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
    The projective structure is an appropriate geometric fiel... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Causation
    HistoryEditSee Inverse

    The projective structure is an appropriate geometric field for defining zero 3-acceleration.

    Causation
    ?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.The transformation law of the projective structure has the same inhomogeneous form as the transformation law of 3-acceleration.
      ?

      Think about whether this reason is strong or weak

    • 2.The projective structure depends only on spacetime location and 3-velocity, both of which are independent of 3-acceleration, as required for a well-defined standard.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The projective structure presupposes a prior affine connection to be defined, making it explanatorily circular as a ground for inertial standards.
      ?

      Think about whether this reason is strong or weak

    • 2.Weyl's own 1918 gauge program shows that projective and conformal structures together determine the affine structure, so projective structure alone underdetermines zero acceleration.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.Malament and Weatherall have shown that geodesic motion is derivable from field equations, making an independent projective standard for zero acceleration redundant.
      ?

      Think about whether this reason is strong or weak

    • 2.A geometric field that varies with 3-velocity cannot serve as a frame-independent standard, since 3-velocity is itself observer-relative in relativistic spacetimes.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Topics

    CausationTruth & Knowledge

    Connections

    1 topic

    Modality & Possibility1 linked

    Related

    A geometric field that varies with 3-velocity cannot serve as a frame-independen...Malament and Weatherall have shown that geodesic motion is derivable from field ...The projective structure depends only on spacetime location and 3-velocity, both...The projective structure presupposes a prior affine connection to be defined, ma...
    +2 moreShow less
    The transformation law of the projective structure has the same inhomogeneous fo...Weyl's own 1918 gauge program shows that projective and conformal structures tog...

    Similar

    The projective structure depends only on spacetime location and 3-velo...83%A geodesic directing field (guiding field / projective structure) must...82%The projective structure provides such a standard by supplying the mis...81%There must exist a geometric structure field — the inertial structure ...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: weyl
    View source passageHide passage
    The above argument for the necessity of geometric fields also holds for 3-velocity and 3-acceleration, denoted respectively by \(\xi^{\alpha}_{1}\) and \(\xi^{\alpha}_{2}\). The transformation law for the 3-acceleration is much more complicated than that of the 4-acceleration. However, analogous to the case of 4-acceleration, the transformation law of 3-acceleration is linear and is inhomogeneous in the 3-acceleration variable \(\xi^{\alpha}_{2}\). Consequently, there does not exist a unique s
    Extraction notes

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

    Details

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