  Determining the level of chemical homogeneity in open clusters is of
fundamental importance in the study of the evolution of star-forming clouds and
that of the Galactic disk. Yet limiting the initial abundance spread in
clusters has been hampered by difficulties in obtaining consistent
spectroscopic abundances for different stellar types. Without reference to any
specific model of stellar photospheres, a model for a homogeneous cluster is
that it forms a one-dimensional sequence, with any differences between members
due to variations in stellar mass and observational uncertainties. I present a
novel method for investigating the abundance spread in open clusters that tests
this one-dimensional hypothesis at the level of observed stellar spectra,
rather than constraining homogeneity using derived abundances as traditionally
done. Using high-resolution APOGEE spectra for 49 giants in M67, NGC 6819, and
NGC 2420 I demonstrate that these spectra form one-dimensional sequences for
each cluster. With detailed forward modeling of the spectra and Approximate
Bayesian Computation, I derive strong limits on the initial abundance spread of
15 elements: <0.01 (0.02) dex for C and Fe, <~0.015 (0.03) dex for N, O, Mg,
Si, and Ni, <~0.02 (0.03) dex for Al, Ca, and Mn, and <~0.03 (0.05) dex for Na,
S, K, Ti, and V (at 68% and 95% confidence, respectively). The strong limits on
C and O imply that no pollution by massive core-collapse supernovae occurred
during star formation in open clusters, which, thus, need to form within <~6
Myr. Further development of this and related techniques will bring the power of
differential abundances to stars other than solar twins in large spectroscopic
surveys and will help unravel the history of star formation and chemical
enrichment in the Milky Way through chemical tagging.
