While special relativity says inertial mass is equivalent with energy, there are at least two more types of mass, for which equivalence seems not so certain - let me briefly summarize and ask for more arguments for/against their equivalence.

Gravitational mass is hypothesized to be equal by equivalence principle, and gravitational interaction of antimatter now seems nearly certain to be the same (?) However, all these tests are for baryons and bulk matter made of them, for non-baryons I am aware only of this 1967 Witteborn, Fairbank test for electron - measuring maximal time for thermal electrons reaching upper electrode tmax=sqrt(2h/g), which turned out infinite, suggesting g=0. But later it was explained as due to gravitational charge gradient in shielding, so seems experimentally we still don't know (good slides).

de Broglie clock, zitterbewegung - e.g. relativistic QM requires E=mc^2 for psi ~ exp(-iEt/hbar). For electron it was directly confirmed ( https://link.springer.com/article/10.1007/s10701-008-9225-1 ) by observing increased absorption of 81MeV electron beam when agreeing with spatial lattice of crystal, however, they got 0.28% disagreement. The same oscillation formula was used to introduce 3 masses based on neutrino oscillations, but experimental confirmation they are equivalent to energy seems quite difficult (maybe GERDA?)

Are there some more arguments they are equal or not? Past and future experiments to improve the situation?

What about negative mass and effective mass ?

Seems we need negative Hamiltonian terms to explain why resting electron and neutrino are oscillating - making them https://en.wikipedia.org/wiki/Time_crystal , and such often automatically appear (e.g. https://arxiv.org/pdf/2501.04036 )

In effective descriptions they might need negative energy virtual particles, but are they also used as non-effective?

35 minutes ago, Duda Jarek said:

Seems we need negative Hamiltonian terms to explain why resting electron and neutrino are oscillating - making them https://en.wikipedia.org/wiki/Time_crystal , and such often automatically appear (e.g. https://arxiv.org/pdf/2501.04036 )

In effective descriptions they might need negative energy virtual particles, but are they also used as non-effective?

Not sure why time crystals imply other types of mass ?

Examples of what I was thinking of are Stokes' bubbles, electron and hole mobilities in ordinary crystals, the anomalous Hall effect.

While your examples seem just reduced energy, time crystals are objects oscillating in the lowest energy state, which corresponds to kinetic energy so energy minimization usually kills it ...

But somehow electron and neutrinos do it it - we should try to understand, and it seems to require negative terms in Hamiltonian - in perturbative approximation using negative energy virtual particles.