Suppose I'm able to build a huge analog clock, with a seconds hand very long. I want have hand end running at light speed (300,000 km/s). Needle then has to be 300,000km*60s/(2pi) = about 2,864,788km (or 2,8*109m).

Not too bad, it's more-or-less 7 times distance Earth-Moon.

Question is... if I build the hand like a "cable" 1-copper atom thick (copper atom has a diameter of 2.5*10-10m), I will have a needle made by (2.8*109)*(2.5*1010) atoms, aka about 7*1019 atoms. Since 1g of copper has 6.02*1023/6.3 atoms, aka about 9.5*1022 atoms, our needle has a weight of about 0.0007g. Good, not too expensive.

Well, it is possible to have a needle running at that speed? And since I can (obviously) build a needle longer, what happens to its end, when clock runs? Is it possible to run a clock like that? How many energy do I have to put to run the clock, if possible?

Thank you :)

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    $\begingroup$ There are no rigid bodies in relativity... $\endgroup$ – ACuriousMind Jun 10 '16 at 10:48
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    $\begingroup$ What happens, briefly, is that the needle breaks. And in more detail you find that it is not possible to fix it so it does not break. $\endgroup$ – tfb Jun 10 '16 at 10:55
  • $\begingroup$ You can't build such a clock, but you can use a laser to make a really long beam of light that can sweep really fast... and that is actually an interesting thought that you should carry on. $\endgroup$ – CuriousOne Jun 10 '16 at 11:46

If you're going to give that many significant numbers, you might as well learn by heart that $c=299 792 458 m/s$

But no, for many reasons.

1) Your clock is too heavy, it will collapse in on itself, even when outside of the pull of the earth.

2) The clock will tear itself apart, try stopping something that heavy, that fast in a fine system like a clock. $\vec{p}=m\gamma\vec{v}$

3) Relativity. The amount of energy required to even approach such a speed would be staggering, but no amount of energy can get anything to $c$. Your clock will also have different parts of it running at different relativistic speeds, not handy when you want to tell time. That's ignoring all the other things that get screwy at relativistic speeds. $$E_{k}=m\gamma c^{2}-mc^{2}$$ Where $\gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$ Which, as you can see doesn't work when $c=v$

4) Even a normal clock wouldn't work with a 1 atom thick chain. Too brittle.

  • $\begingroup$ All true, but I think (3) comes closest to addressing the OP question. The angular speed at the distal end is limited by the speed of light, but the angular speed near the axle is essentially unlimited (assuming you can get arbitrarily close to the axis of rotation). The result: the second hand would wind up like a watch spring and eventually break. $\endgroup$ – garyp Jun 10 '16 at 13:36

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