Virtual Particles in Inter-Quark Space

Islam Hassan
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This oft-referenced picture depicts a simulation of virtual particles popping into and out of existence in the empty space inside a proton, ie between the quarks:

http://bsturge93.files.wordpress.com/2014/02/empty-space.jpg?w=300&h=242

My question is whether the intensity of this popping to-and-fro is higher for inter-quark space because of the energy of the quarks themselves or whether this intensity would be substantially the same in open empty space, ie in empty space far removed from a proton.

Is it correct to say that the energy of these virtual particles is equivalent to that which would have been inherent to the now-discredited notion of relativistic mass (ie, of the quarks)?IH
 
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In my understanding(as an undergrad) in a hadron there are quarks which interact via the strong interaction. That means they're constantly sending gluons to each other. And these gluons split in more quark-antiquark pairs and more gluons, so actually there are an infinite amount of particles inside it(the closer you look, which is the same as the higher the energy of your collision, the more you see). And it's merely the kinetic energy of this quark-gluon sea that causes the mass of the proton, rather than the 3 original quarks which get their mass via the higgs-mechanism. I'm not sure if the particles I mentioned are technically speaking real or virtual though.
 
You should have a look at nucleon structure functions measured in deep inelastic scattering; they are a generalization of form factors (for elastic scattering) and encode the quark and gluon distributions inside the nucleon.
 
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