I am not sure that things are so simple. Let me take as an example the hydrogen molecule H2. Suppose that in the reference frame at rest I have a Hamiltonian H which describes interaction between 2 protons and 2 electrons. I can find the ground state of this Hamiltonian and calculate the equilibrium distance R between two protons. If my theory is fully relativistic, I should be able also to write the electron-proton Hamiltonian H', which is valid in the moving reference frame. (Note that H and H' must be different.) I can also find the ground state for H', and thus determine the equilibrium distance R' in the hydrogen molecule from the point of view of the moving observer. Now, your claim is that R and R' will be related exactly by the Einstein's length contraction formula. I am not convinced.I'm not sure I understand what you're saying here. Are the "relativistic" "dynamical" theories you're talking about formulated in the framework of special relativity or not? (See my previous post for a clarification of what I mean by the "framework"). If they are, then this is all very trivial. One of the things that such a theory of inter-atomic forces would tell us is that the length of the moving rod can be calculated by calculating its rest length and doing a Lorentz transformation.