Tuesday, April 27, 2004

The government and general relativity

Gregg Easterbrook is complaining about the cost of Gravity Probe B.
Well, maybe we don't hear enough about far-reaching implications for the nature of matter and structure of the universe, but is it really worth $700 million of taxpayers' money to gain an increment of abstract knowledge regarding minute distortions in space-time?
This a valid point, which I shall return to. Then Easterbrook wonders off into ignorance.
Einstein made his breakthroughs via thought experiments, using a chalkboard; the cost of deriving the two theories of relativity was extremely small, and that's appropriate, since the practical benefits of the theories are small.
Easterbrook should consider GPS-guided smart bombs, which allowed the U.S. military to avoid civilian casualties to an unprecedented degree in the invasions of Iraq and Afghanistan. GPS would take a big hit in accuracy if we didn't know of relativity:
To get accuracies of order 10 m, light travel times with an accuracy of order 30 ns (nanoseconds) have to be measured. Special relativistic time dilatation (caused by the velocity) and gravitational redshift corrections in these satellites are of order 30000 ns per day.
Actually, according to this book that I used in a class a few years ago, it's 39000 ns per day. To observers on the ground, the GPS satellites' clock appear to gain 39000 ns each day. This correction has two parts. First, clocks at higher altitudes appear to run fast to observers at lower attitudes. For GPS, altitude difference leads to a 50000 ns daily disparity. However, the satellites are moving relative to us, and, according to special relativity, moving clocks appear to run slow. This reduces the daily disparity to 39000 ns.

Another big application of relativity comes from the relativistic Doppler effect, which police use to catch speeders and meteorologists use to detect rain and show us cute color-enhanced Doppler radar images on the nightly news. I will skip the countless applications of relativity to other parts of physics, as most of these are not "real-life" applications, and move on to the big enchilada, E=mc^2, which includes nuclear power and nuclear bombs among its applications.

Getting back to Easterbrook's valid point, Gravity Probe B will test a part of general relativity that will not provide any practical benefit to humanity for the foreseeable future. One might say Gravity Probe B is a purely aesthetic public good. Truth be told, if I were the appropriator of the funds, I would not spend so many taxpayer dollars on a purely aesthetic pursuit. (I want to privatize the national parks too.)

The other reason to fund Gravity Probe B is national prestige. I half-suspect that the reason theoretical science gets the public funding it does in America is less that the people think theoretical science is beautiful than that people want the United States to be the best at science. However, I don't agree with this rationale for public funding either. I think we should just let private actors decide on their own how important prestige is to them. (I would have opposed the Apollo missions were I alive at the time.) Bottom line: things like Gravity Probe B should be privately funded.

In the interest of full disclosure, I should point out that, starting this fall, I will receive funding from the National Science Foundation to do theoretical mathematics research that is even less likely than Gravity Probe B to produce practical benefits. And yes, were I the appropriator of the funds, I would not fund myself. I believe that theoreticians like myself should support ourselves by teaching or from funding from private foundations. But, just as I don't refuse to visit national parks that I think they should be privatized, I don't refuse government funding that I think should come from a private source. If a gift is to be given and the question is just "To whom?", then it doesn't make sense to refuse the gift just because one thinks it is imprudent to give the gift, for one's refusal will not prevent the giving.

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