Wednesday, April 17, 2013

$\Lambda$ as a source of energy

this week, CQW has a guest question by U. Bastian:
is it possible to tap dark energy as a source of (mechanical) energy? could you set up a machine that would accomplish this?

bonus question: assume you're trying to compute the expectation value $\langle x\rangle$ of a random distribution $p(x)\mathrm{d}x$, which has the cumulative distribution $P(x)$. you could write:
\begin{equation}
\langle x\rangle = \int\mathrm{d}x\:xp(x) = \int\mathrm{d}x\:x\frac{\mathrm{d}}{\mathrm{d}x}P(x) = xP(x) - \int\mathrm{d}x\: P(x)
\end{equation}
by integration by parts, where all integration boundaries are taken to be $-\infty\ldots+\infty$. both expressions in the final expression are not finite. where's the mistake?

2 comments:

  1. Let's try this: Assume we have a satellite on a chain and call the distance from us R. The effect on this test mass is determined by the energy content inside a sphere around us with radius R. So all we have to do is make R large enough so the vacuum energy will dominate over the matter inside the sphere. Gravity will then be repulsive and the satellite is pushed away. Its movement along the chain can drive a generator and we can enjoy free, unlimited energy.

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  2. Exactly this was also my idea. Great.

    One morning last winter, while having a shower, this cqw suddenly struck my mind. My immediate gut feeling was that this could not be possible, because it is so close to the perpetuum mobile. But then I thought to myself: Since the dark energy is not obviously connected to a non-zero temperature T, its free energy density F might be F = E - T S = E, whatever its entropy S is. So, could it be possible after all ??

    Just a few minutes more of contemplating led me to the tether (chain) idea. My first mechanism was less clever than letting the dark energy actually do mechanical work by stretching the chain (as Steffen proposed). I first kept the tether (chain) at fixed length and let the accelerated cosmic medium pass by, driving a windmill-type device.

    Steffen's much more efficient mechanism struck me only later. But the two mechanisms found now mean that there actually are more than one - and maybe somebody *very* clever could some time find one less unrealistic than ours ... :)

    Uli Bastian

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