Relativity goes underwater with Supplee's Paradox

Too often relativity is confined to space ships and interplanetary travel. It's time to dive and see what weird ideas relativity can bring to us from beneath the sea.

Jim Supplee first thought up a novel spin on the weirdness of relativity when he was a graduate student, and came back to it years later as a professor. Let's say a submarine has the exact same density as the water around it. It therefore has neutral buoyancy and neither sinks nor rises. Once the engines engage it shoots forward.

When something moves at high speed (with respect to the viewer), the effects of relativity make its length contract. From the point of view of someone sitting on the sea floor, that makes the submarine more dense than the water around it, and so it sinks. Then again, from the point of view of the submariners, the submarine stays still while the water flows by it. The water contracts, getting denser, and the submarine floats upwards.

Which way does it work? According to Supplee, the submarine sinks — not because of density, but because special relativity causes the dimensions of the ocean to change. The sea floor seems to curve upwards, so the submarine, going in a straight light, crashes into the ground. Another physicist, George Matsas, agrees with the results, but doesn't use the same method. Matsas argues that, although special relativity causes the ocean water to look denser to the submariners, general relativity amps up the gravity they feel so much that this dense medium can't save them. The submarine sinks under ultrastrong gravitational forces and, yes, crashes into the ground. The moral is, if the universe were a sea, any starships we sent out would end up at the bottom.

Image: U.S. Navy.

[Via Nature, The Dilated Times.]