  We consider linear preferential attachment trees which are specific
scale-free trees also known as (random) plane-oriented recursive trees.
Starting with a linear preferential attachment tree of size $n$ we show that
repeatedly applying a so-called lifting yields a continuous-time Markov chain
on linear preferential attachment trees. Each such tree induces a partition of
$\{1, \ldots, n\}$ by placing labels in the same block if and only if they are
attached to the same node in the tree. Our main result is that this Markov
chain on linear preferential attachment trees induces a partition valued
process which is equal in distribution (up to a random time-change) to the
arcsine $n$-coalescent, that is the multiple merger coalescent whose $\Lambda$
measure is the arcsine distribution.
