The current-carrying states in a one-dimensional system of interacting
electrons are considered. The new exact results for the Hubbard model
and for the bosonization method are used. Away from half filling both
spin and charge excitations were found to carry currents which are pr
oportional to their momenta for most cases. Being in a qualitative agr
eement with a single-particle picture of the noninteracting 1D Fermi g
as, this result contradicts the spin-charge separation concept, since
it is usually derived, e.g., from the bosonization approach or in stro
ng repulsion picture. The paradox can be resolved by taking into accou
nt the spectrum parabolicity and re-examining the structure of the cur
rent operator within the bosonization approach.