  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.
