Physics – Quantum Physics
Scientific paper
2006-02-17
International Journal of Modern Physics C19(2008)291-305.
Physics
Quantum Physics
7 pages, 9 figures, Extended version
Scientific paper
10.1142/S0129183108012194
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 $\tau_N$ (the mean interval between two successive self-reductions) of a cluster consisting of more than $N$ neighboring tubulins (basic units composing a microtubule). $\tau_N$ is interpreted there as an instance of the stream of consciousness. We analyze the dependence of $\tau_N$ upon $N$ and the initial conditions, etc. For relatively large electron hopping amplitude, $\tau_N$ obeys a power law $\tau_N \sim N^b$, which can be explained by the percolation theory. For sufficiently small values of the electron hopping amplitude, $\tau_N$ obeys an exponential law, $\tau_N \sim \exp(c' N)$. By using this law, we estimate the condition for $\tau_N $ to take realistic values $\tau_N$ \raisebox{-0.5ex}{$\stackrel{>}{\sim}$} $10^{-1}$ sec as $N$ \raisebox{-0.5ex} {$\stackrel{>}{\sim}$} 1000.
Hiramatsu Takashi
Matsui Tetsuo
Sakakibara Kazuhiko
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