Self-Reduction Rate of a Microtubule

We formulate and study a quantum field theory of a microtubule, a basic element of living cells. Following the quantum theory of consciousness by Hameroff and Penrose, we let the system to reduce to one of the classical states without measurement if certain conditions are satisfied(self-reductions), and calculate the self-reduction time τN (the mean interval between two successive self-reductions) of a cluster consisting of more than N neighboring tubulins (basic units composing a microtubule). τN is interpreted there as an instance of the stream of consciousness. We analyze the dependence of τN upon N and the initial conditions, etc. For relatively large electron hopping amplitude, τN obeys a power law τN ∼ N , which can be explained by the percolation theory. For sufficiently small values of the electron hopping amplitude, τN obeys an exponential law, τN ∼ exp(c ′N). By using this law, we estimate the condition for τN to take realistic values τN > ∼ 10 −1 sec as N > ∼ 1000.