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    The requirement that causal curves with a future endpoint... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    The requirement that causal curves with a future endpoint in the time travel region and no past endpoint must intersect Σ₀ is too strong, because it rules out Thornian time machines altogether.

    CausationModality & Possibility
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Thornian time machines, built on exotic matter threading a wormhole, require H⁺(Σ₀) generators that are past-endless by construction.
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    • 2.A formation condition demanding causal curves intersect Σ₀ conflates the boundary of causal development with the origin of the time machine itself.
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    • 3.Earman, Smeenk, and Wüthrich's own analysis shows no locally constructed time machine can satisfy this intersection condition without begging the question against wormhole topologies.
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    Reason for 2 of 2
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    • 1.The global hyperbolicity framework presupposes a topology that Thornian spacetimes explicitly violate, making Σ₀-intersection a category error when applied to them.
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    • 2.Requiring past-endless null geodesics to meet Σ₀ imposes a Cauchy-development standard that Morris and Thorne's construction never claimed to satisfy, targeting a straw man.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.For a causal curve of the type in question to reach Σ₀, it must first intersect H⁺(Σ₀).
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    • 2.Once a curve reaches H⁺(Σ₀), it can be continued endlessly into the past without meeting Σ₀.
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    • 3.The generators of H⁺(Σ₀) are past endless null geodesics that never meet Σ₀.
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    Topics

    Modality & PossibilityCausation

    Key Terms

    Causal curves(in time travel physics)
    Paths through space and time that show how one event causes another, like following the chain of cause-and-effect forward through time.
    Endpoint(in describing causal curves)
    The point where something begins or ends; in this case, where a causal path starts (past endpoint) or finishes (future endpoint).
    Intersect(in geometry and physics)
    To cross or meet at a point; here, it means the causal curves must pass through or touch the boundary Σ₀.
    Thornian time machines(in philosophy of time and time travel)
    A type of theoretical time machine concept proposed by philosopher Paul Horwich that allows time travel under certain conditions.
    time travel region(Used to distinguish regions of a space-time containing CTCs from those that do not.)
    The part of a space-time consisting of all space-time points p such that there exists a non-zero length timelike curve that starts at p and returns to p.
    Σ₀ (Sigma-zero)(in relativity equations)
    A mathematical symbol representing a specific surface or boundary in space-time that scientists use as a reference point in their models.

    Related

    A formation condition demanding causal curves intersect Σ₀ conflates the boundar...Earman, Smeenk, and Wüthrich's own analysis shows no locally constructed time ma...For a causal curve of the type in question to reach Σ₀, it must first intersect ...Once a curve reaches H⁺(Σ₀), it can be continued endlessly into the past without...
    +4 moreShow less
    Requiring past-endless null geodesics to meet Σ₀ imposes a Cauchy-development st...The generators of H⁺(Σ₀) are past endless null geodesics that never meet Σ₀.

    Source

    AI-extracted1/3 agreementValid
    SEP: time-machine
    View source passageHide passage
    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

    Details

    The global hyperbolicity framework presupposes a topology that Thornian spacetim...
    Thornian time machines, built on exotic matter threading a wormhole, require H⁺(...

    Similar

    The weakened adjacency requirement phrased in terms of timelike curves...83%For a causal curve of the type in question to reach Σ₀, it must first ...78%The (1+1)-dimensional Deutsch-Politzer spacetime satisfies the weakene...78%For a Thornian time machine to be a live possibility, a condition weak...78%
    Type
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    Perspectives
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    Edits
    1 edit