What does a proton look like?

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In every textbook there are pictures of protons with spheres. This implies that there is some hard case and that that hard case is made of something. is this picture misleading? protons are made of quarks but i think only three of them. if quarks are not spherical with a casing then what is the best way to visualize a proton? do we simply not know?
 

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fzero
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In every textbook there are pictures of protons with spheres. This implies that there is some hard case and that that hard case is made of something. is this picture misleading? protons are made of quarks but i think only three of them. if quarks are not spherical with a casing then what is the best way to visualize a proton? do we simply not know?
The relevant physics is the following. First is that the configuration of uud quarks in the proton has zero orbital angular momentum. Therefore it is spherically symmetric and the probability of finding an individual component is described by a wavefunction that only depends on the radial distance from the center of the proton. The expectation value of the radial distance in this wavefunction (the most likely place to measure a quark) is closely related to what we define as the charge radius of the proton.

Now the natural picture that emerges is the sphere that you describe. The spherical symmetry above explains why it is a sphere and the radius of the sphere is essentially the charge radius. However, this is not a hard case, any more than a spherical picture of a hydrogen atom is a hard case. It is just a schematic picture of the symmetry of the proton along with the most likely place to find one of its quarks. The physical extent of a photon is actually infinite, but the probability to find a quark outside the charge radius falls off exponentially. There's no great way to draw this in 3D other than the "cloud" type pictures familiar from hydrogen, so we're usually left with the sphere illustration and a bit more detail that follows from quantum mechanics, but isn't obvious to the casual observer.
 

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