Ehrenfest trains
editAfter day's work I've decided to try my creative side and aimed for an illustration which may appeal to readers not interested in mathematics.
As most modern authors, I'd suggest to leave the question of expansion of the disk by centrifugal forces aside and take the setup of an (elastic) ring in fixed gearing. IMHO it's gets even more illustrative, when dividing the elastic ring in rigid and and elastic sections.
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Voila! The Ehrenfest train, consisting of 40" boxcars alternating with elastic joiners, at rest also 40" long.
In the example pictures 12 boxcars are choosen. In the left picture you see the situation at rest. On board (light red) and platform-side (light blue) yard sticks agree, that
- a boxcars measures 40"
- a joint measures 40"
- the complete train measures 960"
In the right pictures the trains moves with 0.6c. Now the platform-side (light blue) yard sticks give, that
- a boxcars measures 32"
- a joint measures 48"
- the complete train measures 960"
Whereas the on board (light red) yard sticks give, that:
- a boxcars measures 40"
- a joint measures 60"
- the complete train measures 1200"
BTW, the Ehrenfest train can also do double duty as Bell's spaceship paradox on rails.
Pjacobi 00:44, 3 June 2006 (UTC)