Since the proton is not an elementary particle, why do all protons have the same size gluon string connecting the three quarks? As evidenced by all protons having the same rest mass of 938MeV and size of 10^-15m. Couldn't protons have varying numbers of gluons tieing the quarks together?
The proton is the ground state of uud, so the identical rest mass is due to quantum mechanics. The size however is just quantified by a characteristic scale, analogous to the Bohr radius of the hydrogen atom. Like the electron in the hydrogen atom, the constituent quarks of the proton are better described by wavefunctions that determine the probability to find them at a given distance from the others. The "size of the proton" is just the most probable separation that would be measured. There is no bound on the number of gluons in a proton, just as there are no bounds on the number of virtual photons that bind the electron and proton of the hydrogen atom. The ground state of the bound system is obtained when nature sums over all possible configurations of multiparticle states. These virtual gluons are never observed, so it isn't really meaningful to try to count them or determine an average number of them.
I think it could be different, but we don't recognize any particle with uud as a proton,, it will be a particle with a different mass and spin and a different name.. this is very different from the case of the hydrogen atom where excitation is still a "hydrogen atom". my guess is that the names came from before they new about quarks and only had mass and spin to distinguish things.
Good idea to relate this to the much simpler problem for the hydrogen atom. In the hydrogen atom the electromagnetic field is usually treated classically resulting in energy eigenstates for the electron. The ground state for all hydrogen atoms is identical! Now forget about the complication with the quantized quarks and gluons and the inifinitly many degrees of freedom in the quantum field theory (QCD) for a moment. The proton is the groundstate of the |uud> valence quark system - and all these ground states are identical by similar reasons as in the hydrogen atom. The first excited state with spin 3/2 is no longer called proton but Δ^{+}. The key question is: why are there eigenstates to the Hamiltonian H_{QCD} with discrete spectrum (H_{QCD} - E_{n})|n> = 0 with |n> corresponding to |vacuum> with E_{vacuum} = 0, |pions>, |nucleons> = |proton> & |neutron>, ... This is related to the Clay Millennium Prize Problems http://www.claymath.org/millennium/Yang-Mills_Theory/
1) Is there a most recent report (2004) concerning the problem? 2) Is not the key question somewhere related to our comprehension of what "vacuum" is? 3) Could it be that protons are identical because each of them is automatically defined by some "eigenstate" of something more fundamental (a real flow of energy)? So I stop here and whish you all an happy new year 2012.
1) I don't know 2) yes, definitly; the QCD vacuum itself is not less complicated than its excitations 3) I don't know what you mean; in the context of lattice QCD most of these masses can be calculated quite accurately, so it's QCD and nothing else ;-)
I mean the opening question could be replaced by an equivalent one: "why is a proton always a set of 3 quarks (and not 4 or 5 or any other number)?" Without falling down into esoterism, one may be surprized by that trinity. I mean where ever you are observing the proton and the elementary stones of it, you will always find 3 stones... Since a proton is a moving object for most of the observers, this gives the picture of a set of 3 strings moving together... what ever happens. This is why I was thinking about "eigenstates" or more exactly of the representation of a polynomial of degree 3 with 3 solutions (each of them being one of the quark)... just some obscure intuition - sorry.
A proton is 3 quarks held together by a lot of glue, most of the time. These virtual gluons can split into virtual quarks, so the proton is really in a superposition of quantum states with an odd number of quarks (because the proton is itself a fermion, it must be composed of an odd number of fermions). This is an important consequence of the fact that the strong interactions are so strong: the quantum states describing free particles are not solutions to the interacting theory. So bound states are complicated superpositions of the free particle states, but the proton is distinguished as the lowest energy configuration with its particular quantum numbers. The excited states of the proton are identified with unstable resonances, as you can find in tables: http://pdglive.lbl.gov/listing.brl?fsizein=1&exp=Y&group=BXXX005 Resonances of the same mass and quantum numbers are, as far as we know, identical particles. The relevant representation theory is that of SU(3) flavor, which is the so-called "eightfold way." The flavor symmetry is broken by the differing quark masses, but the qualitative picture is nonetheless useful.
If you replace then word 'proton' with 'quark', then what you describe is more or less the quantum field theory explanation of why all samples of a given type of particle are identical. There is an underlying quantum field, the 'quark' field, which fills all of space, and individual quarks are quantised excitations of this field. It is all the same field though, so all the excitations should be have the same properties.
fzero, I used to think what you said in your opening statement was true too, until I read this article: Is it possible to wrestle this concept an interested layman (engineer) can understand, by analogy perhaps, if it agrees with your understanding of what I just quoted. I was quite startled by it actually, but not surprised. If not, feel free to debunk it with evidence of course. Rhody... :surprised
Strassler and I are describing the same picture: the "glue" I refer to is his “plus zillions of gluons and zillions of quark-antiquark pairs.” This picture is inherently quantum mechanical, so there aren't any analogies in classical physics to make. Nevertheless, one can perhaps shed a little more light on what happens in a quantum system. A quantum system is defined by a set of quantum fields along with their interactions. These fields correspond directly to the free particle states that exist when we ignore the interactions. For the proton, the most important fields describe the quarks and gluons, since the strong interaction is much stronger than the weak and electromagnetic interactions. From the free quark states, we can write down a multiparticle state, uud, that has the correct quantum numbers of the proton. In the free theory, the mass of the proton is just given by adding up the masses of the quarks, which gives a number that is much smaller than the observed proton mass. This discrepancy gets fixed when we turn on the interactions between the quarks and gluons. The uud state is replaced by the superpositions of states which are composed of uud plus arbitrary numbers of gluons and quark-antiquark pairs. The energy eigenstates of the interacting system are linear combinations of these states and the proton is the lowest energy, or ground state combination. The other eigenstates are the resonances. As is usual in quantum mechanics, the square (actually complex modulus squared) of the coefficients in the linear combination gives the probability of finding the system in a particular quantum state. So if we do a measurement on the proton, there is a small probability to find it in the uud configuration, but most of the time it will be in one of the "zillions" configurations.