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    Home/Original/inverse
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    Inverse View

    It is not the case that Misner, Thorne, and Wheeler's treatment in Gravitation establishes that the vanishing of the absolute derivative of the 4-velocity is an invariant, frame-independent condition defining free fall.

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    Reasons For

    1 perspective
    Reason for
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    • 1.The claim conflates the mathematical definition of a geodesic with the physical definition of free fall; they may not always coincide in curved spacetime boundaries.
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    • 2.MTW's treatment presupposes a smooth spacetime manifold; near singularities or in quantum gravity contexts, this condition may fail to define free fall invariantly.
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    • 3.Defining free fall solely by covariant derivative vanishing excludes tidal forces and observer-dependent notions of 'force,' potentially oversimplifying the concept.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The covariant derivative (absolute derivative) is constructed to be tensor-valued, ensuring its vanishing is a frame-independent geometric fact, not coordinate-dependent.
      ?

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    • 2.Free fall as geodesic motion is the foundational principle of general relativity; MTW rigorously derives this from the vanishing covariant derivative of 4-velocity.
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    • 3.MTW's treatment connects this invariant condition to the equivalence principle, showing why freely falling observers experience no force regardless of reference frame.
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