How nerve signals preserve quantum coherence? Roger Penrose in this interview says he was trying to find out "... how it is that nerve signals could possibly preserve quantum coherence".
What does he mean by that?
 A: Penrose believes that the apparently non-deterministic nature of human thought and free will can be reconciled with the laws of physics if quantum uncertainty is somehow involved.
A colleague of his has developed the idea that the brain holds its long-term memory inside microtubule structures within the neurons (these microtubules occur in pretty much all eukaryotic cells including plants and animals and act as both a scaffolding and a transport highway). There is some (highly controversial) evidence that mircotubules exhibit properties which can only be explained via quantum mechanisms such as coherence (it is worth noting that other macromolecules such as chlorophyll are subject to related quantum-weird phenomena).
The problem Penrose faces is how a nerve impulse can transfer the information, encoded via quantum coherence, to and from a given microtubule.
One has to say that, ingenious though the theory is, it is a very long shot and is not taken seriously by mainstream science. Even if the philosophical insight is valid, the microtubule memory mechanism remains wholly speculative. Its QM arguments have also been subject to heavy criticism and accusations of fundamental flaws, but then, that is true of a great many findings related to quantum weirdness.
Still, if anybody can prove the mainstream overly pessimistic, Penrose is far the best qualified to do so; the conformal geometry of spacetime and twistor theory make for a pretty good CV. (Recall too that Shing-Tung Yau first rose to fame for disproving the Calabi conjecture, before winning the Fields medal for tuning his result on its head and proving it true after all, thus giving string theorists their Calabi-Yau manifolds. Maths and physics at this level is full of surprises.)
