I imagine that your idea about the "chemical field" would be the right one:
specifically, the concentrations of some sort of hormone in the plasma. If
a hormone is released by (e.g.:) the heart and is broken down completely by
plasma esterases over the course of one circulation of the CVS then its
plasma concentration at the shoulder will be greater than its concentration
at the fingertip: it could be that the end of the embryonic arm stalk starts
to make fingers when the local concentration of this hormone drops below a
certain level, and stops elongation when the hormone concentration drops
still further. Differences in the (genetically determined) sensitivity of
the stem cells to these hormones (and the environment of the embryo) would
cause different final arm lengths in different individuals.
Interesting question that - cheers.
Jon.