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    The canonical formulation of general relativity yields 10... — Carmelics
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    Home/Causation
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    The canonical formulation of general relativity yields 10 scalar equations, four of which are constraints and six are genuine evolutionary equations.

    CausationTruth & Knowledge
    ?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.The single tensorial Einstein field equation is translated into 10 scalar equations in the canonical formulation.
      ?

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

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

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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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    • 2.Different choices of lapse and shift functions yield structurally different constraint/evolution decompositions, undermining the uniqueness claim.
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    • 3.Dirac's constrained Hamiltonian formalism reveals the constraints are first-class, meaning they generate gauge transformations, not merely restrict initial data.
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    Reason against 2 of 2
    ?
    • 1.The distinction between 'constraints' and 'genuine evolutionary equations' presupposes a determinist causal structure that diffeomorphism invariance explicitly undermines.
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    • 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.
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    Related

    As Earman and Norton argued, hole argument considerations show that no set of eq...Different choices of lapse and shift functions yield structurally different cons...Dirac's constrained Hamiltonian formalism reveals the constraints are first-clas...Four of these scalar equations function as constraints on the canonical variable...
    +4 moreShow less
    The 4+6 split of Einstein's equations is gauge-dependent and presupposes a 3+1 f...The distinction between 'constraints' and 'genuine evolutionary equations' presu...The remaining six equations are genuine evolutionary equations.The single tensorial Einstein field equation is translated into 10 scalar equati...

    Similar

    The canonical formulation of general relativity is a completed project...81%Canonical formulations of general relativity face constraints on their...80%The canonical formulation of general relativity must employ the method...80%The remaining six equations are genuine evolutionary equations.78%

    Source

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    SEP: quantum-gravity
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    When one attempts to write general relativity down in this way, one has to contend with the existence of constraints on the canonical variables that are inherited from the diffeomorphism invariance of the spacetime formulation of the theory. The single tensorial equation that we see in standard presentations of the Einstein field equations is translated into 10 scalar equations in the canonical formulation, with constraints accounting for four of these equations (the remaining six are genuine ev
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    Details

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