SELF-REDUCTION RATE OF A MICROTUBULE

DOI10.1142/S0129183108012194zbMATH Open1156.82353arXivquant-ph/0602144OpenAlexW2146339174MaRDI QIDQ3602298

Takashi Hiramatsu, Tetsuo Matsui, Kazuhiko Sakakibara

Publication date: 12 February 2009

Published in: International Journal of Modern Physics C (Search for Journal in Brave)

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

a u_{N}

(the mean interval between two successive self-reductions) of a cluster consisting of more than

N

neighboring tubulins (basic units composing a microtubule).

a u_{N}

is interpreted there as an instance of the stream of consciousness. We analyze the dependence of

a u_{N}

upon

N

and the initial conditions, etc. For relatively large electron hopping amplitude,

a u_{N}

obeys a power law

a u_{N} s i m N^{b}

, which can be explained by the percolation theory. For sufficiently small values of the electron hopping amplitude,

a u_{N}

obeys an exponential law,

a u_{N} s i m e x p (c^{'} N)

. By using this law, we estimate the condition for

a u_{N}

to take realistic values

a u_{N}

aisebox{-0.5ex}{

s t a c k r e l > s i m

}

1 0^{- 1}

sec as

N

aisebox{-0.5ex} {

s t a c k r e l > s i m

} 1000.

Full work available at URL: https://arxiv.org/abs/quant-ph/0602144

zbMATH Keywords

microtubule consciousness quantum collapse Hameroff-Penrose theory self reduction

Mathematics Subject Classification ID

Percolation (82B43) Cell biology (92C37)

Cites Work