How does color charge work?

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Pfhorrest
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How does color charge work?

The other day I was imagining a conversation wherein I was trying to explain to someone what color charge is. I was trying to say that it's a little bit like electric charge, inasmuch as it's a property that particles can have, except instead of two nonzero values, it can have three, and all three of those add together to zero charge the same way that positive and negative electric charges do, so that a composite composed of particles with all three charges is in aggregate uncharged.

Then I got to thinking about what exactly the third value would be. Having a positive and a negative add together to zero makes sense, but what are the three color-charge values? I know we name them red, green, and blue, but how do you add colors, especially when they are only figuratively named after colors anyway?

So then I thought: imagine we don't know anything about electric charge really. We know that it's some property that a particle can have one of two (nonzero) values of, and that these two values in aggregate add together to zero value. We have no idea what those values actually are, so let's just give them variable names, call them P and N. We know that P + N = 0. Which means by simple algebra that P = -N, and N = -P. P and N are each other's negations. Since particles can only take one or another of these values, we don't really care what they are in numbers, so we can just define our units such that P = 1, and consequently N = -1, and we can just talk about positive or negative charges.

But then (I thought, in this imagined conversation), say we discover there's this other property, and we likewise know that it can take three nonzero values, and that all three of those values add together to zero, but we don't actually know what the values are in any quantitative way. But let's just give them variable names: R, G, and B. We know that R + G + B = 0, so consequently R = -(G + B) and G = -(R + B) and B = -(R + G), but we can't just define units such that R = 1 and let values for G and B fall out of it like we could with P and N before, or anything like that. So we're stuck just using variable names for them still. (And since these values add together to zero the way that primary colors add together to white, let's use primary color names for those variable names, and call the property "color").

I'm wondering if this explanation that my mind just pulled out of its ass is anything at all like the actual physics behind color charge. (And if so, if there's any prospect of ever finding out what the actual values of R, G, and B are, at least in terms of each other, e.g. might we some day discover that G = -R and B = -2R? What implications would that even have?)

Also, after writing this, I'm wondering if the adding-to-zero is somehow responsible for the attraction of positive and negative electrical charges, and for color confinement. The universe somehow doesn't like there being nonzero charges out there alone, so it pulls them together into groups that sum to zero?
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doogly
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Re: How does color charge work?

The long mathy answer is SU(3), it's a lie group theory party up in this particle physics.
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Tchebu
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Re: How does color charge work?

Your mind has an ass?? whoa...

You really shouldn't think of the transition from electric to color charge as a transition from "2 kinds of charge" to "3 kinds of charge". There aren't two kinds of electric charge, there's just one and it can take negative values. Similarly, there are 3 kinds of color charge and they can also take "negative" values in a more loose sense (e.g. anti-quarks have "anti-red/blue/green" color charges). Being color-neutral is not really a matter of things "adding up" to zero.

Depending on what your math background is, you can have a look at this section of the wiki article and the short section just before it. Just skip over the fancy math terminology and see if you can get the general idea. I'll try to post some sort of less technical rendition of that a little later if you'd like (similar to your "unification" thread, though hopefully less long).
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Soupspoon
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Re: How does color charge work?

A_Colour = ³√(1+i), maybe?

Xanthir
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Re: How does color charge work?

Pfhorrest wrote:
So then I thought: imagine we don't know anything about electric charge really. We know that it's some property that a particle can have one of two (nonzero) values of, and that these two values in aggregate add together to zero value. We have no idea what those values actually are, so let's just give them variable names, call them P and N. We know that P + N = 0. Which means by simple algebra that P = -N, and N = -P. P and N are each other's negations. Since particles can only take one or another of these values, we don't really care what they are in numbers, so we can just define our units such that P = 1, and consequently N = -1, and we can just talk about positive or negative charges.

But then (I thought, in this imagined conversation), say we discover there's this other property, and we likewise know that it can take three nonzero values, and that all three of those values add together to zero, but we don't actually know what the values are in any quantitative way. But let's just give them variable names: R, G, and B. We know that R + G + B = 0, so consequently R = -(G + B) and G = -(R + B) and B = -(R + G), but we can't just define units such that R = 1 and let values for G and B fall out of it like we could with P and N before, or anything like that. So we're stuck just using variable names for them still. (And since these values add together to zero the way that primary colors add together to white, let's use primary color names for those variable names, and call the property "color").

Your error here is in assuming that the charges work via "simple algebra" - the integers under addition/subtraction form *one particular* algebra that things can act like, that happens to be usefully model quite a lot of things in the real world, but not everything follows it. Electric charge does, and as Tchebu points out, the individual colors of color charge do (red and anti-red cancel each other just like positive and negative do, etc), but the colors as a whole follow a different algebra, the SU(3) algebra that doogly talks about. (Note: don't read Wikipedia for this - it's useless abstract-algebra wordvomit that makes zero sense unless you already have a good understanding of the subject.)
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