April 30, 2004

What to do about the universe?

Slashdot mentioned the paper Universal Limits on Computation by Lawrence M. Krauss and Glenn D. Starkman. They demonstrate that in a de Sitter spacetime (which the universe will approximate if dark energy is dominant) the amount of energy that can be scooped up and used for computation by any civilization is finite.

It is a nice example of clearly reasoned physical eschatology, even if the conclusion is a bit depressing. But then again, it is hard to get the fire-and-thunder drama of Tiplerian omega points in an open universe in the first place, and rapidly expanding open universes are especially nasty. We need to fix it.

The basic result of the paper seems very robust. In a de Sitter spacetime there is a horizon beyond which no information or matter can reach an observer. Hence the amount of computation a finite-sized system can achieve is finite, even given infinite time. They show that you can get 3.5e67 J by spreading replicating von Neumann probes converting rest mass into energy and sending it back to their origin, roughly the total energy of baryonic matter within today's horizon. They also show that distributed processing achieves 1/6 less information gain than having it all at the origin (and this assumes no energy losses due to transmission).

The real killer is the hbar H/2 pi k_B Hawking radiation from the horizon, since it is constant. This makes the cost of erasing one bit of information (necessary for error correction even if reversible computation is used otherwise) constant, and the total amount of information processing finite. If the universe got cooler fast enough the amount of information processed could diverge.

So we need to either find a way of cooling off parts of the universe so that we can do more computation, change the spacetime topology to get rid of horizons or construct a more liveable baby universe.

Cooling requires a heath bath colder than the horizon Hawking radiation. A neat idea suggested by Wei Dai is to use big black holes. But to get colder than the horizon, we need holes with radii larger than it, so that scheme won't work. To my knowledge there are no other suitable heat baths, although maybe one could pump entropy from baryonic matter into weakly interacting particles like neutrinos (neutrino cooling). Unfortunately they do interact weakly (duh!), so in the long run both heat reservoirs will tend to equilibrate. But as a short run or local solution it might work well.

Changing spactime topology seems to be hard, since any action done to remove the horizon has to reach it, but the accelerating expansion of the universe makes it recede. There are likely other, deeper. reasons why they can't be removed like the Penrose inequalities and other global constraints.

That leaves building a new universe. The Krauss and Starkman paper gives us how much mass-energy we could in principle gather together. It is obvious that we could just pile it up into a big black hole (which, according to some models such as the Linde-Smolin model, might spawn a baby universe or more), but it might be possible to convert it to something more useful. Especially if inflation holds it ought to be possible to cause the formation of a new inflationary domain, which would hopefully be more hospitable. Energy-wise it seems plausible that 1e67 J could be used to drive the energy density to the Planck level in a fairly large region enabling inflation to kick in. The key problem here might be that the new domain receedes too fast from the current spacetime for us to follow, and of course (as noted by Tipler) that the amount of information we can squeeze into the "wormhole" into it is finite. However, when using it as an escape hatch to an universe with unbounded future this might be acceptable. A more pressing and interesting problem is whether it is possible to do chaos control on chaotic inflation to achieve the right symmetry breaking for pleasant physics and the right kind of vacuum energy.

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