call them O-regions for short. As it hap- 

 pens, the most distant objects visible from 

 Earth are about 40 billion light-years away, 

 so the diameter of our own O-region is 

 twice that number. 



This fact might seem to imply that radia- 

 tion from those distant objects left for our 

 Milky Way before the big bang, about 14 

 billion years ago. But actually, shortly after 

 the big bang, the initial separation velocity 

 between the matter that would become our 

 Milky Way and the source of the radiation 

 was enormous, far greater than the speed of 

 light. Points in different parts of the uni- 

 verse can separate from each other at speeds 

 faster than light, because Einstein's ban on 

 such speeds does not apply to geometric 

 entities with neither mass nor energy. 

 Today whatever was the source of the radi- 

 ation 14 billion years ago has moved to 40 

 billion light-years away. 



Imagine, then, an infinite island universe 

 packed with gigantic spheres, each 80 billion 

 light-years in diameter. Each sphere is an O-region. 

 The spheres expand with the expansion of the uni- 

 verse; the O-regions were smaller at earlier times. 

 All the O-regions looked pretty much the same at 

 the time of the big bang, or in other words, at the 

 end of inflation. But they were different in detail. 

 Small perturbations in density, brought about by 

 random quantum mechanical fluctuations during 

 inflation, differed from one region to another. 



As the perturbations were amplified by gravity, 

 the macroscopic properties of O-regions began to 

 diverge. By the time of galaxy formation, the de- 

 tails of how galaxies were distributed from one O- 

 region to another varied considerably — though sta- 

 tistically the regions were still highly similar. Later 

 on, the evolution of life and intelligence was influ- 

 enced by chance, leading to further divergence of 

 properties among the O-regions. The histories of 

 distinct O-regions should thus be rather different. 



The key observation was that the number of dis- 

 tinct configurations of matter that can possibly be 

 realized in any O-region — or, for that matter, in 

 any finite system — is finite. One might think that 

 arbitrarily small changes could be made in the sys- 

 tem, thus creating an infinite number of possibili- 

 ties. But that is not the case. 



It I move my chair by one centimeter, I change 

 the state of our own O-region. I could instead move 

 it by 0.9 centimeter, 0.99 centimeter, 0.999 cen- 

 timeter, and so forth — an infinite sequence of pos- 

 sible displacements, which more and more closely 

 approach the limit of one centimeter. There is ,\ 



4 



Big bangs 



Barren oldest regions 

 Star-filled newer regions 

 False vacuum 



Island universes condensing out of a region of the inflating "master" universe are 

 depicted schematically at two successive times, one (left) earlier than the other (right), 

 as they might appear if they could somehow be observed from the "outside. " Existing 

 island universes enlarge and new ones form as the false vacuum decays, giving rise to 

 big bangs at the peripheries of the islands and at random places amid the inflating 

 sea. The hot, dense matter created in the big bangs coalesces into stars and galaxies, 

 while central parts of the large islands are extremely old, and thus dark and barren. At 

 the same time, the sea of false vacuum expands even faster than the islands do, mak- 

 ing room for new islands to form. The diagram is based on a computer simulation. 



problem, though. Displacements too close to one 

 another cannot be distinguished, even in principle, 

 because of quantum mechanical uncertainty. 



In classical, Newtonian physics, the state of a 

 physical system can be described by specifying the 

 positions and velocities of all its constituent par- 

 ticles. But because of the underlying reality of quan- 

 tum mechanics, such a description can apply only to 

 massive, macroscopic objects, and even then, only 

 approximately. In the quantum world, particles are 

 inherently fuzzy and cannot be localized precisely. 



Since the precise positions of particles cannot be 

 pinned down, one can resort instead to a so- 

 called coarse-grained description. Suppose the vol- 

 ume of our O-region is divided into cubic cells of a 

 certain size, say one cubic centimeter each. You can 

 specify a coarse-grained physical state by indicating 

 the cell occupied by each particle in the region. To 

 make a more refined description, you just make the 

 cells smaller, say, a cubic nanometer. But this kind 

 of refinement has its limits, because there is a quan- 

 tum mechanical energy cost of localizing particles 

 to small cells. That cost will eventually exceed the 

 available energy in the O-region. 



Evidently, the number of ways a finite number of 

 particles can be distributed into a finite number of 

 cells is also finite. Hence the material content of 

 our O-region can take on only a finite number of 

 distinct states. A very rough estimate of this num- 

 ber gives 1(1 to the power 10 , or I followed by 

 l<>'"' zeros. This number is fantastically huge, too 



July/August 2006 NATURAL HISTORY 



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