= Solution
The <weak equivalence principle> states that freely falling, sufficiently small test bodies have the same motion in a given gravitational field irrespective of composition or <mass>, neglecting their own gravity and nongravitational <forces>. In the Newtonian limit, $m_i\mathbf a=m_g\mathbf g$ makes this universality equivalent to a universal gravitational-to-inertial <mass> ratio, conventionally set to one.
The <Einstein equivalence principle> adds that local nongravitational experiments in a freely falling, nonrotating laboratory have the laws of <special relativity>, independent of the laboratory's position and <velocity>. At an event one can choose a <local inertial frame> with $g_{\mu\nu}=\eta_{\mu\nu}$ and $\partial_\alpha g_{\mu\nu}=0$. A freely falling observer feels no supporting <force>, while a supported observer can model a locally uniform gravitational field by an accelerated laboratory. This explains why freely moving particles follow <timelike geodesics> and <light> follows <null geodesics> when other interactions are negligible.
The locality qualification is essential. The <Riemann curvature tensor> generally remains nonzero; separated freely falling bodies have tidal relative acceleration, measured by <geodesic deviation>. A finite-size experiment can therefore distinguish a curved gravitational field from a merely accelerated coordinate description of flat <spacetime>. Equivalence alone also does not select the complete <Einstein field equations>.
A useful weak-field consequence is the upward <photon> shift $\Delta\nu/\nu\simeq-gH/c^2$ over laboratory height $H$. In an upward-accelerating laboratory the receiver gains recession <velocity> during the <light> flight, giving the same leading redshift. The <Pound-Rebka experiment> tested this with resonant absorption of 14.4-keV <gamma rays> over about 22.5 m. A controlled source <velocity> calibrated the Doppler sensitivity; interchanging source and absorber reversed the gravitational contribution while retaining an intrinsic source–absorber offset. Monitoring their <temperature> difference was essential because lattice-motion shifts could mimic the small signal.<Apparent Weight of Photons by Robert Vivian Pound and Glen Rebka>[pp. 338–340, baseline, velocity calibration, reversed source/absorber positions and temperature corrections]{ref} This verifies a gravitational clock-shift prediction; by itself it is not a unique test selecting <general relativity> over every alternative metric theory.
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