Submarine paradox softened
arXiv:2112.11162 · doi:10.1119/5.0084185
Abstract
In Supplee's submarine paradox, a naive argument based on Lorentz contraction leads to a contradiction that a fast submarine should sink in the water's reference frame but float in the submarine's reference frame. Due to the submarine's rigidity constraints, it is not easy to resolve the paradox in a manifestly covariant form. To simplify the problem, we consider a version of the paradox in which one fluid moves through another fluid. An analysis of ideal relativistic fluids in a weak gravitational field shows that the moving fluid has a larger pressure and hence sinks, in agreement with known results for the rigid submarine.
8 pages, 1 figure, significantly revised and extended, accepted for publication in Am. J. Phys