There is lots of mathematical evidence that every quantum state maps 1-to-1 on a physical state¹, or at least be uniquely determined by the physical state². The main assumption both make is that there is some physical state.
So it doesn't really matter if it's a map or not - it tells you something about the territory.
I'm not sure what your point is, but it doesn't have to be hidden and in this case, objective just means two parties agree on the outcomes of experiments.
At some level, if we take scientific theories seriously as descriptions of the world out there, and not merely tools for prediction, then we have to assume some sort of isomorphism between the map (our theory) and the territory (the world), even if they're not the same thing. This isn't only for quantum theory.
> we have to assume some sort of isomorphism between the map (our theory) and the territory (the world)
But a mathematical model != a theoretical model. The very same mathematical model will be compatible with uncountably many theoretical models. (By 'theoretical model' I mean something like 'an interpretation of what the math is representing'.)So you can't read off theoretical structure from mathematical structure. And so you can't read off the structure of the world from mathematical structure.
> (By 'theoretical model' I mean something like 'an interpretation of what the math is representing'.)So you can't read off theoretical structure from mathematical structure. And so you can't read off the structure of the world from mathematical structure.
Occam's razor favours a theoretical model that corresponds more closely to the mathematics, rather than one that adds a bunch of epicycles to arrive at a different interpretation. If you follow your logic then you can never reject geocentrism, because it's possible to create a geocentric model that generates the same predictions as a heliocentric one; nevertheless we would generally say that heliocentrism is "more true" and "more physically real" than geocentrism.
Physics tends to be simpler than we originally thought, and Occam's razor correctly predicts this: electricity, magnetism, and light turn out to be facets of the same phenomenon, electricity and the nuclear forces turn out to conform to the same theory, electromagnetism, gravity, and spacetime turn out to behave in the same way. Your link's lazy "11 dimensions! OMG!!!1one" non-argument is in no way an adequate refutation of that history.
You're cherry picking. You pick the places where Occam's razor picks the correct answer and ignoring all the places it doesn't. For any new situation we can't predict which of those possibilities the answer will fall. Hence my statement that Occam's razor has no predictive powers.
I just linked to the first article I found that talked about the subject. And it's interesting that you look for something lazy instead of addressing more serious issues like Newton's model vs Einstien's. Very clearly the (much!) more complex answer is more correct than the simple one. Here's [1] another link discussing the issue and gives 2 examples.
But what does 'corresponds more closely to the mathematics' mean? The relevant point is just that the mathematics, alone, doesn't settle the theoretical question.
In general, it's hard to use Occam's razor in a non-question-begging way.
Well, the mathematics describes reality. If humans can't agree about whether one way of interpreting the mathematics in human terms is more or less complex than another way of doing so, then that's a human problem and potentially insoluble. But I don't think things are actually that bad: people are generally capable of reaching consensus about what a given piece of mathematics "means", and the relevant cases here are pretty clear-cut: either we interpret the wavefunction as being physical reality, or we interpret some derived structure as being physical reality, and the latter gets us further away from the wavefunction.
Isomorphism, yes, exactly—that's the basic principle of a map: it's a description that enables us to make predictions about the territory, because it's possible to put the two into systematic correspondence. However once you start considering the 'representational' features of the map, which aren't an essential part of the isomorphism, as equally real (because you've made the simplification: dealing with the map is the same as dealing with the territory—our minds are predisposed to do this in many cases)—then you're in trouble.
In physics the map IS the territory. Or, if you prefer, we're not merely constructing a map, but a model, that is, we try to feel out and understand the territory, what it's made of, and how it works.
So you think an electron IS a mathematical expression, not that a mathematical expression describes its behavior?
> ...we're not merely constructing a map, but a model, that is, we try to feel out and understand the territory, what it's made of, and how it works.
'map' is a metaphor there. You're description of what physics is doing still fits within the metaphor. It doesn't change the fact that there is something 'out there' and then there's our description of it, via physics, and our description is not the thing that's out there.
Suppose we develop a unified theory in physics which supersedes current formulations of quantum theory. Then would the old quantum theory still BE the territory at that point? Or would it be just a less accurate description than the new one we came up with?
>So you think an electron IS a mathematical expression, not that a mathematical expression describes its behavior?
No, I think that a mathematical expression describes the behavior of something real as close as possible to our knowledge -- it's not just a picture of how it looks.
In other words, in contrast with the map analogy, the equations for electrons etc can be used for a simulation.
>Suppose we develop a unified theory in physics which supersedes current formulations of quantum theory. Then would the old quantum theory still BE the territory at that point? Or would it be just a less accurate description than the new one we came up with?
Why assume one can describe the territory in just a single (perfect) level of representation? For some things not even the full precision we can muster today is even needed (e.g. I don't need Relativity to know where a baseball will land).
> So you think an electron IS a mathematical expression, not that a mathematical expression describes its behavior?
To the extent that "is" means anything, yes.
> Suppose we develop a unified theory in physics which supersedes current formulations of quantum theory. Then would the old quantum theory still BE the territory at that point? Or would it be just a less accurate description than the new one we came up with?
I think it's useful to treat "isness" as something analogue rather than binary here. The old theory sort-of-is the territory. The new theory a-bit-more-is the territory. But there's no Platonic ideal of the territory as a separate thing from the mathematical model that reality implements. There is no there there.
> I think of many worlds as kind of a literal interpretation that quantum superpositions are fundamentally real, as opposed to quantum superpositions merely being a very accurate mathematical model.
If the stance is predicated on that assumption, as you suggest (and I'm inclined to agree, having read other of Carroll's writings), then I have to continue disagreeing. If the rest of the world of physicist luminaries were unanimously aligned with Carroll it would be more difficult (but still tempting...)—but luckily that's not the case.
So it doesn't really matter if it's a map or not - it tells you something about the territory.
[1] The completeness of quantum theory for predicting measurement outcomes, https://arxiv.org/abs/1208.4123
[2] On the reality of the quantum state, https://arxiv.org/abs/1111.3328v3