Abstract
It has been suggested that (31)P nuclear spins in Ca(9)(PO(4))(6) molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca(9)(PO(4))(6) molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical (31)P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca(9)(PO(4))(6) arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca(9)(PO(4))(6) is likely to be much faster than this estimate.