 Solution

inertial mass sets the response to force, $\mathbf{F}=m_i\mathbf{a}$. Passive gravitational mass sets the response to a given gravitational potential, ${\mathbf{F}}_g=-m_g\nabla \Phi$; active gravitational mass describes a body's gravitational sourcing. Universality of the passive-to-inertial mass ratio makes freely falling trajectories independent of composition. torsion balance comparisons and differential free-fall experiments test this weak equivalence principle by searching for composition-dependent acceleration, with environmental forces and instrumental asymmetries controlled.

The Einstein equivalence principle further says that local nongravitational experiments in a freely falling laboratory obey special relativity, independent of the laboratory's location and velocity. A local inertial coordinate system can remove Christoffel symbols at one event, but cannot remove a nonzero Riemann tensor throughout a finite region. Relative acceleration of separated freely falling particles reveals tidal gravity. Thus a uniformly accelerating laboratory in flat spacetime can mimic a local gravitational field, while extended tidal measurements distinguish genuine curvature. Equality of the measured mass responses does not make every gravitational field globally equivalent to acceleration.