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

    ?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.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 for 2 of 2
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    • 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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    Reasons Against

    1 perspective
    Reason against
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    • 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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    Strongest counterpoint
    Explore the most compelling reason on the other side.