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    The counterexample relies on solutions that are not globa... — Carmelics
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    Challenges→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.

    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.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Penrose-Hawking theorems rigorously derive singularities under causality conditions satisfied by all observed astrophysical systems.
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    • 2.Non-globally hyperbolic spacetimes lack predictability from initial data, making them physically unrealistic for observable universes.
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    • 3.Counterexamples exploiting pathological causality violate the generic conditions required by physically justified field equations.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Global hyperbolicity is a sufficient but not necessary condition; weaker causality may hold in realistic scenarios near singularities.
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    • 2.Penrose-Hawking assumptions (geodesic completeness, energy conditions) may fail in quantum gravity, undermining classical theorems' scope.
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    • 3.Counterexamples demonstrate mathematical possibility; dismissing them requires independent empirical evidence, not just assumption-matching.
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    Key Terms

    Globally hyperbolic(as used in physics and cosmology)
    A mathematical property of spacetime (the fabric of space and time combined) that ensures cause and effect work in a predictable, well-behaved way throughout the entire universe.
    Physically realistic(as used in physics)
    Consistent with how the actual universe actually behaves, based on observation and experiments rather than pure mathematical possibility.
    Roger Penrose(as the originator of the gravitational entropy arguments being discussed)
    A renowned British physicist and mathematician who has written extensively about consciousness, cosmology, and the nature of time; he's known for proposing unconventional ideas about how the universe began.
    Singularity theorems(as used in cosmology and general relativity)
    Mathematical proofs developed by Penrose and Hawking showing that under certain conditions, the universe must contain points where the laws of physics break down (like at the center of a black hole).
    Spacetime(as one criterion for whether something is physically real)
    A physics concept combining space (location) and time into one continuous system—basically, every physical object exists somewhere at some moment in time.
    Stephen Hawking(as a key figure in modern physics)
    A legendary British theoretical physicist famous for discovering that black holes emit radiation and for his work on the nature of time, space, and the universe.
    Strong causality conditions(as used in relativity and cosmology)
    Mathematical requirements ensuring that cause and effect follow a strict, logical order with no weird time-travel-like loops or violations of cause coming before effect.
    counterexample([IHT] arg. 2)
    A possible obligational situation (casus possibilis positus) that verifies the antecedent and falsifies the consequent of an inference

    Connections

    2 topics

    Causation1 linkedModality & Possibility1 linked

    Related

    An isometry between neighborhoods of spacelike hypersurfaces in two vacuum solut...Counterexamples demonstrate mathematical possibility; dismissing them requires i...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Counterexamples exploiting pathological causality violate the generic conditions...
    Global hyperbolicity is a sufficient but not necessary condition; weaker causali...
    +3 moreShow less
    Non-globally hyperbolic spacetimes lack predictability from initial data, making...Penrose-Hawking assumptions (geodesic completeness, energy conditions) may fail ...Penrose-Hawking theorems rigorously derive singularities under causality conditi...