.I agree. It could really be that the halting-state is reached and simply all the matter as we know today (that makes our universe) is simply reproduced in same variables.
If true we will live for eternity, and be reincarnated
Ah. I think you've missed the logic of your own premise there. That's the wrong conclusion. Maybe I can explain why.
The "Eternal Return" argument, in layman's language, goes something like this: "Look, it's admittedly highly improbable that all the billions and billions of variables that come together in our universe would ever come together in precisely the same way a second time. Admittedly, we have zero empirical evidence it has ever happened or ever will again. But the universe is a really, really, really big place that has been going on for a really, really, really long time. So given enough time and space, the admittedly improbable becomes the likely...then the necessary...then the certain...and hence, though we don't know it, we are all "Eternally Returning" to the same exact collocations and interactions of atoms that form the universe as we know it."
But as I've pointed out, take out that element of "really, really, really" big, or "really, really, really" long (i.e. "infinite" or "eternal") and the idea of a "return" at all starts to look totally mythical. There would be no reason even to entertain it as a possibility if a) the universe were not so mind-bogglingly big as to cause us to imagine that *anything's* possible, and b) the variables and permutations in question were not limited in number. If these variables were infinite, then there's "Eternal" but no "Return."
Now to your conclusion. You seem drawn to two things: the idea of "eternity" making the Eternal Return plausible (which mathematically speaking, it simply does not, if the variables themselves are "eternal" in number, i.e. infinite), and secondly, the idea of reincarnation.If true we will live for eternity, and be reincarnated
Well, "reincarnation" isn't the "Eternal Return" of course. "Reincarnation" is the Hindu/Buddhist idea that we are recycled in *different* forms to pay off our karma and eventually escape the wheel of samsara (suffering) that is our material reality. Nietzsche's idea of the "Return," in contrast, is that we recur in *the same form* an infinite number of times, and with absolutely no teleological purpose in view: it just happens, and we're trapped. No escape. No karma. No enlightenment. Just 'round and 'round we go.
Neither Nietzsche's "Return" nor "reincarnation" are plausible if the universe is as you now redescribe it: i.e. limited in size and duration. And if it's actually infinite, then the "Return" is simply mathematically impossible.
Finally, an additional problem is introduced by the idea of a "halting state." It would mean that the universe was obeying some sort of "law" external to the universe itself (for it would be necessary for it to establish all natural laws in all the "returns") a "force" which made it "halt" and "return," and which did so infinitely. Otherwise the mathematics goes wrong again, and you have simple infinity with no "returns." And what sort of force would that be? Why would we be rational to think it existed, and why would we think it did what you say it does?
For, of course, in thinking about this we always need to bear in mind that there is ZERO empirical (or scientific) evidence for an "Eternal Return." The truth is that the whole idea is actually premised on nothing more than a mistaken mathematical postulate, a theoretical guess without evidence or even the accurate use of concepts, as we have seen.
I actually think the whole appeal of the idea is purely aesthetic and irrational (i.e. it's fun to think it's so). But given the mathematical problems, I don't think it can be rationally sustained, even as a possibility.