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    Therefore the projective structure alone is insufficient ... — Carmelics
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    Challenges→The presence of a projective structure on spacetime prevents arbitrary realignment of the worldlines of material bodies in the neighbourhood of any given event.

    Therefore the projective structure alone is insufficient to prevent arbitrary realignment of all material worldlines, not merely freely-falling ones.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Projective structure encodes only incidence relations and cross-ratios, not metric properties needed to distinguish physical worldlines.
      ?

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    • 2.Conformal rescalings preserve null cones but leave timelike geodesics underdetermined, allowing arbitrary reparameterization of material paths.
      ?

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    • 3.Without additional structure beyond projective geometry, no constraint prevents simultaneous relabeling of all massive particle trajectories.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Affine structure on projective space does constrain geodesics; arbitrary worldline realignment violates affine-geometric consistency conditions.
      ?

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    • 2.Matter stress-energy couples to metric structure, which imposes additional constraints beyond pure projective/conformal invariance.
      ?

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    • 3.Physical clocks and particle interactions provide operational definitions that break projective symmetries and fix worldline identities.
      ?

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    Related

    Affine structure on projective space does constrain geodesics; arbitrary worldli...Conformal rescalings preserve null cones but leave timelike geodesics underdeter...Matter stress-energy couples to metric structure, which imposes additional const...Physical clocks and particle interactions provide operational definitions that b...
    +3 moreShow less
    Projective structure encodes only incidence relations and cross-ratios, not metr...The presence of a projective structure on spacetime prevents arbitrary realignme...Without additional structure beyond projective geometry, no constraint prevents ...

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    claim
    Perspectives
    2 (1 for, 1 against)
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