  How does Deutsch avoid these complications? Deutsch assumes a mixed state S3 of the older system prior to the interaction with the younger system. He lets it interact with an arbitrary pure state S1 younger system. After this interaction there is an entangled state S′ of the two systems. Deutsch computes the mixed state S2 of the younger system which is implied by this entangled state S′. His demand for consistency then is just that this mixed state S2 develops into the mixed state S3. Now it is not at all clear that this is a legitimate way to simplify the problem of time travel in quantum mechanics. But even if we grant him this simplification there is a problem: how are we to understand these mixtures?