  We use sensitive observations of three high redshift sources; [CII] fine
structure and CO(2-1) rotational transitions for the z=6.4 Quasar host galaxy
(QSO) J1148+5251, and [CII] and CO(5-4) transitions from the QSO BR1202-0725
and its sub-millimeter companion (SMG) galaxy at z=4.7. We use these
observations to place constraints on the quantity Dz = z(CO) - z(CII) for each
source where z(CO) and z(CII) are the observed redshifts of the CO rotational
transition and [CII] fine structure transition respectively, using a
combination of approaches; 1) By modelling the emission line profiles using
`shapelets' to compare both the emission redshifts and the line profiles
themselves, in order to make inferences about the intrinsic velocity
differences between the molecular and atomic gas, and 2) By performing a
marginalisation over all model parameters in order to calculate a
non-parametric estimate of Dz. We derive 99% confidence intervals for the
marginalised posterior of Dz of (-1.9 pm 1.3) x10^-3, (-3 pm 8) x10^-4 and (-2
pm 4) x10^-3 for J1148+5251, and the BR1202-0725 QSO and SMG respectively. We
show the [CII] and CO(2-1) line profiles for J1148+5251 are consistent with
each other within the limits of the data, whilst the [CII] and CO(5-4) line
profiles from the BR1202-0725 QSO and SMG respectively have 65 and >99.9%
probabilities of being inconsistent, with the CO(5-4) lines ~ 30% wider than
the [CII] lines. Therefore whilst the observed values of Dz can correspond to
variations in the quantity Delta F/F with cosmic time, where F=alpha^2/mu, with
alpha the fine structure constant, and mu the proton-to-electron mass ratio, of
both (-3.3 pm 2.3) x10^-4 for a look back time of 12.9 Gyr and of (-5 pm 15)
x10^-5 for a look back time of 12.4 Gyr we propose that they are the result of
the two species of gas being spatially separated as indicated by the
inconsistencies in their line profiles.
