Volume 116, Number 5, December 2016
|Number of page(s)||7|
|Published online||25 January 2017|
Solution of Supplee's submarine paradox through special and general relativity
Universidade Federal de São Carlos - Caixa postal 676, CEP 13565-905, São Carlos-SP, Brasil
Received: 6 January 2017
Accepted: 12 January 2017
In 1989 Supplee described an apparent relativistic paradox on which a submarine seems to sink to observers at rest within the ocean, but it rather seems to float in the submarine proper frame. In this letter, we show that the paradox arises from a misuse of the Archimedes principle in the relativistic case. Considering first the special relativity, we show that any relativistic force field can be written in the Lorentz form, so that it can always be decomposed into a static (electric-like) and a dynamic (magnetic-like) part. These gravitomagnetic effects provide a relativistic formulation of Archimedes principle, from which the paradox is explained. Besides, if the curved spacetime on the vicinity of the Earth is taken into account, we show that the gravitational force exerted by the Earth on a moving body must increase with the speed of the body. The submarine paradox is then analyzed again with this speed-dependent gravitational force.
PACS: 04.20.-q – Classical general relativity / 03.30.+p – Special relativity / 04.40.Nr – Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
© EPLA, 2016
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