Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Arbitrary particles (not just freely falling ones) must be used in the axioms that establish the local differential structure of spacetime

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Freely falling paths are empirically distinguishable prior to any coordinate system via local inertial effects (e.g., absence of tidal forces in Einstein's equivalence principle).
      ?

      Think about whether this reason is strong or weak

    • 2.Reichenbach and Ehlers-Pirani-Schild demonstrate that P_f can be operationally identified through coincidence observations requiring no prior differential structure.
      ?

      Think about whether this reason is strong or weak

    • 3.If physical observables can fix a class of trajectories pre-coordinately, circularity in the supporting argument is avoided without invoking arbitrary particles.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Weyl's own axiomatic program in Raum-Zeit-Materie shows projective structure can be recovered from geodesic paths constrained by symmetry axioms alone.
      ?

      Think about whether this reason is strong or weak

    • 2.The move from P_f to arbitrary P introduces underdetermination: distinct incompatible differential structures may satisfy axioms built on unconstrained particle paths.
      ?

      Think about whether this reason is strong or weak

    • 3.A more parsimonious foundation using only geodesic paths avoids this underdetermination, making arbitrary particles epistemically costlier, not less presuppositional.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The set of freely falling particle paths P_f can only be properly characterized after a coordinate system (differential structure) is available
      ?

      Think about whether this reason is strong or weak

    • 2.To constructively establish the projective structure of spacetime, one must single out P_f from the broader set P
      ?

      Think about whether this reason is strong or weak

    • 3.Since P_f presupposes differential structure, one cannot use P_f in the axioms that ground that very structure
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.