Submarine paradox softened

TL;DR

This paper resolves the submarine paradox by analyzing relativistic fluid dynamics, showing that a moving fluid's increased pressure causes it to sink, aligning with classical expectations.

Contribution

It introduces a simplified fluid dynamics model to clarify the submarine paradox within relativistic physics, emphasizing the role of pressure and rigidity constraints.

Findings

Moving fluid has higher pressure when in motion.

The moving fluid sinks, consistent with classical intuition.

Rigidity constraints are crucial in resolving the paradox.

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.