The Equivalence principle was the formalism to the assumption of the "the equivalence of gravitational and inertial mass".
However, was there an "Equivalence principle" for the energy of the different systems, i.e. the mechanical energy(gravitational energy/potential), the chemical energy(electromagnetic energy/potential), and the energy involved in the strong and weak interaction? or just the energy between two different thermal reservoir?
How did they knew or assume that the energy in a system/theory, sometimes could be viewed as an eigenvalue or a Lagrangian multiplier(very similar to the usage of the renormalized mass in some cases), was "equivalent" to the energy a different system/theory? For example, according to the Wikipedia the "Tests of the weak equivalence principle" was still being performed, but had any experiments done to show the "equivalence" of the energy?
