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    Tidal force detection requires measuring relative acceler... — Carmelics
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    Challenges→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).

    Tidal force detection requires measuring relative acceleration across finite separation—but 'local' effects cannot rigorously extend to multiple spacetime points without coordinate embedding.

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    Key Terms

    Coordinate embedding(as used in mathematics and physics)
    A mathematical system that assigns numbers (coordinates) to points in space to describe their locations and relationships.
    Finite separation(as used in physics and mathematics)
    A measurable, limited distance between two points—as opposed to zero distance or infinite distance.
    Local (in physics)(as used in physics and relativity)
    Confined to a single point or small region in space, without involving distant locations.
    Relative acceleration(as used in physics)
    How quickly the speed or direction of one object changes compared to another object, rather than compared to a fixed point.
    Spacetime(as one criterion for whether something is physically real)

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    A physics concept combining space (location) and time into one continuous system—basically, every physical object exists somewhere at some moment in time.
    Tidal force(as used in physics and relativity)
    The difference in gravitational pull across two points separated by some distance—like how the Moon pulls slightly harder on the near side of Earth than the far side, causing ocean tides.

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