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    The presence of a projective structure on spacetime preve... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    The presence of a projective structure on spacetime prevents arbitrary realignment of the worldlines of material bodies in the neighbourhood of any given event.

    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.If a projective structure exists at any event of spacetime, the microsymmetry group that preserves that structure is a 20-parameter Lie group.
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    • 2.A 20-parameter Lie group provides only twenty degrees of freedom, not infinitely many.
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    • 3.A finite number of available parameters is insufficient to achieve an arbitrary realignment of worldlines in the neighbourhood of an event.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.A projective structure constrains only the unparameterized geodesics of free particles, leaving non-geodesic (accelerated) worldlines unconstrained by that structure.
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    • 2.Arbitrary realignment of worldlines in a neighborhood includes accelerated trajectories, which the projective structure's 20-parameter group does not govern.
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    • 3.Therefore the projective structure alone is insufficient to prevent arbitrary realignment of all material worldlines, not merely freely-falling ones.
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    Reason against 2 of 2
    ?
    • 1.Ehresmann and Cartan connection theory shows that projective structure is a gauge-dependent construct requiring a choice of connection, not an intrinsic feature of spacetime points.
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    • 2.If projective structure is gauge-dependent, its restrictive power over worldline realignment is relative to a chosen representational framework, not an objective physical constraint.
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    • 3.Weyl's own gauge-theoretic program, as criticized by Einstein in 1918, illustrates that structural constraints derived from connection choices lack direct empirical bite without independent physical stipulation.
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    Related

    A 20-parameter Lie group provides only twenty degrees of freedom, not infinitely...A finite number of available parameters is insufficient to achieve an arbitrary ...A projective structure constrains only the unparameterized geodesics of free par...Arbitrary realignment of worldlines in a neighborhood includes accelerated traje...
    +5 moreShow less
    Ehresmann and Cartan connection theory shows that projective structure is a gaug...If a projective structure exists at any event of spacetime, the microsymmetry gr...If projective structure is gauge-dependent, its restrictive power over worldline...Therefore the projective structure alone is insufficient to prevent arbitrary re...Weyl's own gauge-theoretic program, as criticized by Einstein in 1918, illustrat...

    Similar

    In a spacetime with only a differentiable structure and no post-differ...79%To constructively establish the projective structure of spacetime, one...78%The affine and projective spacetime structures are G-structures.77%To determine the projective structure of spacetime (and thus its geode...77%

    Source

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    SEP: weyl
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    Employing the concept of the microsymmetry group (definition 4.1), Coleman and Korté (1982) have analyzed Weyl’s plasticine example in the following way: Consider a space-time manifold equipped only with a differentiable structure, the plasticine of Weyl’s example. Then our spacetime does not have an affine, conformal, projective or metric structure defined on it. In such a world it is possible do define curves and paths; however, there are no preferred curves or paths. Since there is only
    Extraction notes

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

    Details

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