Inside a proton or a neutron, quarks are in constant motion. However, it's important to note that the concept of the velocity of an individual quark within a hadron (proton or neutron) is not well-defined. This is because the strong force that binds quarks together does not allow for the isolation of individual quarks.
The strong force, described by quantum chromodynamics (QCD), is a fundamental force that becomes stronger as quarks are separated. As quarks move apart, the energy stored in the strong force field increases, leading to the creation of additional quark-antiquark pairs, resulting in the formation of new hadrons. This phenomenon is known as color confinement.
In the context of hadrons like protons and neutrons, the quarks are tightly bound and interact with each other through the exchange of gluons, which are the force-carrying particles of the strong force. The overall motion of quarks and gluons within the hadron is described by their collective behavior rather than individual velocities.
Quantitatively describing the velocities of quarks within hadrons is challenging due to the non-perturbative nature of the strong force and the complex dynamics of QCD. Therefore, it is more appropriate to think of quarks inside protons and neutrons as being part of a system in which their motion is interconnected, rather than focusing on their individual velocities.