I was thinking about a sci-fi microwave-like device to make a banana ripen more quickly. Assuming that the various technical hurdles had been solved, how might this, in simple terms, operate?
edit: I guess this question is asking what mechanism, given our current understanding of how time works, could warp it in such a way time passes more quickly inside a microwave sized object. Maybe by somehow manipulating the rate at which entropy takes place, if that makes sense.
Leave your banana on Earth. You get into your device. Launch into space at very close to the speed of light and then come back after whatever period you are prepared to wait.
Very roughly speaking, the rate at which time is "speeded up" for the earthbound banana is the Lorentz factor $\gamma = (1-v^2/c^2)^{-1/2}$ (for constant velocities in flight and instantaneous accelerations; for more realistic scenarios the calculations are more complex but no more illuminating - see Twin Paradox, calculating spacetime intervals from both perspectives ).
Thus if you wanted to eat a banana in 24 hours that would have ripened in 10 days then you would need to travel into space (and come back again) over the course of a day at roughly $$ \frac{1}{\sqrt{1 - v^2/c^2}} \simeq 10$$ i.e. at $v \simeq 0.995c$.
Of course everything else on Earth would have moved on by 10 days too, so that milk you left in the refrigerator has gone off.
