Perhaps the most disturbing of which would be the fact that, by definition, at some distance, there would have to be a duplicate of yourself.
Wouldn't it also mean that there are an infinite number of duplicates out there? Including one typing this very comment, but who typos and leaves the "s" off "duplicates"?
I'm very much not a mathematician nor physicist, can this really be true if the universe is infinite in size? Asking as a layman, at what point when dealing with infinite possibilities and probabilities does something become certain? That's what really terrifies me.
If the universe is flat, and therefore infinite, yes it means that most probably there are an infinite number of identical duplicates of you. It does not mean, however, that there are any duplicates of you that make a particular typo. I should think that there are an infinite number of such duplicates for any given typo, BUT it may also be the case that such worlds are impossible. E.g., physics is deterministic enough and chaotic enough that there is no slight nudge to the initial conditions of a world that will result in such a minor eventual difference to occur.
I.e., just because there are an infinite number of parallel worlds, doesn't mean that every imaginable thing occurs in them. What occurs in a parallel world, must be possible.
I think you make a very important point. Even if the universe was infinitely large, there might be a point where past that the conditions can't exist that would allow something like our planet to function. For infinity to grant you duplicates of yourself the possibility must exist within that "zone of infinity". Gravity for example might be stronger or weaker.
What if the universe is empty beyond a certain distance from the origin/central point, like a tiny explosion in the middle of an unending emptiness? Then there wouldn't have to be duplicates of you.
(This is about the same thing as the question asked below about whether infinite size implies infinite mass.)
In a flat universe, the universe starts off infinitely large and infinitely dense at time 0. As the universe expands, it gets less dense. Imagine an infinitely dense rubber sheet that starts to stretch at time 0, and after time 0 it is no longer infinitely dense, and it keeps slowly stretching forever, getting less and less dense over time. That's the universe as it is currently envisioned.
But our "Hubble sphere" is in no way special compared to other Hubble spheres. Our Hubble sphere is the part of the universe surrounding us from which light has arrived. Outside that sphere, nothing has a causal connection to us, since nothing can travel faster than the speed of light.
I.e., it just wouldn't be the case that our Hubble sphere is full of stuff and all the other Hubble spheres are are so different as to be empty.
If the universe is infinite in size, does that automatically imply that it is infinite in mass?
That is, I can imagine a mass distribution that decreases as it moves away from the center, such that the total amount of mass is finite. In which case these problems don't apply.
I'm not sure whether that's possible though. If space-time is flat, that means there's a specific mass density in that universe, in which case infinite mass exists. For an infinite universe to have finite mass would mean a density that tends to zero, in which case we should observe a saddle shape in the experiments described. That is, unless space is just -locally- (in 14.6 billion light years) flat.
I don't claim to be right. But, you can use this possibility to ease your existential dread at being one of infinitely many near-identical copies. Of course you still have to deal with many-world quantum physics...
Right, as long as you look through an amount of space that scales superexponentially with the complexity of the entity you want to find a copy of. (With stronger assumptions, like attractors in development of matter according to physical laws, you might be able to improve the bound.)
But don't worry, you get to search in three dimensions, so its distance only scales with the cube root of that!
The way I've heard this describes is with an analogy. If you have an infinite number of decks of cards, shuffled randomly, the same shufflings will show up an infinite number of times. There are only so many ways to put together an infinite number of particles, do the shufflings get reused.
You don't. There are bounds on how much matter can be contained within your past light cone before it turns out you are simply in a black hole.
The number of possible past light cones that could originate from the same Big Bang using reasonable assumptions about QM is staggeringly large, but nevertheless, finite.
http://space.mit.edu/home/tegmark/PDF/multiverse_sciam.pdf
Perhaps the most disturbing of which would be the fact that, by definition, at some distance, there would have to be a duplicate of yourself.