The word Atman is derived from the root Ad which means to pervade (Ad vyApane). Atman thus means the invisible reality or substance that pervades the individuated visible forms, just as gold is the substance that pervades the visible form of an ornament. This visible form in the case of living beings includes in it the physical phenomenon called body as well as the phenomenon known as the soul.
From Karma and Reincarnation, Swami Muni Naryanana Prasad, D.K. Printworld (P) Ltd., 1993, ISBN 81-246-0022-8. Buy from Amazon US, Buy from Amazon UK
The word ‘brahman’ has brih to expand, to spread out as its root.
No wonder we have the equality expression, atman = brahman.
Just a stray thought comes to me. I invite all comments/criticisms on this thought:
As per the most acceptable theory of the Origin of the Universe, there was an initial inflationary phase followed by the Big Bang rate of “expansion” which is still going on, perhaps at an accelerated rate. It’s like ever increasing entropy which is said to be the possible cause of the one way “arrow of time.” Does this expanding universe correspond to the ‘pravRitti’ phase justifying the name ‘brahman’? Would the same “Beingness” (‘sat’, which is the primordial undifferentiated ‘Isness’) get a different name i.e. the opposite of ‘brahman’, if we were to be in a universe in its nivRitti phase (going by the cyclic theory of universe)?