I read this interesting passage in Deep Down Things:The question is what we mean by physical? CLASSICAL gauge theory is one thing. Here the whole notion of "observer" is kind of nonexistant anyway. And gauge ina measurement theory is something else.
IMO, herein there is something fishy. What is physical anyway? What are the ontologies? I think some people think about what's out there, in a realist ense, while people like me think ontologies are inferrable states, and these are fundamentally observer dependent.
There are different thinking here. And this partly relates to inmperfection in QM if you ask me.
"For the case of regular spin, we had to take spin-space seriously because
it was associated with a concrete, measurable, physical quantity—angular
momentum. This was only mildly uncomfortable because, although spinspace
has the somewhat hard-to-stomach property that you have to turn all
the way around twice to get back to your original condition, it’s otherwise
pretty much like regular space. Isospin space, however, is completely abstract;
it bears no relation whatsoever (other than through analogy) to anything
we can grasp with our faculties of perception. How could rotations in
such a space possibly have anything to do with the physical world? And yet
the physical manifestation of the invariance of the strong force with respect
to rotations in this space, the conservation of isospin, is a solidly established
fact in the world of experimental science.
So, what then is isospin-space from a physical point of view? Physicists
usually describe it as an internal symmetry space, but what’s that, really? It’s
your old buddy again, telling you that your car’s carburetion system “works
on a vacuum principle.” How’s that going to help you to understand and fix
the thing? It isn’t.
Regarding the physical interpretation of the notion of isospin space,
again your guess is as good as mine. Perhaps its experimental manifestations
are hinting at some new and deeper truth about the universe that lies just
beyond the current limits of our comprehension. Perhaps not. But one
thing, however, is true: The introduction of the idea of internal symmetry
spaces, of which isospin space was the first example, was an essential step
forward in our understanding of the universe and the nature of the laws that
Note The invariance of physical laws with respect to rotations in ordinary space is associated by Noether's theorem with the conservation of angular momentum. The conserved quantity associated with invariance with respect to rotation in the abstract space of isospin is isospin itself. Any connection between the two?
For those so tired of pondering quantum interpretations. It is refreshing to instead ponder on interpretations of gauge symmetry.. lol..