Estimation of time decoherence in neuronal microtubules

Kaushik Naskar, P. S. Joarder

Zuoxian Xiang, Chuanxiang Tang, Lixin Yan

Microtubules (MTs) are part of the cellular cytoskeleton and they play a role in many activities, such as cell division and maintenance of cell shape. In recent years, MTs have been thought to be involved in storing and processing information. Several models have been developed to describe the information-processing ability of MTs. In these models, MTs are considered as a device that can transmit quantum information. However, MTs are affected by the “wet and warm” cellular environment, thus it is essential to calculate the decoherence time. Many researchers have attempted to calculate this parameter but the values that have been obtained vary markedly. Previous studies considered the cellular environment as a distant ion; however, this treatment is somewhat simplified. In this study, we develop a model to determine the decoherence time in neuronal MTs while considering the interaction effects of the neuronal fluid environment. The neuronal environment is considered as a plasmon reservoir. The coupling between MTs and neuronal environment occurs due to the interaction between dipoles and plasmon. The interaction Hamiltonian is derived by using the second quantization method, and the coupling coefficient is calculated. Finally, the decoherence time scale is estimated according to the interaction Hamiltonian. In this paper, the time scale of decoherence in MTs is approximately 1 fs-100 fs. This model may be used as a reference in other decoherence processes in biological tissues.

S. Hagan, Stuart R. Hameroff, Jack A. Tuszyński

The Penrose-Hameroff orchestrated objective reduction (orch. OR) model assigns a cognitive role to quantum computations in microtubules within the neurons of the brain. Despite an apparently "warm, wet, and noisy" intracellular milieu, the proposal suggests that microtubules avoid environmental decoherence long enough to reach threshold for "self-collapse" (objective reduction) by a quantum gravity mechanism put forth by Penrose. The model has been criticized as regards the issue of environmental decoherence, and a recent report by Tegmark finds that microtubules can maintain quantum coherence for only 10(-13) s, far too short to be neurophysiologically relevant. Here, we critically examine the decoherence mechanisms likely to dominate in a biological setting and find that (1) Tegmark's commentary is not aimed at an existing model in the literature but rather at a hybrid that replaces the superposed protein conformations of the orch. OR theory with a soliton in superposition along the microtubule; (2) recalculation after correcting for differences between the model on which Tegmark bases his calculations and the orch. OR model (superposition separation, charge vs dipole, dielectric constant) lengthens the decoherence time to 10(-5)-10(-4) s; (3) decoherence times on this order invalidate the assumptions of the derivation and determine the approximation regime considered by Tegmark to be inappropriate to the orch. OR superposition; (4) Tegmark's formulation yields decoherence times that increase with temperature contrary to well-established physical intuitions and the observed behavior of quantum coherent states; (5) incoherent metabolic energy supplied to the collective dynamics ordering water in the vicinity of microtubules at a rate exceeding that of decoherence can counter decoherence effects (in the same way that lasers avoid decoherence at room temperature); (6) microtubules are surrounded by a Debye layer of counterions, which can screen thermal fluctuations, and by an actin gel that might enhance the ordering of water in bundles of microtubules, further increasing the decoherence-free zone by an order of magnitude and, if the dependence on the distance between environmental ion and superposed state is accurately reflected in Tegmark's calculation, extending decoherence times by three orders of magnitude; (7) topological quantum computation in microtubules may be error correcting, resistant to decoherence; and (8) the decohering effect of radiative scatterers on microtubule quantum states is negligible. These considerations bring microtubule decoherence into a regime in which quantum gravity could interact with neurophysiology.

