  A submarine moving at relativistic horizontal velocity sinks in Earth's rest
frame due to length contraction while appearing to float in its own frame.
Using spacetime geometry and the Lorentz transformations, we show that the
resolution lies in how metric components transform between reference frames in
relative motion. This solution frees us from assumptions made in previous
studies on how a Newtonian gravitational force should transform. The method of
background Lorentz transformations is technically simpler than previous
treatments in the framework of general relativity. Moreover, we find a novel
and intuitive understanding of the paradox, and correct an erroneous expression
for the gravitational force obtained by Supplee and used again in the
literature.
