When listing energies for the purposes of keeping track of conservation, or when writing down a Laplacian for a given system, we blithely intermix mass-energy, kinetic energy and potential energy; they are all forms of energy, they all have the same units, and so this looks OK. For example, in the LHC, turning kinetic energy into new particles of mass-energy is routine. We just converted "energy which does not gravitate" (kinetic energy) into "energy which does gravitate". Isn't it a bit peculiar that this same thing called energy can manifest into two different kinds of forms – those forms which gravitate, and those which do not?
How about potential energy? It would be of course ridiculous to calculate your potential in relation to the galactic centre and expect that huge (negative, by convention) quantity of energy to gravitate; and yet if we allow its conversion into kinetic energy, and thence into particle creation, lo and behold we end up with something that does gravitate.
We know that the massless photon gravitates, because it can be "bent" around a star, per GR. A photon also expresses energy in the form E = p c. So clearly finite rest mass is not a requirement for certain forms of energy to gravitate.
So what's the rule here? When does energy gravitate, and why? Isn't it all supposed to be "just energy"?
Then there's the flip side of the equivalence principle – inertia. Do fields have inertia? – they do gravitate, so if they possess no inertia, doesn't that break EEP?
Best Answer
This is a topic many get confused on. Energy(more specifically, the energy-momentum tensor, but in non-relativistic cases, the momentum is negligible compared to the energy aka rest energy + kinetic energy) is what gravitates, NOT mass, a common misconception. If fields carry energy(such as electromagnetic fields), then they gravitate.
ALL types of energy(the non-potential forms, at least) gravitate. According to General Relativity, the current widely accepted theory of gravitation, gravitation is coupled to the energy momentum tensor, which basically includes all forms of energy including contributions from momentum, pressure, rest energy, stress, and kinetic energy. However potential energy is not included in the energy momentum tensor so is non gravitating. So take your example, in LHC, the 'kinetic energy' does gravitate and the mass also gravitates, so there's no change in 'degree of gravitationess'. Note that on such small scales, gravitation is so small that its highly negligible.
Now, I don't think it would be meaningful or is aware of any general definition of inertia for fields, so I suppose it doesn't exist. Answering your question: an equivalent formulation of the EEP is that on local scales, acceleration is indistinguishable from gravitation. As long as the field behaves this way, then it doesn't break the EEP.