Context: Derivations for the relativity formulations for the Lorentz are conventionally\nbased on continuum mechanics. Purpose: This paper derives the\nformulations from a particle perspective. Approach: A non-local hidden-\nvariable (NLHV) approach is adopted, based on the specific particle\nstructures of the Cordus Theory. Findings: The Lorentz and relativistic\nDoppler formulations are shown to be derivable from a NLHV particle perspective.\nUnexpectedly, the equations contain an additional term relating to\nthe difference in the distribution of matter (fabric density) between situations.\nFor a homogenous fabric, which is the assumption of general relativity, the\nconventional formulations are recovered. Originality: The novel contribution\nis deriving the relativistic formulation from a NLHV theory. Also novel is the\nidentification of the fabric density as a term in the Lorentz. Implications: It is\npredicted that inertial frames of reference are only situationally equivalent in\nthe special case where they also have the same fabric density. We find against\nthe cosmological principle with its assumption of homogeneity. The resulting\nsituational theory of relativity has further implications for interpreting gravitational\ninteractions at the galactic scale and larger.
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