Einstein generalized this to the Equivalence Principle, which says (roughly) that a gravitational field is equivalent to an accelerating reference frame. It is sometimes expressed as the equivalence of gravitational and inertial mass, namely that objects with the same inertia (resistance to acceleration) experience the same gravitational force. This is the foundation of General Relativity.
Weak EP: Local test masses vacuum free fall along identical (parallel) trajectories independent of composition and internal structure. Inertial and gravitational masses are fundamentally indistinguishable.
The major footnotes are falling light
http://arXiv.org/abs/gr-qc/9909014 Amer. J. Phys. 71 770 (2003)
Phys. Rev. Lett. 92 121101 (2004)
plus gravitoelectric and gravitomagnetic effects (e.g., frame dragging, Lense-Thirring effect). Hyper-bound, hyper-spinning, hyper-magnetized, superconducting neutronium - as in binary pulsars - orbits by the book.
However... One can totally ignore the Equivalence Principle and obtain wholly different maths that sum to an indistinguishable theory of gravitation - prediction vs. observation - with
one exception. In Weitzenb?ck's teleparallel spacetime, opposite parity mass distributions fall differently. Einstein vs. Weitzenb?ck can be tested,
http://www.mazepath.com/uncelal/qz3.pdf Only one of them can be correct. Einstein is the less inclusive case. Somebody should look.
