My motivations for asking this question are philosophical but I think this is a question that is best answered by the physics community.
There is a problem in the philosophy of science called the 'underdetermination' problem. There are two versions.
One is the idea that for any set of data, theory choice is underdetermined. There could be multiple theories which explain the data in the same way and we don't yet have the ability or the data required to choose between them on completely empirical grounds.
This is the idea that two theories could predict exactly the same thing in all situations but use different unobservable entities to explain it.
As far as I know (early on in the process at least) Lorentzian interpretation of SR vs Einstein's interpretation of SR could be compared in this way. Both made similar or the same predictions but many favoured SR in terms of its simplicity, not having to posit the existence of an unobservable ether. (Obviously later the empirical differences were evaluated and the ether theory had to be modified to account for its failed predictions and slowly lost favour but these empirical considerations aren't really the point of this post).
There are three main questions from this:
What are the main criteria that physicists approach when deciding between two theories that make the same predictions or which have yet to be decided up on experimentally?
Is it even possible to construct empirically identical theories which posit different unobservable entities to explain phenomena? Is there any reason to believe that this is impossible?
In practice, does this ever actually happen?
P.s. It seems as though the conflict between the Lorentzian and Einsteinian interpretations (at least early on) was an example of this but I may have some details about the history of these ideas wrong. As far as I know, the Lorentzian interpretation was able to be modified to fit with experimental failures but was later rejected on the grounds that it was much more complex (I assume this means it required many additional assumptions?) and therefore was rejected by the community at large.
It does seem however that both interpretations posit some unobservable thing. In the Lorentzian case, it seems as though he outright assumes the existence of an ether. In the Einsteinian case, there is some unobservable warping of space time. I say this warping is unobservable because you can only observe the effects of it, though this may also be wrong. So if anyone wants to clear up any misunderstanding I have about the important differences between the ether and Einstein's idea of spacetime warping, please do. Similarly, if I'm wrong to say that only the effects of spacetime warping can be observed, please correct me. Although, at this moment in time, I don't know what it would mean to directly observe the warping of spacetime since spacetime is the canvas on which we make observations??
The tag 'popular-science' is here because I'm not studied in theoretical physics very much. I have just completed A-level physics (somewhere in between high school and university by US standards) and wish to study theoretical physics at university which is why I find the problem so interesting and I used the Einstein vs Lorentzian argument as the example for this question because during my study I did a report about this argument and about simple derivations of Lorentz transformations etc... so it's an argument that I'm more familiar with than others.
I suppose a similar debate would have been during he original development of kinetic theory as kinetic theorists posited the existence of atoms which were unobservable at the time in order to explain certain phenomena which could have been explained with some other kind of unobservable (maybe, I don't know)?