I would say there is no way to predict experimental outcomes than mathematics. But "expressing physics" can be rather different. For example, how many times have we asked ourselves, "I see that the mathematics works out this way, but I want a physical explanation." Indeed, I have found that asking myself for a physically motivated explanation has often led to key insights. If one says "there's nothing but the mathematics," then special relativity reduces to "the Lorentz transformation with the Einstein simultaneity convention," and that's it, done-- all the invariants follow, all the experimental outcomes are extended to all SR frames. So we would never need to mention "length contraction," or "time dilation", or the "relativity of simultaneity", for none of those things are necessary if we have the Lorentz transformation. But we do mention those things-- because they give us a sense of something physical that is going on. It can be problematic, to be sure-- but we seek the physical explanation all the same. You simply drop the uniqueness requirement-- you don't imagine that you are looking for "the" physical explanation, only "a" physical explanation. So you say "let's look at the situation from the point of view of observer X, how do they account for what is going on?", and we look for a physical language that translates the mathematics into more everyday terms, from that perspective. If the observer is in the initial rocket frame, we say the rope length contracts and can no longer span the constant distance between rockets. If the observer is on the rope, we say the lead rocket burns fuel faster and accelerates more. If the observer is in the eventual inertial frame of the coasting rockets, we say the lead rocket took off first. Each of these explanations sounds like everyday language, so they give us a sense of physical understand that goes beyond "the mathematics works out that way." I would say we do answer "why" questions all the time (why is the sky blue, why does the rope break, why does light bend in a lens, etc.), but we do not answer them uniquely. It's what we mean by an explanation. The mathematics of a chosen theory is unique, but the explanations are not.