= Solution
The <weak equivalence principle> is universality of <free fall> for sufficiently small test bodies, independent of composition, when non-gravitational forces and self-gravity are negligible. Equality of inertial and passive gravitational <mass> makes this possible in the Newtonian limit. The <Einstein equivalence principle> adds <local Lorentz invariance> and <local position invariance> for nongravitational experiments: a small freely falling laboratory has the local physics of <special relativity>.
This motivates a universal <spacetime metric>. Freely falling unforced test particles follow <geodesics>, $u^\nu\nabla_\nu u^\mu=0$. At a point one can choose local inertial coordinates with vanishing connection, but curvature and tidal relative acceleration remain measurable over a finite region. Gravity cannot be transformed away globally. A uniformly accelerating small laboratory and a local gravitational field can have the same nongravitational experimental behaviour without having identical global geometry.
Clock comparisons predict a fractional rate difference of order $g\Delta h/c^2$ in a weak static field. The <Pound-Rebka experiment> tested the associated <photon> <redshift> through resonant gamma-ray emission and absorption at different heights, using controlled Doppler shifts to match the tiny <energy> displacement. Such a result tests the metric <redshift> prediction, not uniquely every component of the gravitational field equations.<Apparent Weight of Photons by Robert Vivian Pound and Glen Rebka>[1960 laboratory gravitational-redshift measurement]{ref}
<general relativity> adds the dynamical <Einstein field equations>,
$$
G_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}.
$$
The <equivalence principle> alone does not derive this unique equation; assumptions about covariance, dynamics and the Newtonian limit are also needed. The <strong equivalence principle> extends the universality claim to self-gravitating systems and gravitational experiments. Alternative metric theories can satisfy the weaker local principles while differing in gravitational dynamics, so composition tests, clock/<redshift> tests and self-gravity tests probe distinct claims.
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