I just started reading A Fire Upon the Deep by Vernor Vinge. Interestingly in Vinge’s universe there is a stratum for the laws of physics in the universe. In particular in the galaxy proper, the speed of light is finite, but as one gets farther away from the galaxy this changes. The futher one gets from the galaxy, the more amazing technology which one can build and operate.
Which got me thinking about Scott Aaronson’s paper NPcomplete Problems and Physical Reality. In this paper, one issue Scott discusses something which you will hear over many coffee breaks at quantum computing conferences: can one use relativity to create exponential speedups in computational power. One way you might think of doing this involves using time dialation. Set your computer up to calculate some hard problem. Then board a spaceship and head off for a leisurely trip around the galaxy at speeds nearing the speed of light. When you return to your computer, via the twin paradox the computer will be much older than you, and will, hopefully have solved the problem. Roughly if your speed is [tex]$beta=v/c$[/tex], then you can get a speedup for your computation which is proportional to [tex]$(1beta^2)^{frac{1}{2}}$[/tex]. The problem with this scheme, it appears, is that in order to work, you need to get your [tex]$beta$[/tex] exponentially close to the speed of light, and this would require an exponential amount of energy. So it doesn’t seem that such a scheme would work. Another proposal, along similar lines, is to set up your computer, and then travel very close to a black hole (not recommended, only trained professionals should attempt this.) Then due to the gravitational time dilation, you can mimic the twin experiment and return to a (hopefully) solved problem. However, again, it seems that to get yourself out of the computational well requires an amount of energy which will destroy the effect.
But what Vinges’s novel got me thinking about was the following: there appears to be a computational advantage to being away from masses. Assume that there is some form of life surrounding a black hole (OK, big assumption, but hey!) Then it seems to me that this computational advantage for an intelligent species might contribute to a competetive advantage in the evolutionary sense. Thus we might expect that a civilization for which gravitational time dilation is a real effect will live in a world, much like Vinge’s world, where lesser intelligent animals live close to the mass and the more intelligent, more magic wielding creatures live farther away (“Any sufficiently advanced technology is indistinguishable from magic”Arthur C. Clarke.) Following Vinge’s novel, one might even speculate about the comutational advantage of being outside the galaxy. The time dilation effect there is about one part in one million (as opposed to one part in a one billion for the effect from being at the surface of the earth versus “at infinity.”) Unfortunately this seems like to small of a number to justify any such effect.
OK, enough wild speculation for a Tuesday.
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Actually, you don’t necessarily need a lot of energy to see the time dilation effects around black holes, if you can carefully insert yourself onto a nearzero energy orbit that happens to pass very close to the horizon; you will do many orbits, have huge time dilation effects, and then return back to radii at which you started. So energy is not the problem. But other material orbiting, radiation, and orbital insertion can all make for significant difficulties. I mean, besides the problem of getting to a nearby hole…
Interesting. What sort of precision will you need to obtain such an orbit? Maybe this is where you lose?
Good question. Could be worked out in a hard afternoon of taking derivatives, at least for a simple, symmetrical, unrealistic case.