S.Eh. Shirmovsky, D.V. Shulga

Anthony L Perry

D. Ryan Grover

GRUT ToE v4 Sector 13: Consciousness and 1 Space Beyond the Thermal Wall GRUT (Grand Responsive Universe Theory) Sector 13 extends the framework's consciousness application beyond the thermal wall that decisively killed the Penrose-Hameroff Orchestrated Objective Reduction (Orch-OR) hypothesis. The gravitational decoherence rate per tubulin dimer (3.02 × 10⁻¹¹ Hz, zero free parameters from the Universal Scaling Law) produces 40 Hz gamma oscillation with approximately 38,000 neurons — a biologically realistic cortical network corresponding to roughly half a cortical column. But water at brain temperature (310 K) destroys quantum coherence 10²⁵ times faster than gravity acts, creating a 25–28 order gap that no known mechanism bridges. This sector systematically computes what lies beyond that wall, separating computed results from speculative content throughout. Six computed investigations probe the thermal wall from different angles. Ordered water corrections for confined microtubule channels (~15 nm diameter) produce less than 0.01 orders of improvement at the physical confinement estimate of 0.97, leaving the ~28.6-order gap effectively unchanged. The topological winding number on the 13-protofilament microtubule ring degrades faster than local phase coherence under uncorrelated dephasing (ratio 0.70×) — topology does not help. GHZ entanglement entropy decays N times faster than single-qubit coherence, actively disfavoring naive pattern survival via entanglement. The resonance condition is computed across all major brainwave bands: theta (6 Hz, ~253,000 neurons), alpha (10 Hz, ~152,000 neurons), beta (20 Hz, ~76,000 neurons), and gamma (40 Hz, ~38,000 neurons) — all biologically feasible network sizes. The information-theoretic antenna coupling bound yields a coupling fraction of ~10⁻¹⁰⁸ between a 38,000-neuron network (D_sub ~ 10¹⁵ bits) and the universe (holographic bound ~10¹²⁴ bits). The impedance matching between gravitational collapse timescale and neural oscillation period is exact at this network size (Z = 0.002), though this is explicitly noted as a tautology of the linear scaling. The sector introduces "1 Space" — the totality of the universal target functional F[z] — as a speculative framework for consciousness at the quantum-classical boundary. In this interpretation, the classical world is where the response field z has fully relaxed toward F[z], the quantum world is where z maintains superposition, and consciousness is proposed as an edge state sitting at the boundary between the two regimes. The brain functions as an "antenna" maintaining pattern-level coupling to the target functional rather than shielding quantum states from decoherence. This framework is explicitly labeled as speculative: no dynamical equation for the edge state is proposed, no coupling mechanism is derived, and no prediction beyond the structural coincidences is made. Seven falsification conditions (K13-1 through K13-7) are defined, all testable: bulk-like water collision rates in microtubule channels, absence of topological protection, network insignificance of the 38,000-neuron count, lack of cross-species gamma-tubulin mass correlation, anesthetic non-binding to microtubules, consciousness persistence under microtubule disruption, and mutual information decaying at the same rate as local coherence. The honest assessment: 7 computed results, 4 model-dependent results, 5 speculative proposals. The thermal wall stands — total improvement from all computed corrections is less than one order, leaving ~25 orders unbridged. The structural coincidences are real and unexplained; the physical hypothesis is killed by thermal physics. All computations are implemented in 7 modules with 15 validated tests and are reproducible via the grut_solver package. Key Insights: Gravitational decoherence rate per tubulin dimer: 3.02 × 10⁻¹¹ Hz (zero free parameters) — a single dimer takes ~1,050 years to gravitationally decohere ~38,000 neurons match the 40 Hz gamma oscillation target scale — a biologically realistic network corresponding to roughly half a cortical column The thermal wall stands: water at 310 K decoheres tubulin 10²⁵ times faster than gravity, a 25–28 order gap that no computed mechanism bridges Ordered water confinement in microtubule channels (~15 nm) improves the gap by less than 0.01 orders at the physical estimate — effectively zero Topological index on the 13-protofilament ring degrades 0.70× faster than local coherence under uncorrelated noise — topology hurts rather than helps GHZ entanglement entropy decays N times faster than single-qubit coherence, actively disfavoring quantum pattern survival via entanglement Resonance condition holds across all brainwave bands (theta through gamma) with feasible neuron counts at each frequency "1 Space" framework proposed as speculative interpretation: consciousness as an edge state at the quantum-classical boundary of the target functional F[z] — no dynamical equation derived Seven testable kill conditions defined (K13-1 through K13-7), including cross-species correlation and anesthetic binding tests Honest assessment: 7 computed, 4 model-dependent, 5 speculative — all categories explicitly separated throughout the document The structural coincidences (mass-frequency matching, feasible network size, brainwave-band coverage) are real and unexplained; the physical hypothesis is killed by thermal physics All computations reproducible via grut_solver/sectors/consciousness/ with 15 validated tests