## How can gluons interact via color force?

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jewish_scientist
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### How can gluons interact via color force?

Gluons have a color and an anti-color. Quarks interact via the color force because they have color. The exchange particle of the color force is the gluon. Because gluons have color, they must also interact with each other. That means that gluons send gluons to each other. The new gluons must also send gluons to each other gluons. This creates a infinite digression where every interaction requires another interaction to occur. How is this problem solved?
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mosgi
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### Re: How can gluons interact via color force?

I don't know enough about the strong force to answer your question exactly, but I can give you a classical explanation - in other words, I'm going to treat QM as if it worked with ordinary probabilities. Technically that isn't quite how it works, but I think it's close enough to explain what's going on here.

So, basically: not every gluon interacts with every other gluon all the time. In other words, when you say "Because gluons have color, they must also interact with each other", that isn't quite right - instead, it just means that they can interact with each other, not that they must. In fact, if you start with two gluons, there's a chance that they don't exchange any gluons (ie, that they don't interact at all) and a chance that they will exchange one, or two, or three, and so on. Importantly, the average number of these exchanges (per gluon) is less than 1. This means that, while the total number of gluons might be really big (or might be just the original two), it will be finite with probability 1.

In other words, it's analogous to why "x = (x+1)/2" has a solution; if you described it iteratively, you'd say "Well if we started with x=0, then we'd next have to say x=1/2, then x=3/4, etc. How is this solved?"

Charlie!
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### Re: How can gluons interact via color force?

In practice, you calculate the number that's the "amount of reality" of exchanging 1 gluon, exchanging 2 gluons, exchanging 3 gluons, etc. In many cases, if you try to calculate the expected number of gluons, it really does go to infinity - the series of "amount of reality" decreases slower than 1/n2, so the expected value of gluons is infinite. But it turns out that when we've checked, if you ignore the divergence and just take the first few terms, you get very good agreement with experimental results! So something not captured by the above calculation is going on that cuts off this divergence in the real world.
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Aiwendil
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### Re: How can gluons interact via color force?

Yeah, gluons are weird in that they have the self-interactions you've mentioned. I believe this is related to the non-perturbative nature of QCD at certain energies, and it may be responsible for quark confinement (though quark confinement is really not very well understood).

jewish_scientist
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### Re: How can gluons interact via color force?

Mosgi, your answer very good. I never thought about it that way. I do want to make sure that I understand what you are saying though.

A red-antiblue gluon and a green-antired gluon interact via color force. Another pair of identical gluons do not interact via color force. The reason identical situation have different results is because whether the color force will interact between to gluons is probabilistic. The probability of the interaction happening is < 0.5, meaning that on average no interactions happen.

If this is what you mean, then there are some very weird consequences. If the probability of to quarks interacting via color force < 0.5 and the color force is strong enough to cause quark confinement, then every gluon must carry a huge amount of force. When two particles interact by P exchange particles to produce net force F, then the force carried by each particle must, on average, be F/P. The color force is 137 times stronger than the electromagnetic force. The equation 137 * Fe/Pe = Fc/Pc describes this relationship. Photons do not interact with each other, so there is no problem with many being exchanged between two charges constantly. The gluon, which is unlikely to be exchanged, must carry a proportionately larger amount of force.

There is not really a problem with this; it would just mean that an individual gluon would carry magnitudes more force than I thought it did. However, I think that it is more likely that I misunderstood you.
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Nicias
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### Re: How can gluons interact via color force?

I don't think that the probabilities work quite that simply, but yes, the gluons are huge.

The mass of the proton is about 900 MeV/c^2. The mass of its constituent quarks is less than 15 MeV/c^2. The rest is gluons.

doogly
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### Re: How can gluons interact via color force?

The particle model is really bad when you want to talk about self-interactions, because nothing that we got our word "particle" from does this. You have to drink deeply from the well of quantum field theory.
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jewish_scientist
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### Re: How can gluons interact via color force?

I though of another question. What do gluons interact with? Quarks have 1 color, while gluons have 2. Can they still interact, or do gluons only interact with other gluons?
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doogly
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### Re: How can gluons interact via color force?

Gluons interact with quarks and other gluons.
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