TL;DR Why does the Einstein equivalence principle imply that all forms of (non-gravitational) energy source curvature? Now, as understand it, the Einstein equivalence principle (EEP) implies (or at least suggests) that gravity is the manifestation of spacetime curvature, the reason being that it is impossible to locally distinguish, through conducting any non-gravitational experiment, between inertial acceleration and acceleration due to the presence of a gravitational field. As a consequence, all non-gravitational forms of energy will fall at the same rate in a gravitational field. This observation suggests that the curved trajectories of energy in a gravitational field is due to geometric nature of spacetime itself, and not due to a force, i.e. spacetime is curved. We know from Newtonian gravity that mass sources gravity and thus, if gravity is the manifestation of spacetime curvature, the presence of mass must curve spacetime. I’ve read that the EEP implies that all forms of non-gravitational energy source curvature, but I don’t understand why this is so? I thought that it was simply due to the consequence of mass-energy equivalence from special relativity that energy sources curvature?! Is the point that the weak equivalence principle neglects other contributions to mass energy (e.g. electromagnetic binding energy) and so in principle it could be that mass sources curvature, but that the electromagnetic binding energies etc. do not, and so would respond differently in a gravitational field. However, the EEP claims that all forms of energy couple to gravity in the same way and so they must also be considered sources of curvature?!