If I have a huge analog clock, what happens to the seconds hand if I build it longer than 2.864.788 kms?

Question

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 :)

Answer 1

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.