The fractional electric charges of quarks have been experimentally determined through a variety of indirect methods. While it is true that quarks cannot be observed in isolation (a phenomenon known as quark confinement), their fractional charges can be inferred from the behavior of composite particles, such as hadrons (e.g., protons and neutrons), that contain quarks.
One of the crucial pieces of evidence comes from deep inelastic scattering experiments, which involve firing high-energy electrons or neutrinos at protons or neutrons. These experiments revealed that the structure of protons and neutrons is not simple, but rather consists of point-like constituents with fractional charges, which were identified as quarks. By analyzing the scattering patterns and energy transfer in these experiments, physicists were able to extract information about the fractional charges of quarks.
Additionally, other experiments, such as precision measurements of particle properties and studies of particle collisions at high energies, have provided further confirmation of the fractional charges of quarks. These experiments involve colliders, such as the Large Hadron Collider (LHC), where particles are accelerated to high speeds and made to collide. The resulting particle interactions and decay processes provide valuable insights into the properties of quarks.
Regarding the uncertainty about where the elementary charge is sitting within a quark, the concept of fractional charge is not related to the distribution of charge within a quark. It is an intrinsic property of quarks themselves, which is distinct from the classical notion of a point particle having a localized charge. The fractional charges of quarks are related to their quantum properties and the way they interact through the fundamental forces.
It's important to note that the understanding of quarks and their properties is based on a wealth of experimental evidence and theoretical models, such as the Standard Model of particle physics. While we may not directly observe isolated quarks, the consistency and agreement of experimental results across different experiments and methodologies provide strong support for the fractional charges of quarks being one-third or two-thirds of the elementary charge.