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    A geodesic directing field (guiding field / projective st... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    A geodesic directing field (guiding field / projective structure) must be posited to provide a standard of zero 3-acceleration.

    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.There is no unique standard of zero 3-acceleration intrinsic to the differential topological structure of spacetime.
      ?

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    • 2.Physical theories require a determinate standard for zero acceleration.
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    • 3.The projective structure provides such a standard by supplying the missing geometric field extrinsic to bare topology.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The projective structure can be read off from the metric tensor, making it a derived feature rather than an independently posited field.
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    • 2.In general relativity, the metric already encodes geodesic structure, so positing a separate guiding field introduces unmotivated ontological duplication.
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    • 3.Weyl's own conformal-projective decomposition program presupposes metrical underdetermination that standard GR does not exhibit.
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    Reason against 2 of 2
    ?
    • 1.Dynamical approaches to spacetime structure, as defended by Brown and Pooley, ground inertial standards in the symmetries of matter laws rather than autonomous geometric fields.
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    • 2.If geodesic behavior is explained by the dynamical dispositions of matter, the projective structure is an unnecessary postulate that violates Occam's razor in its strongest form.
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    Modality & PossibilityCausation

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    Truth & Knowledge3 linked

    Related

    Dynamical approaches to spacetime structure, as defended by Brown and Pooley, gr...If geodesic behavior is explained by the dynamical dispositions of matter, the p...In general relativity, the metric already encodes geodesic structure, so positin...Physical theories require a determinate standard for zero acceleration.
    +4 moreShow less
    The projective structure can be read off from the metric tensor, making it a der...The projective structure provides such a standard by supplying the missing geome...There is no unique standard of zero 3-acceleration intrinsic to the differential...Weyl's own conformal-projective decomposition program presupposes metrical under...

    Similar

    The projective structure is an appropriate geometric field for definin...82%The projective structure depends only on spacetime location and 3-velo...74%There must exist a geometric structure field — the inertial structure ...73%The same reasoning that requires geometric fields for 4-acceleration a...73%

    Source

    AI-extracted1/3 agreementValid
    SEP: weyl
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    The above argument for the necessity of geometric fields also holds for 3-velocity and 3-acceleration, denoted respectively by \(\xi^{\alpha}_{1}\) and \(\xi^{\alpha}_{2}\). The transformation law for the 3-acceleration is much more complicated than that of the 4-acceleration. However, analogous to the case of 4-acceleration, the transformation law of 3-acceleration is linear and is inhomogeneous in the 3-acceleration variable \(\xi^{\alpha}_{2}\). Consequently, there does not exist a unique s
    Extraction notes

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

    Details

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