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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.
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.

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.

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.
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.

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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Lynch101 and gentzen
Lynch101
Gold Member
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.
It's not a case of looking for a 'higher truth' rather extrapolating the consequences of the individual interpretations. Take the Many Worlds Interpretation (MWI) for example; we might not be able to fully grasp a metaversal structure comprising multiple 'universes' similar to our own, but we can certainly fathom, to some extent, that such a reality is different from a reality where there is only one single universe.

Why do you think that a universe where simultaneity is relative is in any way different from an absolute one? Because it's not.
If you are familiar with [some of] the different interpretations of relativity you can see how a universe where simultaneity is relative is different from an absolute one. A universe where simultaneity is absolute is one where only the present state [of the universe] exists and is the same for all observers. A universe where simultaneity is relative necessitates that past and/or future states co-exist with present states.

There are different interpretations of universes where simultaneity is relative such as the Block Universe (with and without a moving spotlight), the Growing Block Universe, @RUTA's Relational Block Universe, and @PeterDonis's interpretation.

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.
While the mathematics is the same and makes the same predictions, the interpretations say very different things about the universe. In a universe where simultaneity is absolute then there is a fundamental and objective simultaneity, which is true for all observers. Our ability to determine which events are truly simultaneous is a separate issue.

In a universe where simultaneity is relative there is no such fundamental simultaneity, but this itself has consequences. It necessitates that past and/or future states co-exist with present states.

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.
I think you're right about not over-interpreting the mathematics but I think it is important to extrapolate the consequences of different interpretations because that can reveal what the interpretations say about the world we are trying to describe.

If we think of it in terms of a black box. On the left hand side of the black box we have our inputs, on the right hand side we have our outputs. For some, it is sufficient to simply be able to be able to predict what outputs we will get when we have the given inputs. Others however, want to know what happens in the black box. The different interpretations of the mathematics are attempts to say what happens in the black box. By extrapolating their consequences we can probe the models themselves to see what they necessitate. In some cases, this might suggest a possible self-contradiction, while for others it might reveal a contradiction with existing theories. For others still, it might reveal an incompleteness according to the mathematical requirements of the model it is based on.

PeterDonis
Mentor
2020 Award
a generalized Lorentz aether
Please review the PF policy on discussions of LET. You will find it mentioned under "Non-Mainstream Theories" in the terms and rules.

This thread is closed. (Not just because of the LET reference, but because it has gone way off topic for a thread in the QM interpretations forum.)

vanhees71
PeterDonis
Mentor
2020 Award
@PeterDonis's interpretation.
That article of mine did not give an interpretation of relativity (note, relativity, not QM, and this is the QM interpretations forum). It simply refuted a common argument regarding the implications of the relativity of simultaneity (which here refers to the well-known property of Special Relativity that goes by that name, not to any "interpretation" of it). Please do not put words in my mouth when referring to something I have posted.

vanhees71 and Lynch101