I'm going to trace back ἦν
to their Proto-Indo-European root. I know the Greek verb εἶναι
is derived from the Indo-European root *h1es-. *h1es- means 'to be' and φύω
, from which physics and physical are derived, is derived from the Indo-European root bhū
. The root bhū
probably meant 'to grow', but also 'to become'.
The root as, which still lives in our he is, is a very old root: it existed in its abstract sense previous to the Aryan separation. Nevertheless we know that as, before it could mean to be, meant to breathe.
The simplest derivation of as to breathe, was as-u, in Sanskrit, breath; and from it probably asu-ra, those who breathe, who live, who are, and at last, the oldest name for the living gods, the Vedic Asura.
When this root as, to breathe, was felt to be inconvenient to trees and other things which clearly do not breathe, a second root was taken, bhū, meaning originally to grow, the Greek φυ-ω, which still lives in our own to be. It was applicable, not to the animal world only, but also to the vegetable world, to everything growing, and the earth itself was called Bhūs, the growing one.
F. Max Muller, Origin and Growth of Religion, pp. 191-192