SELF-REDUCTION RATE OF A MICROTUBULE

Takashi Hiramatsu (), Tetsuo Matsui () and Kazuhiko Sakakibara ()
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Takashi Hiramatsu: Department of Physics, Kinki University, Higashi-Osaka, 577-8502, Japan
Tetsuo Matsui: Department of Physics, Kinki University, Higashi-Osaka, 577-8502, Japan
Kazuhiko Sakakibara: Department of Physics, Nara National College of Technology, Yamatokohriyama, 639-1080, Japan

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 02, 291-305

Abstract: 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 timeτN(the mean interval between two successive self-reductions) of a cluster consisting of more thanNneighboring tubulins (basic units composing a microtubule).τNis interpreted there as an instance of the stream of consciousness. We analyze the dependence ofτNuponNand the initial conditions, etc. For relatively large electron hopping amplitude,τNobeys a power lawτN~ Nb, which can be explained by the percolation theory. For sufficiently small values of the electron hopping amplitude,τNobeys an exponential law,τN~exp(c'N). By using this law, we estimate the condition forτNto take realistic valuesτN≳ 10-1secasN ≳ 1000.

Keywords: microtubule; self reduction; consciousness; Hameroff-Penrose theory; quantum collapse (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108012194

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