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You should be very careful here in not making the mistake to look for a higher truth in those theories. This is an easy pitfall to fall into. From mathematics we have learned instead to look for how can we describe the same thing equivalently by other means. Analysis of that kind have brought a lot of insight and same should apply for physics.Taking an instrumental approach uses the mathematics to make predictions about what will be observed in experiments. Interpreting the mathematics attempts to go beyond the simple observations to, as you say, differentiate what a theory (and the observations which support the theory) says about nature. It attempts to explain how/why we make the observations we do.

As you alluded to, there are different interpretations of the mathematics of both quantum mechanics and relativity. In both cases, the different interpretations all predict the same observations [in their respective domains]. However, the different interpretations of quantum mechanics tell us very different things about nature, as do the different interpretations of relativity. A universe with 'many worlds' is a very different universe to one where there is only one 'world' where particles move about on pilot waves. Similarly, a universe where simultaneity is relative is a very different universe to one where simultaneity is absolute.

Why do you think that a universe where simultaneity is relative is in any way different from an absolute one? Because it's not. It instead just shows that the concept of simultaneity is a construct of our own making that we impose onto reality, but which is not inherent to it. Why would you think reality needs this concept? where would it use it? In fact, nature itself seems to care about the space time merely in terms of its topological properties and it is we that impose a metric on in when we start measuring it: measuring means mapping objects of reality onto an artificial space build from real-numbers (hmm, the irony is hard to escape here) and it is them which bring the metric structure along which we now can apply back to nature. But this construction should make it clear where any length-measure originates from.

So which of them is closer to a higher truth? neither. If anything it is both of them together show us a truth about our own perceptions and how we chose to model things.

However, you are right in the thought that different theories give us different ideas of generalization whenever we encounter new phenomenon. As such it is most valuable to have many different theories for the same to begin with.Fleshing out these interpretations can allow us to make further deductions about what each model tells us about what type of universe we live in. It's possible that doing so might reveal necessary consequences about different interpretations or perhaps even contradictions that are not otherwise obvious.

There is another way in which the models can be informative. Since the mathematical models follow mathematical rules, it allows us to determine certain necessary requirements with respect to the mathematical models. If our models are indeed complete and representative of nature, it means that nature must correspond to certain necessary requirements. In a sense, the models allow us to go where experiment has not yet gone, or where experiment cannot go. This is, essentially, part of the predictive process.

If we say that nature does not correspond to the necessary requirements of our model, then we conclude that either our model is incomplete or that a different kind of model is required.

For example a generalized Lorentz aether is actually a description that has quite a few more degrees of freedom then GRT which makes it indeed the better staring point for many questions. For example if an aether is allowed to flow in a curl it creates a scenario where the shortest path from A to B is different from B to A (and there might not even exist a path back, if the aether rotation is close to the speed of light), which GRT is unable to represent as this case breaks the metric tensor. But it also reduces the angular momentum of objects rotating along that curl. So in the case of problem understanding the physics of spinning galaxies, a Lorentz aether gives us that additional degree of freedom to reduce the angular momentum of stars just so their behavior fits the otherwise know physics.

But does that mean that GRT must be wrong? not really, because what it really does is to highlights the perspective of each observer over a very complicatedly synchronized shared perspective of simultaneity. It points out the critical property that an observer cannot measure the aether by local means and even globally we can at best only observe the changes to the aether, never its absolute value. So what relativity allows us to do here is to tailor the mathematics best to the case of a single observer to make it the most convenient to use. As such it is a ideal solution for a specific scenario. You could say that an aether approach takes a communist view whereas the GRT is simply egocentric.

Sometimes it is best not to overinterpret mathematics, because more often then not it tells more about us and how we perceive the world, then about the world we describe with it.

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