Length contraction leads to a (relatively speaking) fixed observer measuring lengths along the direction of relative motion as shorter than the observer in the (relatively speaking) moving frame. The usual example of a clock working in this way is a light clock, but what if it's a gear clock? The gears would appear ovoid, but ovoid gears don't work. My sense of what the observer would see is that the gears are sort of flexible and as they turn, they change in length, so that the gears actually work by virtue of their flexibility. A bike's spoked wheel would be a simpler example, and the simplest would the usual pole, rotating in line with the direction of motion, one should see it get shorter and longer (and also thinner and fatter, assuming it has with a length and width). Right?
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$\begingroup$ That ovoid gears don't work is not completely true. Watch these gears that were shown in the intro of the Swedish TV program "Tekniskt Magasin" once upon a time: youtube.com/… $\endgroup$– md2perpeCommented Dec 24, 2021 at 19:16
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2 Answers
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You have discovered the Ehrenfest paradox.
Also see Relativistic Bicycle Wheel
It gets weird when you consider a propeller. Global vs Rolling Shutter at Relativistic Speeds
answered Dec 24, 2021 at 19:14
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$\begingroup$ Thanks! (Actually, I've seen the rolling shutter effect on pictures that I've taken from prop plane windows. Never really thought of the relationship to relativity, though!) $\endgroup$ Commented Dec 24, 2021 at 19:45
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Yes, the gears would change shape, but they would still work. Imagine looking at the gears of a clock from some acute angle- because of your perspective, they would appear oval in shape, but their change of appearance wouldn't affect their function.
answered Dec 25, 2021 at 7:57