It's just a mathematical tool of curiosity that we have found very useful.
Here's an analogy: You find a box, and you can't see inside it. You have no reason to think there's something inside it. But also, boxes have stuff in them sometimes. So, you shake the box, and hear something clinking around. Therefore, you infer there's something in the box.
Somebody next to you says "This sounds like a hack. There was a box and you had to go shake it until it started making sounds that it wasn't making before. UNLESSSSS we now magically have to agree that there's something in the box."
It's a perfectly reasonable question, and I'm just turning your words on you in good faith :)
To take the technical discussion a bit further, it's exactly this kind of reasoning that led to the discovery of the Higgs boson. Strictly speaking, it's impossible for gauge bosons (that's what the particles are called that show up when you add these locally-varying symmetries) to have nonzero mass.
The photon and gluons (from the SU(3) strong force) are massless, but the W and Z bosons are VERY massive.
This was a big problem with the Standard Model; the vector gauge bosons had every property expected from the gauge theory, except for this one point about their mass, which was experimentally incontrovertible.
That is, until Brout/Englert/Higgs came along.
They said "Yeah the vector bosons must be massless UNLESSSSSSSS you assume there's this magic additional field that couples to every particle's mass, in which case it perfectly cancels out all the problems and allows the W and Z bosons to be heavy".
It took 50 years but we found that particle eventually.
You're a really great writer on this topic. If you're not already, and you have the time, you should seek out ways to do this in a way that has more reach. Thank you!
You know I tend to agree with the previous poster, not that it's a hack, but that I've always felt its a bit backward reasoning. You say the physics should be invariant under curvature of the field, but it isn't unless you add another field to cancel it. But you might as well have said from the start that the field is curved by another field and we need to consider that in our derivatives that describe our local physics, making them covariant. The explanation that "it makes sense that the fields are locally gauge invariant" always seemed a bit constructed after the fact so to speak.
The argument isn't against physicists inventing new fields or interactions to fit data. The argument is about why you can motivate it as "something that has to be added out of pure logic" :)
I don't think it's backwards. We started out with this big sweeping and simple statement that (seems to) holds true for physical reality, but it doesn't account for everything. The statement allows for two realities, one where there is one single global phase, and another where each point has its own local phase.
The first option might be true, no real way to measure it and that's sort of it, no explanation for all the other stuff going on. The second option is a little more complex, it requires an extra construct to make it work. And apparently when we do the math and work out this construct, it exactly maps to things we can measure in reality, that were not explained by the other simpler option.
So it's not backwards because it's simply the first full match in a depth first search through the possible realities that follow from this wave function theory.
It makes a lot more sense if you have the historical context though. When this is taught the context is left out and then it feels more like mathemagics to me and probably others as well. Maybe there are good books that explain this from a historical point of view, while still teaching the theory, but they must be pretty rare.
My comment (the GG..GGP) was an (over)reaction to the posted article. The article presents the new approach like a very "natural" explanation, but there are already some other "natural" explanations.
In a Physics degree, the order is quite historical. Like one full course for the three first next items, and all the other together. I'm not sure if there is a book with all of them, you probably need 4 or 5 books.
1) Non-Quantum Non-Relativistic Electromagnetism
2) Quantum Non-Relativistic Electromagnetism
3) Non-Quantum Relativistic Electromagnetism
4) Quantum Relativistic Electromagnetism
5) By the way, you can interpret the Quantum Relativistic Electromagnetism as a U(1) symmetry. (my comment)
6) It looks like a good idea. Let's use other groups to explain other known forces: the weak and strong force. (The G...GP comment about SU(2) and SU(3).)
7) ???
[See note 1]
For some reason, popular science articles love to show something almost magical and prefer to present something like the "5)". It makes it easier to hide the math and use hand waving.
Also, Physicist working in physic particle also believe that "5)" and "6)" are the correct approach, and the other are just useful for teaching and for historical reasons. But to discover "7)" it's better to think about some weird new symmetry group [2].
For examples, a few years ago, it was popular to think the next step "7)" was using a new group SU(5) that combines SU(2) and SU(3). The problems is that the experiments gave different results than then new proposed theory, not too bad but like 1% off. I still remember my professor talking about how great was SU(5) and how the experiment disagree, and he looked heartbroken because he really liked SU(5).
[1] You should add some material about the historical discovery of the weak and strong forces between "5)" and "6)".
[2] Other's prefer superstrings for "7)", there are other approach, but all are weird.
Here's an analogy: You find a box, and you can't see inside it. You have no reason to think there's something inside it. But also, boxes have stuff in them sometimes. So, you shake the box, and hear something clinking around. Therefore, you infer there's something in the box.
Somebody next to you says "This sounds like a hack. There was a box and you had to go shake it until it started making sounds that it wasn't making before. UNLESSSSS we now magically have to agree that there's something in the box."
It's a perfectly reasonable question, and I'm just turning your words on you in good faith :)
To take the technical discussion a bit further, it's exactly this kind of reasoning that led to the discovery of the Higgs boson. Strictly speaking, it's impossible for gauge bosons (that's what the particles are called that show up when you add these locally-varying symmetries) to have nonzero mass. The photon and gluons (from the SU(3) strong force) are massless, but the W and Z bosons are VERY massive. This was a big problem with the Standard Model; the vector gauge bosons had every property expected from the gauge theory, except for this one point about their mass, which was experimentally incontrovertible.
That is, until Brout/Englert/Higgs came along. They said "Yeah the vector bosons must be massless UNLESSSSSSSS you assume there's this magic additional field that couples to every particle's mass, in which case it perfectly cancels out all the problems and allows the W and Z bosons to be heavy". It took 50 years but we found that particle eventually.