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.
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