The distance between quarks within a proton is not a straightforward concept due to the nature of quantum chromodynamics (QCD), the theory that describes the strong interaction between quarks. In QCD, quarks are confined within hadrons (particles made of quarks, such as protons and neutrons) and cannot be observed as isolated particles.
The concept of distance in QCD is not the same as the distance we are familiar with in everyday life. Instead, the interaction between quarks is mediated by gluons, which are particles that carry the strong force. The strong force becomes stronger as quarks move farther apart, making it energetically favorable for new quark-antiquark pairs to form between the original quarks, resulting in the creation of additional hadrons. This phenomenon is known as quark confinement.
As a result of quark confinement, it is not meaningful to talk about the exact distance between quarks within a proton. Instead, it is more appropriate to describe the distribution of quarks within the proton in terms of their probability density. This distribution is described by the parton distribution functions (PDFs), which provide information about the likelihood of finding a quark with a certain momentum fraction within the proton.
Experimental measurements, such as deep inelastic scattering experiments, have provided valuable insights into the parton distribution functions and the internal structure of protons. However, these measurements do not provide a direct measurement of the distance between individual quarks within the proton.