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Relativistic Statistical Arbitrage

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54 pointsyummyfajitas17 comments

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.

http://www.princeton.edu/~pkrugman/interstellar.pdf

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.

Detector size would be a problem ( http://upload.wikimedia.org/wikipedia/en/6/62/Super-k.jpg )

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:

http://nwg.phy.bnl.gov/~diwan/nwg/fnal-bnl/report.pdf

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).

One big problem with your theory - is there even that much argon on the earth? Argon, like all noble gases is extremely rare.

Not really. It's not rare, it's 1% of the atmosphere or about 50 trillions tons. And it's not essential for neutrino detectors anyway.

http://en.wikipedia.org/wiki/Atmosphere_of_Earth

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.

There's more argon in Earth's atmosphere than CO_2. There's a fun fact for ya.

I'm a fan of dry satire, and this is the best commentary I've seen so far on high frequency trading.

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.

What are the two exchanges shown as being about 500 miles east of the Carolinas and five hundred miles east of Madagascar?

I would guess Bermuda and Mauritius, in order.

(edit) That is the case, although it's rather a joke because these exchanges are ridiculously tiny...

http://www.world-exchanges.org/member-exchanges

Although I suppose they'll grow in importance as this relativistic arbitrage stuff becomes mainstream.

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.

[1]: http://project64.c64.org/maps/Pirates%20map.jpg

Bermuda and Mauritius? Not sure why there would be exchanges there.

They're centers of offshore financial activity in the West and India, respectively.

Oh boy... So many friends of mine went to finance precisely because they didn't like physics...

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