# Could a universe with 3 or more $U(1)$ charges that are all equivalent to each other be self consistent?

In alternate universe there are at least 3 $$U(1)$$ charges. An elementary fermion can have a value of $$±1$$, or $$0$$ for any of these types of charge. The value an elementary fermion has for one of these charges is independent from the value it has for the others. For example if a particle has a value of $$+1$$ for one of these charges it can have a value of $$±1$$ or $$0$$ for another of these charges. Also if we designate one of these charges as A and one of these charges as B then, as far as the laws of physics are concerned there is no way to tell the difference between charge A and charge B.

Would a universe with a set of independent charges with the above characteristics be self consistent?

• Is there only 2 U(1) charges in our current universe? Perhaps a bit of descriptions or definitions and comparisons? Jun 22, 2020 at 4:31
• If there's no way to tell the difference between A and B, how do we know there is a difference? Jun 22, 2020 at 5:30
• So you really just want to allow lepton/quark fermions take a +1 charge, unlike they do now? Is that the gist of it? Jun 29, 2020 at 14:20
• If a particle has charge A+1 and charge B-1 what do we measure? AorB =+1 and AorB=-1 ? how? Feb 25, 2021 at 10:59
• If "as far as the laws of physics are concerned there is no way to tell the difference between charge A and charge B" then the three putative charges are indistiguishable from one charge with possible values ±3, ±2, ±1, and 0. Dec 25, 2021 at 18:17

Maybe. But the math is massively difficult.

In our universe there is a GL(4) symmetry for gravity, SU(3) for the strong nuclear force, and U(2) for the electro-weak force. This last is "broken" such that only the U(1) of electromagnetism is retained.

One notion of unification is spontaneous symmetry breaking. The idea is that at higher energy there is a unifying symmetry group. At lower energy this symmetry is broken into sub-groups, smaller symmetry groups that hang around at low energy. This process is supposed to have occurred in the cosmological early universe, say some tiny fraction of a second after the Big Bang. The particular "direction" that was randomly chosen then gets frozen in. This is suggested as the source of the various constants of physics, the speed of light, the charge of electrons, etc.

In some models the symmetry that breaks also includes changing the geometry of space. So, in some theories there are additional dimensions that get curled up into tiny balls so that we don't notice them at low energy. This is the basic idea of Kalusa-Klein theories. So one of the things that might have changed in the very early universe was the number of dimensions that stay "large." Things might have changed from 10 space dimensions to 3 plus 7 curled up dimensions.

There are lots of theoretical works along this line of thought. But so far, no experimental support for it. It produces lots of keen things that science fiction plays with. For example, what if different regions had different symmetry groups as their low energy retained symmetry? The boundary between such regions would be very unusual indeed. If you were able to move across this boundary the "laws of physics" might seem to change. Even the dimensionality of space might change.

Your idea would be that in one region things froze out with three different U(1) groups. Since we don't know if the idea of symmetry breaking actually works or really happened, we don't know if any other arrangement is possible. And even if it is, we are not really sure what those alternatives might be.

On the other hand, we don't know it isn't.

So it might be that you could have three different types of charge, call them A, B, and C. If the particles carrying these charges were equivalent to electrons and quarks, you might get equivalent nuclear and chemical reactions. They'd just be in three sets.

But there would be crossings. An A-type quark would also have strong nuclear force. And it's strong force that binds quarks into neutrons and protons and so build the nucleus. That will mean that different combos of charge will give different masses for a nucleus. And different energy levels and reaction rates. So star formation becomes very different.

So a proton (a hydrogen nucleus) might have different types of quark. Say it's AAB. That would mean that the charge on such a proton was a fraction of A and a fraction of B. That would mean it could attract an A-electron and a B-electron. The energy levels of these would depend on the relative charges of the quarks. Chemistry is quite drastically different.

So things could be self consistent. But they would be extremely different to our universe. It would not simply be that there were three different types of matter.