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Required fields*

Rev

Required fields*

Special theory of relativity paradox (buoyancy)

We have a submarine (sub) in a frictionless liquid and the average sub density is equal to the density of a liquid. Sub is fully submerged not touching the bottom. Now the sub moves at near speed of light. In the reference frame of liquid the sub undergoes relativistic contraction, has higher density now and must sink. In the reference frame of a sub the liquid undergoes relativistic contraction, is now more dense. Hence, the sub must resurface. Contradiction. How to resolve it? Idon't think we need GTR, Newtonian gravity should be enough.

Answer*

Density of a submerged body is obviously determinative of the direction of its motion only when the sub is initially at rest with respect to the water.

If the sub already moves horizontally even a bit, lots of water of the same volume moves in the opposite direction in the frame of the still water far from the sub, with the opposite velocity (the water moves and fills in the space the sub was in previously). This motion of water could be directed by the sub control surfaces (diving planes) to produce thrust in any direction, up or down. Then, density of the sub and the water alone is not enough to determine the direction of motion; the shape of the sub enters the analysis too.

We can eliminate this effect - if the sub and the flow are very  symmetric (topside vs bottomside), there may be zero thrust in vertical direction on the sub of the above kind. Then, if the sub is fast enough to undergo substantial relativistic contraction, its density increases, so the usual simple argument is that in the frame of the water, the sub should move down, due to greater density of the sub. *However*, this argument assumes, erroneously, that whether the sub goes up or down is determined by densities of the sub and still water far from the sub alone.

In fact, the pressure forces on the sub are not due to hydrostatic forces of still water, but they are forces due to *moving water*. Water is moving near and around the sub, and this motion is relativistic too (moving in the opposite direction to fill in the space the sub was in). Thus that water undergoes contraction as well, and its density increases as well. Not all water gets denser, only that moving fast, near the sub. This denser water itself is not hydrostatically stable and experiences net force downwards. A complicated flow of dense water mixing with slower, less dense water, may occur. Net result of this on the sub is not clear; this complicated flow can send the submarine in any direction.

Edit Summary*

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$\begingroup$ We ignore viscosity, structural considerations, control surfaces, shock waves. As well as the fact that if we rub hands at half light speed, we get energy yield of a thermonuclear bomb. $\endgroup$

sixtytrees
– sixtytrees

2025-10-12 10:22:54 +00:00
Commented 2 days ago

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