Georgina,
and there-in lay the crux of the matter. Yes, take away enough energy and atomic structure not only ceases moving, it behaves as if each atom is identical to the others (theoretically). and etc., no quibble from me.
But that brings us back to the point of energy being associated with matter not the stuff matter is made of. And we are stuck with that if we adhere strictly with deductive reasoning because logically we cannot point to an observable proof.
That is the fall-back argument for the QM methodology, and realists have yet to come up with an experimental protocol that solves the naive problem that; If e=mc^2, and a proton at rest or at less than relativistic velocity behaves as a measurable mass but behaves as a measurable energy quantity at relativistic velocities, how do we get a square proportion of equivalence from one magnitude of light velocity acceleration? What's the matter? If it's made of energy, then how does the action of accelerating it to light velocity result in that square proportional increase?
I am personally of the persuasion that energy is the stuff of matter and electric, magnetic and gravitational fields are distinctive behavioral characteristics of density ranges each being a c magnitude of difference. A greater density magnitude will exhibit the characteristic of lesser densities but not vice-versa. But strictly speaking under pain of penalty of scientific discipline, I have no proof. It is and will likely remain, my preferred choice of paradigm. :-) jrc