spatial positions. We have not studied this in detail yet, but it appears that this type of decoherence could be even more promising from the point of view of experimental detection [@SiJa].

Conceptual implications
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The fact that pure states evolve naturally into mixed states has conceptual implications in at least three interesting areas of physics. We will discuss them separately.

The black hole information paradox
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The black hole information paradox appeared when Hawking [@hawking] noted that when quantum effects are taken into account, black holes emit radiation like a black body with a temperature $T_{\rm BH}=\hbar/(8\pi k G M)$ where $M$ is the black hole mass, $k$ is Boltzmann’s constant and $G$ is Newton’s constant. As the black hole radiates, it loses mass, and therefore its temperature increases. This process continues until the black hole eventually evaporates completely and the only thing left is outgoing purely thermal radiation. Now, suppose one had started with a pure quantum state of enough mass that it collapses into a black hole. After the evaporation process, one is left with a mixed state (the outgoing purely thermal radiation). In ordinary quantum mechanics this presents a problem, since pure states cannot evolve into 