CONTEXT: Derivations for the relativity formulations for the Lorentz are conventionally based on continuum mechanics. PURPOSE: This paper derives the formulations from a particle perspective. APPROACH: A non-local hidden-variable (NLHV) approach is adopted, based on the specific particle structures of the Cordus theory. FINDINGS: The Lorentz and relativistic Doppler formulations are shown to be derivable from a NLHV particle perspective. Unexpectedly the equations contain an additional term relating to the difference in the distribution of matter (fabric density) between situations. For a homogenous fabric, which is the assumption of general relativity, the conventional formulations are recovered. ORIGINALITY: The novel contribution is deriving the relativistic formulation from a NLHV theory. Also novel is the identification of the fabric density as a term in the Lorentz. IMPLICATIONS: It is predicted that inertial frames of reference are only situationally equivalent in the special case where they also have the same fabric density. We find against the cosmological principle with its assumption of homogeneity. The resulting situational theory of relativity has further implications for interpreting gravitational interactions at the galactic scale and larger.