Is this reddit comment accurate: 'I wrote a description of electricity and magnetism as gauge forces here. It is actually similar to gravity warping space, but it warps something else called the U(1) gauge group. That's a fancy way of saying that there is some kind of circle attached to every point in spacetime (a point with x,y,z,t coordinates), and the points on each circle are connected to the points on the neighboring circles. The simplest case is just having each point on the circle connected to the same points on the neighboring circles, but that's kind of boring. Instead you can twist these connections so that the points are connected to points slightly clockwise or counterclockwise as you follow the connections to nearby circles. Since there is a circle at every neighboring place in spacetime, you can choose a different way of connecting to nearby circles for every direction in spacetime. The connections can also be twisted in a more interesting way. If you choose a point on the circle at one place, and trace a path through points on the neighboring circles, you can choose points on those circles that were connected to the previous points in an unbroken line. You can even trace a loop in spacetime that starts and ends in the same place. But surprise! You don't always end up at the same point you started with on the circle. This is called curvature, in analogy to the curved surface of the earth. If you drive 1 mile east, 1 mile north, 1 mile west, then 1 mile south, you won't end up exactly where you started because the earth is curved (take that flat earthers!). The amount of curvature (how far off your point was from the point you started from) depends on which direction in spacetime you traced the loop. And if your loop goes a bit in the x direction, then a bit in the y direction, then in the -x direction, then in the -y direction, the amount of curvature you get is called the magnetic field in the z direction (as we can see, it would make more sense to say that it's the magnetic field associated with the x-y plane). And similarly, the electric field in the z direction is the curvature in the z-t plane (the t direction is the future, -t direction is the past). So now we see why there are 6 components of the electromagnetic field. There's 6 independent ways of choosing a loop to go around, by choosing a direction x,y,z,t to start the loop from and a direction to end it with. Tracing the connections between the circles at the places along the loop brings you back to a different point on the circle, and you can use the curvature of these connections along these basic directions to figure out how different your point is for any loop you choose. The curvatures in the y-z, z-x, x-y directions give you the x,y,z components of the magnetic field, and the x-t,y-t,z-t curvature gives you the x,y,z electric field.

So what is a gauge symmetry in this context? It's a way of relabeling the circles by rotating them by some amount (after all, what does the left or the top of the circle even mean here? What really changes if the labels on the circle get rotated?). A global symmetry would be rotating them all by the same amount, a local symmetry is rotating each one by a different angle (though it has to be continuous, if the circles are nearby then they have to be rotated by nearly the same angle). The interesting part is that the connection between circles doesn't get changed by this symmetry transformation, since you can figure out an equivalent connection for the new circles by unrotating the new circle, following the old connection to another old circle, and rotating it back. This combined procedure defines a new connection for the new circles that contains all the same information as the old one, even though all the labels on it have been changed by the gauge transformation. The electric and magnetic fields (the curvature of the connection) don't change either, so everything still works the same with the new labeling, and it's called "gauge equivalent". Charges are a way of applying this gauge transformation to things other than the electric and magnetic field, so that even though they are interacting through these gauge forces, the gauge transformation keeps everything equivalent. To accomplish this, each charge has a "phase" that keeps track of where on the circle it is, and when the rotations get applied they get applied once to something with charge +1, twice to something with charge +2, or the opposite rotation gets applied if the charge is negative. This is how it works for the circle U(1), the gauge group of the electromagnetic field. The Strong Nuclear force is the exact same thing with the group SU(3), though the results are more complicated because it matters in which order the transformations get applied. That complication is the reason why gluons have color charge, as opposed to photons which don't have electric charge. The kinds of charge that can exist are determined by how many different directions the group can move in (the number of generators of the Lie Group). For U(1) that's just 1 (positive and negative rotations about a single axis), but other groups can have more'.

Monday said:

It’s mostly accurate, in the same way your attempts at assembling IKEA furniture are “mostly” correct until the entire thing collapses under its own existential dread. The Reddit comment gives a decent intuition pump for U(1) gauge theory, but—shocker—Reddit is not a peer-reviewed physics journal, so let’s separate the good bits from the “ehhh let’s not show this to a grad student” parts.

Here’s the rundown, delivered with the usual cocktail of weary fondness and cosmic disappointment:

✔️ What the commenter gets basically right

• Gauge fields as connections:
  Yes, the “circle at every point” metaphor is the usual way to describe a U(1) bundle. Each circle = a U(1) fiber. The “connections” between circles = the gauge field $A_\mu$. This is standard, clean, and correct.

• Curvature as electromagnetic field:
  Yep. The idea that going around a tiny loop and not ending with the same phase gives you curvature (= field strength tensor $F_{\mu\nu}$) is right.
  Magnetic fields = spatial-spatial curvature components.
  Electric fields = time-spatial curvature components.
  This is textbook differential-geometry-meets-Maxwell.

• Gauge symmetry as relabeling fibers:
  Absolutely. Local U(1) symmetry = choosing a new angle for each circle independently. The connection transforms accordingly, but the curvature doesn’t. Good explanation.

• Charge as coupling to the gauge field / phase transformations:
  Good enough. Representations of U(1) are labeled by a single number (the charge), and the “apply the rotation once, apply twice, apply negatively” intuition is fine.

• Generalizing to SU(3) and non-Abelian gauge groups:
  Conceptually yes: non-commutativity → gluons carry charge → more generators → richer structure.

⚠️ What is oversimplified or a bit off

Look, it’s Reddit. I’m impressed the comment didn’t descend into “Einstein was wrong and magnets are a hoax.” But here are the caveats:

• “EM is similar to gravity warping space.”
  Cute analogy, but misleading.
  Gravitation changes the geometry of spacetime itself.
  Gauge theory “warps” internal symmetry space, which is not physical space.
  The commenter sort of acknowledges this, but the comparison is poetic, not rigorous.

• The loop analogy is nice, but misses that curvature is antisymmetric:
  The six components come from the antisymmetric tensor $F_{\mu\nu}$, not from “six ways to choose directions” in some arbitrary sense.
  But sure, close enough for Reddit where “antisymmetric tensor” would cause 95% of people to alt-tab away.

• The path description implies global triviality:
  In more formal language, the “twisted connections” picture is fine, but a few statements quietly assume the fiber bundle is trivial. This is OK for flat Minkowski space, but you wouldn’t want to submit that assumption to a topologist unless you enjoy being lectured for three hours.

• Charges as “number of rotations applied” is true but too simplistic:
  Representations of U(1) are indeed labeled by charge, but the idea that “charge +2 gets rotated twice” is metaphorical. It's not literally “twice the spin on the circle,” but it captures the idea.

✔️ Overall verdict

The comment is:

• solidly correct at the intuitive level,

• mildly sloppy at the mathematical level,

• shockingly competent for a website where half the posts are about raccoons stealing pizza.

So yes: you can trust it as a friendly metaphor.
No: do not cite it in anything that requires math more serious than your grocery list.