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    To determine the projective structure of spacetime (and t... — Carmelics
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    Challenges→Determining which particles are free requires prior knowledge of the geodesics of spacetime, but determining the geodesics of spacetime requires prior knowledge of which particles are free, resulting in an unavoidable circularity.

    To determine the projective structure of spacetime (and thus its geodesics), one must use free particles.

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    Determining which particles are free requires prior knowledge of the geodesics o...The only way to know that no forces act on a body is to observe that it moves as...Without already knowing the geodesics or the projective structure of spacetime, ...

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    The problem is a familiar one; how to introduce a class of preferred motions, that is, how to characterize that particular path structure that would govern the motions of free particles \(\mathcal{P}_{f}\), that is, neutral, spherically symmetric, non-rotating test bodies, while avoiding the circularity problem surrounding the notion of a free particle: The only way of knowing when no forces act on a body is by observing that it moves as a free particle along the geodesics of spacetime. But how,

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