Ray! As you might imagine, I think "Eternal" is not a word bandied about very often by Scientists. But if we were to hold a cyclotron to their head and compel them to use the word "Eternal", this is what I would suggest:
1) The evidence is overwhelming that there was a start to time - - back at the big bang.
2) There are various arguments as to whether the Universe will continue to expand forever ....
3) Or, somehow, something will arrest the expansion ushering in a phase of contraction, to eventually arrive at the Big Crunch!
Ray, I think - - definitionally speaking - - if (3) above were true ... nothing is Eternal. Everything has a finite timeline back to Creation ... and a finite timeline back to the ultimate destruction.
But what if (2) is true? Can the Universe be said to be Eternal if it only has one timeline that is infinite ?
Some people like to use "Infinite" and "Eternal" as synonyms. Mathematicians would say that even if we only go in one direction on a number line, All Positive Integers would still be Infinite (a countable infinity, because discrete integers can be named, in order, as we proceed down the number line).
[For the curious, an Uncountable Infinity references such number sets as "All the Positive Fractions": since no matter what fraction you start with - - say, 1/100 ... or 2/34323938439 - - there is still a smaller fraction between the selected fraction and the number Zero! And so, this number set is "uncountable" ... but still infinite like "All Positive Integers"!]
So while math folks would agree that an ever expanding Universe could be said to be Infinite, is this really the same thing as Eternal? I think most academics would say No. "Eternal" implies infinite in both directions. In a way, I'm glad I wasn't an adult before the development of the Big Bang Theory. I would be a little embarrassed by the idea that the Universe "Always Existed"; this seems to be a fairly odd idea in my own personal view of things. And yet, for some reason, I have no qualms about thinking God is Eternal. I'll have to ponder that.
But first, let's move on to some of the final comments from Ray's question:
Ray, I have to say I'm rather intrigued that you are so "taken" by this topic of Eternal. This issue must trigger some major gravitas in your noggin ....
But as I mentioned last night, in reference to @Jonathan_Burke's interest in the question of immortality when comparing Greek vs. Hebrew philosophies, my view is that this conundrum makes for a rather thin soup.
I assume you want to compare/contrast these terms like so:
"Eternal Life" - a soul that has always existed and will continue to exist forever.
"Everlasting Life" - a soul that is created or born at a finite point, and continues to exist forever.
So, first off, we must be setting aside the idea that God, or some other Being, can or will destroy souls (for whatever intentional or unintentional reason). However, if it is a "process" that leads to extinction - - like, say, "old age" - - well, that pretty much ends the whole discussion on "Eternal" or on "Everlasting" - - because neither would appear applicable.
Jon's presentation on the Hebrew view of souls is that when the body dies, so ends the Soul (if I got this wrong, Jon, I apologize). I call this the light bulb analogy of the soul: as long as there is a filament, and power, there is light. Remove the filament [the body, or the brain, or just the neo-cortex unique to primates and/or humans], or remove the power [the body breathes, the heart pumps, etc.], the soul "goes out" like a candle flame.
Enoch, having been lifted up into the heavens while still alive, may live eternally - - because his body is presumed to be immortal in God's heavenly kingdom. And the General Resurrection envisioned by some Jewish theologians is one where God re-creates the body. It's a new body. But it brings back the associated soul just like replacing a broken filament with a new filament brings back the "light" produced by the light bulb.
Frankly, I reject this concept of a soul. It may be Hebrew, but that wasn't the only Hebrew school of thought. I have long proposed that the Essenes (a Persian-influenced ascetic group) believed that the Soul (once born/created) could exist independently of the body of flesh! I believe this school of thought is indicated by Josephus's Zealot Speech he describes made on the night before the Roman entry into Masada (see image below - click on image to enlarge text to full size!):
In this speech, he describes the ability of the soul to travel away from the deceased body. The specifics of such an afterlife are offered in the little known ancient writing called the "History of the Rechabites". This work appears to have had a Jewish core, and then co-opted by an early Christian writer who apparently appended a Christian beginning and a Christian ending.
The protagonist convinces the Divine to let him visit Paradise. The Paradise described is very much like one Greek version - - where there is an impassable river that separates all living humanity (and unworthy souls) from a sacred island - - Elysium (Elysium is sometimes presented as an underworld Paradise, also usually unapproachable except by the Worthy Dead. On this island, we learn that the righteous gather, and pursue meritorious thoughts and prayers, as they wait for the End of Days (where they may or may not receive an even newer body of flesh) - - or until God suddenly needs one of them at His side. If the latter occurs, angels arrive to wisk away the soul (with a spiritual body) to attend to God at his side until the End of Days.
I have always been amused by what I think is a fairly obvious development. The American popular notion of death is that the soul is, more or less, immediately available as a disembodied soul, heading off to God's bosom (or some other divine location). If a child dies, this soul might tarry to be a guardian angel to his or her parents.
If we compare this popular modern view to the views of the afterlife described by Josphus, it is clear that the best match is not the view of the Priests (Sadducees) or the Pharisees - - but of the Essenes! They would have been delighted to know that some of their ideas would become the most popular ideas of the Western world.
Tag! Ray, you're it now!