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Physics

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    $\begingroup$ @Albert I believe what is being said is that the ruler measures the distance between two points in space just as the metronome measures the “distance” between points in time. If you set off a metronome at one tick per second and then move it at close to C then the ticking with slow down. Just as the ruler will contract. But when you bring it back to relative resting it will still be ticking at 1 tick per second. Whereas the clock in the paradox is measuring the time interval from leaving to returning. Just as the odometer is measuring the perceived distance travelled from leaving to returning. $\endgroup$
    – Fogmeister
    Commented Oct 8, 2019 at 12:12
  • 6
    $\begingroup$ @Albert Because the clock tells you the time. If you took two clocks that both read 12:00 and sent one on a relativistic trip before bringing it back to rest, you could end up with, say, 12:05 and 12:10. This 5 minute difference will never vanish. The clocks maintain a permanent record of their dilation. Metronomes have no capacity for this. $\endgroup$
    – HTNW
    Commented Oct 8, 2019 at 13:09
  • 9
    $\begingroup$ The point is that the twin who travelled and then came back does not spend the rest of their life moving in slow motion, or any flatter. They now move at ordinary speed (although are younger than they should be). In a similar way they are ordinary in shape (no space compression) but the total distance they have travelled (according to a machine they brought with them on their space voyage) is a lot less than the total distance that you would have thought it was to their destination and back. $\endgroup$
    – Dast
    Commented Oct 8, 2019 at 13:10
  • 9
    $\begingroup$ @Albert a metronome is not a clock. If you put a counter on it then it becomes a clock and is no longer a metronome. $\endgroup$
    – OrangeDog
    Commented Oct 8, 2019 at 14:16
  • 3
    $\begingroup$ @Albert a metronome is a frequency standard. It measures temporal intervals, $\Delta t$. A clock is a metronome plus a counter. It measures elapsed time $t=n \Delta t$. Similarly a ruler or rod measures spatial intervals, $\Delta x$. An odometer is a ruler plus a counter. It measures elapsed distance $x=n\Delta x$. Hence the similarity. Time dilation affects metronomes the same way that length contraction affects rulers. Time dilation affects clocks the same way that length contraction affects odometers. $\endgroup$
    – Dale
    Commented Oct 8, 2019 at 17:35