This is the sort of place I want to start, yes. This extra 5th dimension, unlike the other 4, which may or may not be curved inward such that they theoretically lead back around to wherever you started from, but it's all academic, because you could never live long enough or even go fast enough to ever actually make the trip in any way; this guy, this 4th spatial dimension, is curved inward on itself so much that it is only recognizable as a direction at all in the very small motions and interactions of the subatomic waveforms/particles. Yes?
Yep, exactly And refering back to your previous post, this is not the same as our 2d tubes - they're not part of this picture, at least not at this basic level.
Good so far?
Yes, not bad at all.
Is there one for each field? One for each boson? Various combinations?
Well, here it gets much more complex. EM is easy as it is the gauge field of the circle - known as U(1). The complexities of the SU(2)xU(1) geometry of electroweak sector are much harder to describe, and require quite a few extra dimensions to build the necessary framework. Similarly with the SU(3) geometry of quantum chromodyanmics (strong). This is going a bit beyond what we can talk about here, but I might come back to describe why an extra dimension gives rose to what we call electromagnetism and the photon, as it's rather cool.
It be like the guy in flat land seeing a white square and the flipping it over, turning it 180 degrees (which would expectedly make it the same old square again) but its now black (white on one side and black on the other) so he has to turn it another 180 degrees to see the same old white square again. This could suggest to him that there has to be another dimension for the black side of the square to exist in.
That might not be the best analogy
I love this stuff
Sadly, I have to point out to you that Mr. A Square cannot see the top and the bottom of the square. He can only see the edges. This is because, for him to see things, light has to pass through the 1-dimensional lens at the front of his eye and strike the 1-dimensional rods/cones inside his eye. This means he can only properly see light that travels directly along the plane he is in, and such light can only show him the edges of things, never the surfaces. The surfaces of stuff in his world are similar to the volume of things in our larger world, we cannot see inside each other, can we?
A better example might be if he and his fellow Flatlanders had an opening on one edge that they used as a mouth, and then to the left of it, an outcropping that they used as a nose. If we were to take one of his buddies and flip him over, his nose would now be to the right of his mouth! This is the sort of thing that would be impossible in a 2-dimensional world view, it would be like someone in our 3d space suddenly having their heart on the right instead of the left. If such a person also became dyslexic, trying to write from right to left for example, and had a gold filling on the left side of their mouth instead of where the dentist put it on the right, we would be bound to eventually start theorizing about a 4th dimension that they had somehow been rotated in.
This is the sort of thing that makes the magic of n-dimensional geometry work. It's what could allow us to do surgery on someone without piercing their skin, or to "walk through walls". Take a coin to represent your flatlander, and stick it in a brownie pan. Move it forward and backward, left and right, it has no way out of the closed area it is in. This is Timmy Leary in San Luis Obispo County Jail, or John Dillinger in Crown Point. There is no way he can possibly escape!
Now, reach down, lift him out, deposit him outside the pan somewhere. Wow! Looks like teleportation, don't it? But really it's just an ordinary day in the third dimension. Meanwhile, his little coin guards are coming up with a story about inside help or a fake gun made out of cardboard to explain this "impossible" feat.
Now, back to the way his eyes work. Interestingly, light travels in all directions, so it IS possible for some light to reach his rods and cones without traveling through his lens properly. This light could give him vague glimpses of worlds near him, but because its dim and unfocused, it will be screened out by his brain entirely as long as his eyes are open and focused on things. If he closes his eyes, he may see vague spots and flashes though, indicating there is still some light coming from somewhere. If he becomes totally relaxed, and stops focusing altogether on what he thinks the world is limited to, he may even be able to get vague cross sections of the other "flatlands" nearby which are quite similar to his own. What he would see though, even under the best circumstances, wouldn't conform to the laws of nature he knows; because, being a composite, effects would not naturally seem to follow their causes and many unreal things would appear that were not really part of any 1 plane, but rather a combination of things happening on many planes.
Now, try this experiment. First, close your eyes. Report what you see? Good, keep them closed for a while, becoming more and more relaxed. 6 to 10 hours ought to do. When you wake up, report what you saw. Keep doing this for some time off and on, decide what it might mean about the universe you appear to be living in