The Concept of Mass, Quarks, and Phase Space

We point out the conceptual problems related to the application of the standard notion of mass to quarks and recall the arguments that there should be a close connection between the properties of elementary particles and the arena used for the description of classical macroscopic processes. Motivated by the above and the wish to introduce more symmetry between the coordinates of position and momentum we concentrate on the classical nonrelativistic phase space with ${\bf {p}}^2+{\bf {x}}^2$ as an invariant. A symmetry-based argument on how to generalize the way in which mass enters into our description of Nature is presented and placed into the context of the phase-space scheme discussed. It is conjectured that the proposed non-standard way of relating "mass" to the variables of the classical phase space is actually used in Nature, and that it manifests itself through the existence of quarks. Some properties of this proposal, including unobservability of "free quarks" and the emergence of mesons, are discussed.