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In a spacetime where the stress-energy tensor is null (no energy, no matter, no entropy), I wonder whether any motion of the variable time in the phase-space is well defined. The arrow of time, meant as parametrisation of succession of changing events, might lose validity, since no events can occur without actors (particles or fields) that can generate them, right?

Could this be a paradox, when using the Minkowski approximation to propagate information?

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