Physics and reality
TL;DR: Physics is about making models about experimentally accessible parts of reality, therefore the limitations on modelling and on experimental verifiability are part of the foundations of physics
I have often been puzzled by the realism vs anti-realism debate in the philosophy of physics. From what I understand, which is not very much, after years of being exposed to the debate, realists posit that the objects of physical theories represent entities that “really exist” in the physical world, while anti-realists do not. The issue is that, like many physicists and engineers, I think that physical theories are models of the real world. So, in a sense, both positions are right… or wrong. The bigger problem, however, is that the framing of the debate distracts us from what I think are more important issues in the philosophy of physics.
Imagine the set of all the things that exist. Or at least, of all the things that you think exist. This would include things like God, or gods, angels, parallel universes, hidden variables, life after death, and so on. That is, it would include things that we have no direct experience of. Let us call it metaphysical reality, to the possible objection of some philosophers. Since science is about empirical confirmation, none of those objects can be the subject of science. Note that this is a limitation of science itself: it cannot tell us anything about those objects.
A subset of metaphysical reality is the set of things we can interact with through our senses. We can see them, touch them or lick them, if you are so inclined. Let’s call this physical reality. This is a step further, but it is not enough. For example, I can percieve my own consciousness and you can percieve yours, but we cannot percieve each other’s. Given that science needs to be testable by everybody, this is a problem. Moreover, we can hear whether a joke is funny or not, but this will change depending on the setting and on how many times I have already heard the same joke. Given that repeatability is a requirement in science, this is also a problem. In the realm of physical reality, then, we can write the history of the world, discuss the arts, but not necessarily write laws about revolutions or creativity.
A subset of physical reality consists of those objects that can be repeatedly prepared and measured. Let’s call this empirical reality. These are the objects that can be studied scientifically. These are real, in the sense that they exist around us: we can prepare them in a lab, we can describe them, we can use them to create artifacts, like the one you are using right now to read this text, that behave in a reliable way. Since physical laws are experimentally testable relationships, they can only be describing those objects that belong to the empirical reality. This is, ultimately, why we do not have laws about gods or Napoleons.
The physical theories themselves, however, are not made of matter. They are represented by abstract symbols that we write on a piece of paper. When we do that, we make approximations, we take limits, so that our description is manageable. For example, we may assume that the system is perfectly isolated even though we know it is not possible (e.g. you can’t remove gravitation). We assume that friction of the pendulum is small enough such that it can be disregarded. Sometimes, we even introduce objects, like potentials, that are not physically defined but make the mathematics easier. That is, the symbols of our theories describe idealizations of the physical reality. They describe things, like ideal gases or perfect measurements, that do not really exist.
In light of this, realism vs anti-realism seems like a false dichotomy. Clearly, there are things out there that we call protons… and we can model them as single quantum systems with their own wave-function. But, clearly, the wave-function is a model, which will cease to apply if, for example, we perform deep inelastic scattering and probe the internal structure of the proton. Moreover, if I am studying the motion of planets, a full description in terms of fundamental particles is not only impossible, but utterly useless to understand what is going on. Therefore, it is not necessarily true that a model that describes the reality more faithfully is necessarily better.
But note that, in our silly model, we uncovered two important things. First of all, there are requirements that objects have to satisfy to be amenable to a scientific description. They need to be experimentally accessible and they need to be reliably reproducible. We can show that those requirements map to the actual mathematical structures (e.g. topologies, sigma-algebras, convex spaces, geometric spaces, … ) that are in our theories. That is, many fundamental features of our physical theories do not describe reality at all, but the requirements of scientific investigation: we see what we see because that’s what can be seen through the lenses of science. Second, the idealizations play a major role in allowing us to write formal theories of empirical reality. In fact, I do not think it is possible to write a formal theory without idealizations. If requirements and idealizations play such a crucial role in our physical theories, then they should play a crucial role in our understanding and/or improvement of said theories.
The question, then, is not whether physical theories represent reality or not. It is understanding how requirements and idealizations create a bridge between reality (i.e. empirical objects) and fiction (i.e. the idealized formal objects).