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Well, reality does exist, it's just not very real, and its the realest thing there is.
>>by virtue of one happening after the other, they are, in fact, different...Well the only way you could know they are different is if you were using different atoms as a way to store that information (atoms that originated outside that hubble volume and had seen that configuration in a prior volume) since there isn't really anything 'different' about them. Under this thought experiment, they would be exactly identical in every physical way, so they would only be 'different' in your mind -- in the same way that our insistence that two ground state Rubidium atoms are 'different' is a sort of psychological illusion.
Let's turn the screw on this another level. Eventually, you would encounter another you, who was exactly like you in every way and lived your life exactly the same (up until the point of you getting on your infinite spaceship, lets assume.) Now, since you would still exist they wouldn't be you, but lets take that part of the equation out (since it's really just to make the thought experiment easier.)
Since the universe is born, dies out, and then recycles the whole process an infinite number of times (in standard cosmology, independent of this thought experiment) and since it will continue to do so afterwards so it's infinite in time and also in space as described above, that means before you were born there were an infinite number of alternate 'you's exactly identical to you, and there will be an infinite amount after. Also, in whatever direction you look up in the sky, there are an infinite number of alternate yous in a line in that direction (although the nearest one is probably 10 to the quadrillionth power hubble volumes away.)
So, are they really 'you' or are they 'different'? You may say that even if they are physically exactly the same, they wouldn't have the same consciousness as you have, so they're just copies. However, if a physical configuration of brain is what generates your consciousness in the first place, and that's exactly the same, then isn't it a violation of the Copernican principle to suggest that, even though this time your brain resulted in your consciousness, an infinite number of times tried again it would never generate your consciousness? That is absurd, it would violate the principle of empiricism and reproducibility. So even down to the level of subjective phenomena like whether you think 'you' are 'you,' if physical realism is even slightly true, as well as the few scientific observations on which this is based, then it implies this kind of cosmic Berkleyan idealism, uniting seeming opposites.
Plato was the first one to bang on about how even if there were no equilateral triangles in the world, the idea of an equilateral triangle still existed, and would eventually manifest itself -- the same is true for everything. So, I think we end up becoming lost if we fixate on if these alters are 'the same' or 'different.' They are all numerous instances of an informational ideal, which is singular.
I know that was kinda rambly, but I hope it made sense.