**#4** by **Teuton** » May 01, 2011 12:20 am

A crucial premise in the infinite replication scenario is that a region of space/spacetime can contain only a finite number of particles, and that there are also only finitely many possible places and speeds for these.

"Consider a region the size of today's cosmic region, a sphere with a radius of 41 billion light-years. A region, that is, which is the the size of a single patch in the cosmic quilt. And consider filling it…with particles of matter and radiation. Here's the question: How many different arrangements of the particles are possible?

Well, as with a box of Legos, the more pieces you have—the more matter and radiation you cram into the region—the greater the number of possible arrangements. But you can't cram pieces in indefinitely. Particles carry energy, so more particles means more energy. If a region of space contains too much energy, it will collapse under its own weight and form a black hole. And if after a black hole forms you try to cram yet more matter and energy into the region, the black hole's boundary (its event horizon) will grow larger, encompassing more space. There is thus a limit to how much matter and energy can exist fully within a region of space of a given size. For a region of space as large as today's cosmic horizon, the limits involved are huge (about 10^56 grams). But the size of the limit is not central. What's central is that there is a limit.

Finite energy within a cosmic horizon entails a finite number of particles, be they electrons, protons, neutrons, neutrinos, muons, photons, or any of the other known or as yet unidentified species in the particle bestiary. Finite energy within a cosmic horizon also entails that each of these particles…has a finite number of distinct possible locations and speeds. Collectively, a finite 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. … Indeed, a short calculation…reveals that the number of distinct possible particle configurations within a cosmic horizon is about 10^(10^122) (a 1 followed by 10^122 zeros). This is a huge but decidedly finite number. … [T]he 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."

(Greene, Brian. The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. New York: Alfred A. Knopf, 2011. pp. 32-3)

"Perception does not exhaust our contact with reality; we can think too." – Timothy Williamson