Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    An isometry between neighborhoods of spacelike hypersurfa... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Modality & Possibility
    HistoryEditSee Inverse

    An isometry between neighborhoods of spacelike hypersurfaces in two vacuum solutions is not in general extendible to an isometry between their future domains of dependence.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Starting from any vacuum solution, one can remove a closed set of points lying to the future of a neighborhood of a spacelike hypersurface and within its future domain of dependence.
      ?

      Think about whether this reason is strong or weak

    • 2.The surgically altered manifold with the restricted metric is also a solution to the vacuum Einstein equations.
      ?

      Think about whether this reason is strong or weak

    • 3.The original and surgically altered solutions share isometric neighborhoods but their future domains of dependence are not isometric.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The surgical removal of points from a vacuum solution exploits the non-uniqueness of maximal extensions, not indeterminism in the physics itself.
      ?

      Think about whether this reason is strong or weak

    • 2.Earman and Norton's hole argument shows such underdetermination reflects representational redundancy in diffeomorphism-invariant theories, not genuine physical ambiguity.
      ?

      Think about whether this reason is strong or weak

    • 3.A physically meaningful notion of determinism should be formulated over equivalence classes of diffeomorphically related models, rendering the non-extendibility result physically vacuous.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.The counterexample relies on solutions that are not globally hyperbolic, but Penrose and Hawking's singularity theorems suggest physically realistic spacetimes satisfy strong causality conditions.
      ?

      Think about whether this reason is strong or weak

    • 2.Restricting the domain of GR to globally hyperbolic spacetimes, as advocated by Geroch's development theorem, restores a robust form of Laplacian determinism within that class.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Topics

    Modality & PossibilityCausation

    Related

    A physically meaningful notion of determinism should be formulated over equivale...Earman and Norton's hole argument shows such underdetermination reflects represe...Restricting the domain of GR to globally hyperbolic spacetimes, as advocated by ...Starting from any vacuum solution, one can remove a closed set of points lying t...
    +4 moreShow less
    The counterexample relies on solutions that are not globally hyperbolic, but Pen...The original and surgically altered solutions share isometric neighborhoods but ...The surgical removal of points from a vacuum solution exploits the non-uniquenes...The surgically altered manifold with the restricted metric is also a solution to...

    Similar

    Geroch's theorem states that if two spacelike hypersurfaces lie in hol...88%Hole freeness requires that the future domain of dependence of a space...81%The original and surgically altered solutions share isometric neighbor...79%Starting from any vacuum solution, one can remove a closed set of poin...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: time-machine
    View source passageHide passage
    The would-be time machine operator need not capitulate in the face of Krasnikov’s theorem. Recall that the main difficulty in specifying the conditions for the successful operation of Thornian time machines traces to the fact that the standard form of causal determinism does not apply to the production of CTCs. But causal determinism can fail for reasons that have nothing to do with CTCs or other acausal features of relativistic spacetimes, and it seems only fair to ensure that these modes of fa
    Extraction notes

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

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit