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.

The submarine paradox can be resolved by considering a moving fluid through another fluid in a weak gravitational field, where the moving fluid has a larger pressure and sinks.

Paper

Submarine paradox softened

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