Abstract
We argue that the geometry of spacetime is a convention that can be freely chosen by the scientist; no experiment can ever determine this geometry of spacetime, only the behavior of matter in space and time. General relativity is then rewritten in terms of an arbitrary conventional geometry of spacetime in which particle trajectories are determined by forces in that geometry, and the forces determined by fields produced by sources in that geometry. As an example, we consider radial trajectories in the field of a single particle expressed in the spacetime of special relativity.
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Roxburgh, I.W., Tavakol, R.K. Conventionalism and general relativity. Found Phys 8, 229–237 (1978). https://doi.org/10.1007/BF00715209
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DOI: https://doi.org/10.1007/BF00715209