Is the relation between mass and energy universal? (Vol. 49 No.5-6)

The energy of ordinary particles is related to their mass through the famous relation E=mC2, where m is both the inertial and the gravitational mass of the particle. This energy is minimum when the momentum p of the particle is p=0. Things are completely different if the energy is minimum for a momentum p=po≠0. The inertial mass density of a gas of such particles is then ρ=npo2/(3kBT), where n is the density of particles, and T the temperature of the gas. It is not related to the energy density.

Condensed matter gives an example of such particles. Rotons, which are excitations of superfluid 4He, have their energy minimum at a finite momentum. They largely contribute to the inertial mass density of the “normal fluid” in the two fluid model of superfluid 4He. Nothing similar has been evidenced, up to now, within the cosmological particles, but one can raise the question: would the gravitational mass be related to the energy or the inertial mass? Assuming that gravitational and inertial mass densities are the same gives for the gas of such particles properties close to those expected for Dark Energy. This work is a discussion about these questions.

B. Castaing, What is the gravitational mass when energy and inertial mass are not equivalent?, EPL 123, 20003 (2018)