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Imagine a tank that accelerates towards a relativistic speed. As the caterpillars are at rest with respect to the ground, the caterpillars will show no length contraction there. But the tank body above it will.

The upper part of the caterpillars, on the other hand, will show more contraction than the tank body does.

What will happen? Will the lower parts of the caterpillars slide along the tank body to "deliver" an extra piece of caterpillar for the upper part which contracts more than the tank body? Will the caterpillars snap? I'm not sure.

Il Guercio
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2 Answers2

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The tank frame measures a track length less than the frame perimeter, so unless the frame perimeter is allowed to compress, or the tracks are allowed to stretch, something breaks.

For the breakage of the tracks in the track frame, you can get the general idea from Bell's Spaceship Paradox if you ignore the vertical movement of the treads and treat the treads as just accelerating in the horizontal direction one way from the farthest back point on the tread and the other way from the farthest forward point on the tread as they round the ends.

For the resolution of amount of track under or over the frame varying depending on which frame you're in, you want the Barn Ladder Paradox.

g s
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"Imagine a tank that accelerates towards a relativistic speed." There is not enough information here to answer your questions. The tank shrinks, expands, or maintains its length depending on exactly when and where you apply the forces that cause it to accelerate. Once you carefully specify all those forces (including forces coming from friction with the ground, etc), all that remains is a straightforward calculation. Until you specify the forces, anything can happen.

WillO
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