Self-Reduction Rate of a Microtubule
arXiv Preprint Archive February 17, 2006 Takashi Hiramatsu, Tetsuo Matsui, Kazuhiko Sakakibara
A quantum field theory of microtubules—basic components of living cells—is formulated and studied, building on Hameroff and Penrose's quantum theory of consciousness. The system is allowed to reduce to a classical state without measurement (self-reduction) under certain conditions, and the self-reduction time τ_N (the mean interval between successive self-reductions) is calculated for clusters of more than N neighboring tubulins. For large electron hopping amplitudes, τ_N follows a power law τ_N ∼ N^b, explained by percolation theory; for small hopping amplitudes, it follows an exponential law τ_N ∼ exp(c' N). Using this law, the condition for τ_N to be at least 0.1 seconds requires N to be at least about 1000.