A Brazilian physicist has resolved a paradox thrown up by Einstein's theory of relativity1.

According to the theory, objects travelling at close to the speed of light appear to get shorter when viewed by stationary observers. But from the viewpoint of those on the moving object, the observers - who are receding at close to the speed of light - appear shortened instead. Other dimensions remain the same.

When these notions are applied to a submarine just below the water's surface, an inconsistency seems to arise. Spectators on an anchored ship would see the submarine shrink as it moves parallel to the surface at near-light speed. The resulting density increase would sink the vessel. The submarine crew would see the opposite: water rushing past them would contract and get denser, making the submarine more buoyant and causing it to rise.

Relativity insists that both viewpoints are equally valid - so does the sub sink or swim?

It sinks, says George Matsas of the State University of São Paulo in Brazil. He has used the theory of general relativity to include the effect of the different reference frames on the space-distorting force of gravity. Although the surrounding water does look denser to submariners, they also experience gravity as being stronger, creating a net downward force.
This explanation is not the first. In 1989 US physicist James Supplee tackled the problem using Einstein's earlier and simpler theory of special relativity, which explains how movement at close to light speed can distort space. But special relativity, unlike general relativity, does not include the space-bending effects of gravity.

Supplee also concluded that the submarine sinks - but he had to factor gravity into his calculations rather artificially. He argued that the sub sinks as it accelerates because relativity distorts the shape of the sea floor, bending it upwards below the sub.

Matsas reckons that similar calculations might help to solve other puzzles. These include how the second law of thermodynamics - which states that nothing can reduce the total disorder, or 'entropy', of the Universe - can be preserved around black holes

References
Matsas, G. E. A. Relativistic Archimedes law for fast moving bodies and the general-relativistic resolution of the "submarine paradox". Physical Review D, 68, 027701, (2003). |Article|