  We make an attempt to describe Carroll particles with a non-vanishing value
of energy (i.e. the Carroll particles which always stay in rest) in the
framework of two time physics, developed in the series of papers by I. Bars and
his co-authors. In the spacetime with one additional time dimension and one
additional space dimension one can localize the symmetry which exists between
generalized coordinate and their conjugate momenta. Such a localization implies
the introduction of the gauge fields, which in turn implies the appearance of
some first-class constraints. Choosing different gauge-fixing conditions and
solving the constraints one obtain different time parameters, Hamiltonians, and
generally, physical systems in the standard one time spacetime. In this way
such systems as non-relativistic particle, relativistic particles, hydrogen
atoms and harmonic oscillators were described as dual systems in the framework
of the two time physics. Here, we find a set of gauge fixing conditions which
provides as with such a parametrization of the phase space variables in the two
time world which gives the description of Carroll particle in the one time
world. Besides, we construct the quantum theory of such a particle using an
unexpected correspondence between our parametrization and that obtained by Bars
for the hydrogen atom in 1999.
