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    The weakened adjacency requirement phrased in terms of ti... — Carmelics
    Home/Modality & Possibility
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    The weakened adjacency requirement phrased in terms of timelike curves rather than causal curves is too weak to adequately characterize time machine spacetimes.

    CausationModality & Possibility
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    • 1.The (1+1)-dimensional Deutsch-Politzer spacetime satisfies the weakened requirement, since every past endless timelike curve emerging from its time travel region meets Σ₀.
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    • 2.Deutsch-Politzer spacetime is not a plausible candidate for a time machine spacetime.
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    • 3.Up to and including time Σ₀, Deutsch-Politzer spacetime is identical with empty Minkowski spacetime.
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    Modality & PossibilityCausation

    Related

    A spacetime identical to Minkowski spacetime up to Σ₀ cannot have its state at Σ...Deutsch-Politzer spacetime is not a plausible candidate for a time machine space...The (1+1)-dimensional Deutsch-Politzer spacetime satisfies the weakened requirem...The state of Minkowski spacetime up to Σ₀ is not responsible for the development...
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    Up to and including time Σ₀, Deutsch-Politzer spacetime is identical with empty ...

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    The requirement that causal curves with a future endpoint in the time ...83%The (1+1)-dimensional Deutsch-Politzer spacetime satisfies the weakene...78%The standard form of causal determinism does not apply to the producti...77%For a Thornian time machine to be a live possibility, a condition weak...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: time-machine
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    Thus, if the operation of a Thornian time machine is to be a live possibility, some condition weaker than causal determinism must be used to capture the sense in which the state on \(\Sigma_0\) can be deemed to be responsible for the subsequent development of CTCs. Given the failure of causal determinism, it seems the next best thing to demand that the region \(V\) is “adjacent” to the future domain of dependence \(D^+ (\Sigma_0)\). Here is an initial stab at such an adjacency condition.
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

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