In Philosophy of Physics: Quantum Theory, Tim Maudlin says the following:
A physical theory should clearly and forthrightly address two fundamental questions: what there is, and what it does. (Introduction, p. XI)
As far as I can tell, describing what it does focuses on the observed effects of matter in motion. Describing what there is focuses on the causes, whether observable or unobservable, that in turn explain the effects.
So one question I have about what seems to be the generally accepted position by at least some, if not many, scientists is, how can mathematical descriptions comprised of abstract mathematical objects representing what it does in a physical theory also be representations of what there is, i.e., actual concrete physical objects, or at least nonphysical objects that somehow are able to morph into physical objects?
I think by using the wave function as an example I can best illustrate where I’m headed with this question. The wave function–an abstract mathematical object in a physical theory–seems also to be equated to some form of an actual concrete physical object, or at least a nonphysical object that somehow morphs into a physical object.
But what’s the underlying reason for such an idea that prima facie seems odd at best? To my understanding the wave function is used in a physical theory, along with other abstract mathematical objects representing amounts and measurements, to answer questions about what it does.
So what then explains how in a physical theory it can be thought to transition, as it were, from the expression of a quantitative description of what it does in terms of an abstract mathematical object, into an expression of a qualitative description of what there is in terms of a concrete physical object, or at least be able to morph into one?
To me this seems like a rather extreme position that calls for some pretty weighty evidence. Now I’m not suggesting in the case of unobservables, as the scientific antirealist seems to, that there is no cause, or that we cannot know what it is. And unlike the pragmatist, I don’t think brushing such issues aside as nonessential is satisfactory.
I simply hold to what could be referred to as metaphysical realism, that through abductive reasoning of following the evidence where it leads knowledge to a reasonable degree of certainty can be determined about unobservable physical causes.
But what is the argument for what at least some scientific realists seem to claim that in physical theories abstract mathematical objects somehow equate to concrete physical objects? The only argument I’m aware of that could possibly be used as support is that the success of the theory regarding what it does in terms of abstract mathematical objects supports the position of equating it to what it is in terms of concrete physical objects.
But on its own that doesn’t seems like sufficient grounds for justifying such an extraordinary position, especially when considering empirical equivalence where there can be two or more theories with equally successful yet unique mathematical formulations that, as far as I can tell, sometimes have some shared elements, yet sometimes none at all.
Setting aside idealism, is there any other support for this position that I’m not aware of? Or could it be that I’m getting the wrong impression in the first place about a significant amount of scientists today holding in some way to this seemingly extraordinary position? Or could it be that maybe it’s just not something that most scientists even concern themselves with?