I got a lot of angry complaints about my slate article because I so cavalierly dismissed the possibility of parallel universes — or at least the parallel universes described by Hugh Everett in his Many Worlds Interpretation of Quantum Mechanics.

I stand by that position, but it did lead to an interesting discussion with a colleague of mine who is now working on a philosophical paper dealing with the question of whether there is an identical “you” somewhere in the universe. He was prompted not so much by Everett, but instead by a paper by Max Tegmark (the link is to one of many similar papers that Tegmark has written on the subject). Tegmark describes a hierarchy of possible “parallel universes” of which Everett’s many worlds happens to be the third possibility.

So even though I reject the Many World Interpretation (and for the record, I mostly reject the idea that we can visit any of those other universes; as a mathematical tool, they work just fine), here’s a question: If we were able to travel far enough, would we encounter an identical you?

**Level 1**

From Tegmark’s figure:

The universe is big, very big. It’s so big, in fact, that we can’t see to the ends of it, even with light traveling toward us since the beginning of time. We can only see (to within a factor of 3) to a distance of about 14 billion light years. This is known as the horizon, and nothing outside the horizon could possibility have affected what happens here on earth. You might think of everything within the horizon as being our “universe” (with a small u).

However, it’s clear that our universe doesn’t encompass the entirety of the Universe (big U). Spaces stretches for vast distances beyond the horizon. How far? Hard to say, but the inflationary model of cosmology (and our best observations from the WMAP satellite) suggest that the Universe (big U) is very nearly flat. Inflation suggests that it is so flat that the “radius of curvature” (size of the Universe) might be ~10^40 times larger than the horizon.

Now quantum mechanics tells us that there’s only a finite (but gargantuan) number of ways to arrange (say) the protons in the universe, and if the Universe is big enough, eventually, you’ll find a duplicate not only of you, but of the entire universe. Spooky, no? This is essentially Tegmark’s argument, and he argues (conservatively) that there should be an identical universe (small u) within 10^10^115 m from here. That is a number so huge that I don’t have an intuitive feel for it. Nevertheless, it’s finite, and if the Universe is infinite, then anything a finite distance away can be found an infinite amount of times.

My philosopher friend’s objections aside, I have two major issues with this.

- It’s not clear that the Universe is actually as large as it needs to be to have duplicates. That is, the observational and theoretical size limits are many, many orders of magnitude smaller that 10^10^115 m. Inflation — the basic theory underlying all of this, suggests that the universe blew up like a balloon at 10^-35 seconds or so after the big bang. But even so, this would just suggest that the Universe is very CLOSE to flat (flat=infinite), but not exactly flat (not exactly flat=finite). And the WMAP satellite puts the limits at even smaller. Basically, our current measurements suggest that the radius of the Universe (big U) is at least 100 times (or so) the horizon scale of the universe (little u).
So while the argument may be theoretically correct, the Universe may not be big enough to accommodate an identical you.

- In the 1990’s, Cornish and Spergel showed observationally that even if we live in a pac-man universe (in which you’d “loop around” if you went far enough) then the scale for that to happen was much larger than the horizon.
However, general relativity (the theory that tells us that the universe might be curved in the first place) has nothing to say about whether or not we live in a pac-man universe or not. It may be that the universe is flat, but much like a piece of paper rolled into a cylinder, it loops back on itself. In that case, the space in our universe, might well be finite, and rather limited — in which case, no duplicate you.

My point isn’t that there isn’t a “level 1 duplicate,” but just that observations don’t demand it.

As for level 2:

that’s a conversation for another day.

**-Dave**

“(to within a factor of 2)”

Don’t you mean a factor of 3? The horizon distance is ~3ct_0.

Sure, why not? Actually, as I recall, it’s 3ct_0 only for an Einstein-deSitter universe (and in comoving and proper distances only; distance depends sensitively on what you want to do with it at z > 1), but you’re right — comoving is the most reasonable interpretation.

I was too lazy to do the calculation at the time, but it turns out that for our universe, the number is closer to 3.5. The point, I think you’ll agree, remains pretty valid.

I’ll fix it in the body of the text to satisfy the nitpickers (although I’m sure some reader living in a radiation-dominated universe will want me to switch it back).

– Dave