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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The canonical formulation of general relativity yields 10 scalar equations, four of which are constraints and six are genuine evolutionary equations.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The 4+6 split of Einstein's equations is gauge-dependent and presupposes a 3+1 foliation that is not intrinsic to the covariant theory.
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      Think about whether this reason is strong or weak

    • 2.Different choices of lapse and shift functions yield structurally different constraint/evolution decompositions, undermining the uniqueness claim.
      ?

      Think about whether this reason is strong or weak

    • 3.Dirac's constrained Hamiltonian formalism reveals the constraints are first-class, meaning they generate gauge transformations, not merely restrict initial data.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The distinction between 'constraints' and 'genuine evolutionary equations' presupposes a determinist causal structure that diffeomorphism invariance explicitly undermines.
      ?

      Think about whether this reason is strong or weak

    • 2.As Earman and Norton argued, hole argument considerations show that no set of equations in GR uniquely evolves spacetime, collapsing the constraint/evolution distinction ontologically.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The single tensorial Einstein field equation is translated into 10 scalar equations in the canonical formulation.
      ?

      Think about whether this reason is strong or weak

    • 2.Four of these scalar equations function as constraints on the canonical variables.
      ?

      Think about whether this reason is strong or weak

    • 3.The remaining six equations are genuine evolutionary equations.
      ?

      Think about whether this reason is strong or weak

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