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By Root 1972 0

number of particles, each of which can have finitely many distinct positions and velocities, means that within any cosmic horizon only a finite number of different particle arrangements are available. (In the more refined language of quantum theory proper, which we’ll encounter in Chapter 8, we don’t speak of particle positions and velocities per se, but rather of the quantum state of these particles. From this perspective, we would say there are only a finite number of observably distinct quantum states for the particles in the cosmic patch.) Indeed, a short calculation—described in the notes, if you’re curious about the details—reveals that the number of distinct possible particle configurations within a cosmic horizon is about 1010122 (a 1 followed by 10122 zeros). This is a huge but decidedly finite number.14

The limited number of different clothes combinations ensures that with enough outings, Imelda’s attire will necessarily repeat. The limited number of different card orderings ensures that with enough decks, Randy’s shuffles will necessarily repeat. By the same reasoning, the limited number of particle arrangements ensures that with enough patches in the cosmic quilt—enough independent cosmic horizons—the particle arrangements, when compared from patch to patch, must somewhere repeat. Even if you were able to play cosmic designer and tried to arrange each patch to be different from the ones you’d examined before, with a big enough expanse you’d eventually run out of distinct designs and would be forced to repeat a previous arrangement.

In an infinitely big universe, the repetition is yet more extreme. There are infinitely many patches in an infinite expanse of space; so, with only finitely many different particle arrangements, the arrangements of particles within patches must be duplicated an infinite number of times.

That’s the result we’ve been after.

Nothing but Physics

In interpreting the implications of this statement, I should declare my bias. I believe that a physical system is completely determined by the arrangement of its particles. Tell me how the particles making up the earth, the sun, the galaxy, and everything else are arranged, and you’ve fully articulated reality. This reductionist view is common among physicists, but there are certainly people who think otherwise. Especially when it comes to life, some believe that an essential nonphysical aspect (spirit, soul, life force, chi, and so on) is required to animate the physical. Although I remain open to this possibility, I’ve never encountered any evidence to support it. The position that makes the most sense to me is that one’s physical and mental characteristics are nothing but a manifestation of how the particles in one’s body are arranged. Specify the particle arrangement and you’ve specified everything.15

Adhering to this perspective, we conclude that if the particle arrangement with which we’re familiar were duplicated in another patch—another cosmic horizon—that patch would look and feel like ours in every way. This means that if the universe is infinite in extent, you are not alone in whatever reaction you are now having to this view of reality. There are many perfect copies of you out there in the cosmos, feeling exactly the same way. And there’s no way to say which is really you. All versions are physically and hence mentally identical.

We can even estimate the distance to the nearest copy. If the particle arrangements are randomly distributed from patch to patch (an assumption that’s compatible with the refined cosmological theory we will encounter in the next chapter), then we can expect that the conditions in our patch will be duplicated as frequently as those in any other. In every collection of 1010122 cosmic patches, we thus expect there to be, on average, one patch that looks just like ours. That is, in every region of space that’s roughly 1010122 meters across, there should be a cosmic patch that replicates ours—one that contains you, the earth, the galaxy, and everything else that inhabits our cosmic horizon.

If you lower