2006/02/28 by Takashi Hiramatsu, Tetsuo Matsui, Kazuhiko Sakakibara · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Amplitude #Biofield Effects and Biophysics #Combinatorics #Exponential function #Geometry #Interval (graph theory) #Mathematical analysis #Mathematical physics #Mathematics #Origins and Evolution of Life #Percolation (cognitive psychology) #Percolation theory #Physics #Power law #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Reduction (mathematics) #Statistical physics #Statistics #q-bio.NC #q-bio.SC #quant-ph
paper · pdf · doi:10.1142/s0129183108012194
published as International Journal of Modern Physics C19(2008)291-305. · 7 pages, 9 figures, Extended version
arxiv created 2007/11/01 · openalex publication_date 2008/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 τ N (the mean interval between two successive self-reductions) of a cluster consisting of more than N neighboring tubulins (basic units composing a microtubule). τ N is interpreted there as an instance of the stream of consciousness. We analyze the dependence of τ N upon N and the initial conditions, etc. For relatively large electron hopping amplitude, τ N obeys a power law τ N ~ N b , which can be explained by the percolation theory. For sufficiently small values of the electron hopping amplitude, τ N obeys an exponential law, τ N ~ exp (c'N). By using this law, we estimate the condition for τ N to take realistic values τ N ≳ 10 -1 sec as N ≳ 1000.