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    Arbitrary particles (not just freely falling ones) must b... — Carmelics
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    Home/Skepticism
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    Arbitrary particles (not just freely falling ones) must be used in the axioms that establish the local differential structure of spacetime

    SkepticismTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The set of freely falling particle paths P_f can only be properly characterized after a coordinate system (differential structure) is available
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    • 2.To constructively establish the projective structure of spacetime, one must single out P_f from the broader set P
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    • 3.Since P_f presupposes differential structure, one cannot use P_f in the axioms that ground that very structure
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    Reasons Against

    2 perspectives
    Reason against 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).
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    • 2.Reichenbach and Ehlers-Pirani-Schild demonstrate that P_f can be operationally identified through coincidence observations requiring no prior differential structure.
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    • 3.If physical observables can fix a class of trajectories pre-coordinately, circularity in the supporting argument is avoided without invoking arbitrary particles.
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    Reason against 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.
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    • 2.The move from P_f to arbitrary P introduces underdetermination: distinct incompatible differential structures may satisfy axioms built on unconstrained particle paths.
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    • 3.A more parsimonious foundation using only geodesic paths avoids this underdetermination, making arbitrary particles epistemically costlier, not less presuppositional.
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    Related

    A more parsimonious foundation using only geodesic paths avoids this underdeterm...Freely falling paths are empirically distinguishable prior to any coordinate sys...If physical observables can fix a class of trajectories pre-coordinately, circul...Reichenbach and Ehlers-Pirani-Schild demonstrate that P_f can be operationally i...
    +5 moreShow less
    Since P_f presupposes differential structure, one cannot use P_f in the axioms t...The move from P_f to arbitrary P introduces underdetermination: distinct incompa...The set of freely falling particle paths P_f can only be properly characterized ...To constructively establish the projective structure of spacetime, one must sing...Weyl's own axiomatic program in Raum-Zeit-Materie shows projective structure can...

    Similar

    The set P_f of freely falling particle paths cannot be used to establi...83%The set of freely falling particle paths P_f can only be properly char...79%The local differential topological structure of spacetime is common to...78%To determine the projective structure of spacetime (and thus its geode...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: weyl
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    It is important to emphasize that the members of \(\mathcal{P}\) represent possible or actual paths of arbitrary massive particles that may have some internal structure such as higher order gravitational and electromagnetic multipole moments and that may therefore interact in complicated ways with various physical fields. In order to constructively establish the projective structure of spacetime, it is necessary to single out a subset of \(\mathcal{P}\), namely \(\mathcal{P}_{f}\), the set of po
    Extraction notes

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

    Details

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