dorsal/arxiv
View SchemaSelf-Reduction Rate of a Microtubule
| Authors | Takashi Hiramatsu, Tetsuo Matsui, Kazuhiko Sakakibara |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602144 |
| URL | https://arxiv.org/abs/quant-ph/0602144 |
| DOI | 10.1142/S0129183108012194 |
| Journal | International Journal of Modern Physics C19(2008)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 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.
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"abstract": "We formulate and study a quantum field theory of a microtubule, a basic\nelement of living cells. Following the quantum theory of consciousness by\nHameroff and Penrose, we let the system to reduce to one of the classical\nstates without measurement if certain conditions are\nsatisfied(self-reductions), and calculate the self-reduction time $\\tau_N$ (the\nmean interval between two successive self-reductions) of a cluster consisting\nof more than $N$ neighboring tubulins (basic units composing a microtubule).\n$\\tau_N$ is interpreted there as an instance of the stream of consciousness. We\nanalyze the dependence of $\\tau_N$ upon $N$ and the initial conditions, etc.\nFor relatively large electron hopping amplitude, $\\tau_N$ obeys a power law\n$\\tau_N \\sim N^b$, which can be explained by the percolation theory. For\nsufficiently small values of the electron hopping amplitude, $\\tau_N$ obeys an\nexponential law, $\\tau_N \\sim \\exp(c\u0027 N)$. By using this law, we estimate the\ncondition for $\\tau_N $ to take realistic values $\\tau_N$\n\\raisebox{-0.5ex}{$\\stackrel{\u003e}{\\sim}$} $10^{-1}$ sec as $N$ \\raisebox{-0.5ex}\n{$\\stackrel{\u003e}{\\sim}$} 1000.",
"arxiv_id": "quant-ph/0602144",
"authors": [
"Takashi Hiramatsu",
"Tetsuo Matsui",
"Kazuhiko Sakakibara"
],
"categories": [
"quant-ph",
"q-bio.NC",
"q-bio.SC"
],
"doi": "10.1142/S0129183108012194",
"journal_ref": "International Journal of Modern Physics C19(2008)291-305.",
"title": "Self-Reduction Rate of a Microtubule",
"url": "https://arxiv.org/abs/quant-ph/0602144"
},
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