recipe for evolution in time then breaks down.
Precise statement
For constrained systems in which every candidate clock function T has turning points along classical orbits (the global problem of time, for example chaotic Bianchi IX minisuperspace), determine whether a consistent unitary relational dynamics exists, by patching local clocks or otherwise, and whether its predictions are independent of the patching. An answer is a construction with proven clock-change consistency in a chaotic model, or a no-go theorem.
What would settle it
A worked chaotic minisuperspace model with a proven consistent, patch-independent relational dynamics, or a proof that none exists.
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