  The geometrical formulation of gravity is not unique and can be set up in a
variety of spacetimes. Even though the gravitational sector enjoys this freedom
of different geometrical interpretations, consistent matter couplings have to
be assured for a steady foundation of gravity. In generalised geometries,
further ambiguities arise in the matter couplings unless the minimal coupling
principle (MCP) is adopted that is compatible with the principles of
relativity, universality and inertia. In this work, MCP is applied to all
Standard Model gauge fields and matter fields in a completely general (linear)
affine geometry. This is also discussed from an effective field theory
perspective. It is found that the presence of torsion generically leads to
theoretical problems. However, symmetric teleparallelism, wherein the affine
geometry is integrable and torsion-free, is consistent with MCP. The
generalised Bianchi identity is derived and shown to determine the dynamics of
the connection in a unified fashion. Also, the parallel transport with respect
to a teleparallel connection is shown to be free of second clock effects.
