## 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:

\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)

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?