This thread is not complete without a link to Paul Krugman's paper, "The Theory of Interstellar Trade". Abstract:
This paper extends interplanetary trade theory to an interstellar setting. It is chiefly concerned with the following question: how should interest charges on goods in transit be computed when the goods travel at close to the speed of light? This is a problem because the time taken in transit will appear less to an observer travelling with the goods than to a stationary observer. A solution is derived from economic theory, and two useless but true theorems are proved.
The forward footnote from the 1978 paper to "Theory capital and travel light-than-faster (Krugman 1987)" is delightful. I hope he remembered to write it!
I notice they restrict themselves to the surface of the earth. Out of curiosity, is it feasible to use modulated neutrino beams to communicate straight through the center of the earth? You could theoretically shave up to 24.3 ms in latency this way.
Not really, it's only about 40 meters in diameter. With trillions of dollars at stake, I imagine they'd find a way to bury one under lower Manhattan.
I've found some figures here -- this is an experiment which creates a focused neutrino beam with an accelerator, and sends it through 810 kilometers of earth to a distant target:
If I'm reading Table IV correctly (page 26, and I doubt it), their expected signal rates are up to 10^3 counts per [(megawatt beam power) * (10^7 seconds time) * (kiloton detector mass), for μ-neutrinos. Some reasonable parameters (skimming in the article) are on the order of 1 MW beam power and 10^2 kilotons detector mass, for a theoretical maximum of 10^-2 counts per second. (But I'm not sure if the accelerator can run continuously, or just in pulses). For a 10,000 km beam the signal rate would up to 100 times lower, because of quadratic beam divergence (though attenuation is negligible). So that's 10^-4 counts per second. To send 10 bits (as on/off pulses) in 10 ms, you'd need a lower bound of 10^3 counts/second. That's 10^7 times more than this experiment. So basically feasible, if you have the resources of a hedge fund: scale the total beam power to ~3 gigawatts (by linear extrapolation ~$300B, but probably much less), and the detector mass to ~300 megatons (of liquid argon?) (also ~$300B by extrapolation. This about 6,000 times Super-K, or a cryogenic sphere ~3 km wide. Or an array of smaller spheres).
Besides, I'm certain my numbers are large overestimates. I extrapolated numbers from a completely different scale; surely optimizing for this problem would yield very different designs. Like more focused neutrino beams. They have a large fraction of their neutrino beam going out >6 km off-axis (at 810 km distance); at 8,100 km, this would be >60 km off axis. So there's maybe 6-7 orders of magnitude potential in designing a lower-divergence beam.
Now that I've finished reading it, I'm kinda bummed that they didn't incorporate the high-res gravitational map of the earth. I wanna see some lorentz transforms in the mix :/
>I wanna see some lorentz transforms in the mix :/
it is somewhat present as they said "for spacelike".
There is also another opportunity - by locating your data center on higher floor where gravitation is lower and thus time is flowing faster you'd get your computers work faster compare to the ones on the ground floors.
Well, I feel OK for not realizing Mauritius is there, but alas, I am guilty of being grossly wrong on where Bermuda is, and I can't even blame the thing that taught me how the Caribbean is laid out, Sid Meier's Pirates! for the Commodore 64, which does in fact include Bermuda [1]. (Though for obvious reasons I didn't spend much time up there.) Mea culpa.
This paper extends interplanetary trade theory to an interstellar setting. It is chiefly concerned with the following question: how should interest charges on goods in transit be computed when the goods travel at close to the speed of light? This is a problem because the time taken in transit will appear less to an observer travelling with the goods than to a stationary observer. A solution is derived from economic theory, and two useless but true theorems are proved.
http://www.princeton.edu/~pkrugman/interstellar.pdf