Pluto vs Earth

But if you’re defining “bacteria” to include the archae, then it’s not a clade, either.

EDIT: Oh, and if you consider “archae” to be a clade, it’s the clade which includes all living things. So it’s trivial to say that it’s the age of archae.

By my rough back of the envelope calculation the potential energy involved is 100 times that necessary to melt the entire Earth.

I don’t think you understand what a clade is. Or else you think that Archaea are ancestral to all living things.

There was a common ancestor to all living things, but it would not have been classified as Archaea, Bacteria, or Eucaryota. Archaea were a very early branch from that ancestral lineage, but they themselves are not ancestral to either Bacteria or Eucaryota.

Likewise the common ancestor of Archaea and Eucaryota would not have been either an archaean or a eucaryote.

The earliest split of the tree of life that we know of is between the sister-groups Bacteria and (Archaea + Eucaryota). Those two sister groups are valid groups for comparison.