Starship enterprises

STARSHIPS (see article) are a fantastical subject. Yet when engineers design them, they try to be as rigorous as possible. After all, the laws of physics apply to a starship just as much as they apply to bridges or motorbikes.

It is not just scientists who enjoy technically rigorous speculation, though. Economists have investigated interstellar travel as well. One of the best-known papers was written by Paul Krugman, a trade theorist, in 1978, in between his duties as an “oppressed assistant professor”. “The Theory of Interstellar Trade” describes itself as “a serious analysis of a ridiculous subject, which is of course the opposite of what is usual in economics”.

Dr Krugman, a science-fiction fan, ponders how trade might work between two widely separated planets, Earth and Trantor. Such trade will be affected by relativity theory, which shows that beings on Earth (or Trantor) will see time pass at a different speed from those who are on board cargo ships moving between the two. This could make it hard to calculate the net present value of a shipment. And the fact that messages can move at best at the speed of light (and cargoes more slowly still) might do odd things to the ability to arbitrage between the economies of the two worlds.

After working through the maths, Dr Krugman came up with two fundamental theorems of interstellar trade. The first is that interest costs on travelling goods should be calculated using clocks on planets, not ships. This is because the opportunity cost of trade—buying a bond on Earth (or Trantor), say—is calculated using planet-bound clocks, regardless of what relativity does to a businessman travelling alongside his cargo.

The second theorem states that, though long travel times mean prices on trading planets will never reach parity, interest rates will. If they differed, then investors could buy bonds on the more attractive planet, driving its rates back to parity with those on its trading partner.

Dr Krugman is not the only economist to have considered such issues. Tyler Cowen, of George Mason University, in Virginia, makes another point. Relativity means that on a starship travelling near the speed of light, a handful of years might pass for the crew while hundreds passed on a planet it was travelling from or to. That makes calculating interest rates hard, since savers could pay starship captains to carry them forward in time, to reap the benefits of centuries of accumulated interest. In a Star Trek-style world, then, Dr Cowen thinks the chief determinant of interest rates would be the price of starship fuel. Better buy antimatter futures while they are cheap.