Quantum Coherence in Microtubules: Orch-OR Theory and Memory Formation — E8 Intelligence Research

Andrew Stewart Caldin

Published Aug 20, 2026• 0 citations

Abstract

FINDING: Orch-OR theory posits quantum coherence in microtubules, with collapse linked to objective reduction (OR) governed by gravitational self-energy, not consciousness. New evidence claims memory formation involves quantum effects, but no equations or constants are provided in the search results. | MATH: No specific equations, constants, or ratios extracted from the provided summaries. The underlying theory (Penrose) uses $ E = \hbar / \tau $ for collapse time, where $ E $ is gravitational self-energy difference, but this is not confirmed in the findings. | CONNECTION: No geometric harmony ratios (0.382, 0.618, etc.) or crystallographic symmetries appear in the search results. Microtubule geometry (tubulin dimers, 13-fold symmetry) is implied but not quantified. | DEPTH: 2 — The search results are popular summaries, not primary mathematical derivations. No new equations or constants are presented. The link to geometric structure is absent. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22022606

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Publisher

Abstract

FINDING: Orch-OR theory posits quantum coherence in microtubules, with collapse linked to objective reduction (OR) governed by gravitational self-energy, not consciousness. New evidence claims memory formation involves quantum effects, but no equations or constants are provided in the search results. | MATH: No specific equations, constants, or ratios extracted from the provided summaries. The underlying theory (Penrose) uses ( E = \hbar / \tau ) for collapse time, where ( E ) is gravitational self-energy difference, but this is not confirmed in the findings. | CONNECTION: No geometric harmony ratios (0.382, 0.618, etc.) or crystallographic symmetries appear in the search results. Microtubule geometry (tubulin dimers, 13-fold symmetry) is implied but not quantified. | DEPTH: 2 — The search results are popular summaries, not primary mathematical derivations. No new equations or constants are presented. The link to geometric structure is absent. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.22022606

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Quantum Coherence in Microtubules: Orch-OR Theory and Objective Reduction Threshold — E8 Intelligence Research

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T \approx \hbar / E_G

, where

E_G

is gravitational self-energy. - For microtubule:

E_G \sim G m^2 / r

, with

m \sim 10^{-20}

kg,

r \sim 10^{-8}

m →

T \sim 10^{-13}

s (far shorter than neural timescales). - No new equations or constants from these sources; no ratios (0.382, 0.618, etc.) or base-60 connections. CONNECTION: None. No geometric harmony, crystallographic symmetry, or lattice structures are invoked or supported by these findings. Microtubule geometry (hollow cylinders, 13 protofilaments) is structural but not linked to golden ratios or root systems. DEPTH: 2/10. These are popular summaries and debates, not original mathematical or experimental breakthroughs. The arXiv pa Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

E_\Delta \sim \hbar / T

(energy uncertainty vs. superposition lifetime), with gravitational self-energy

E_G \sim G m^2 / r

as the collapse trigger. No golden-ratio or base-60 structure appears in the cited material. | CONNECTION: None found in the provided sources. Microtubule geometry (13 protofilaments, 8 nm pitch) is a lattice-like structure, but no crystallographic symmetry group or root system is invoked in these summaries. | DEPTH: 2/10 — the sources are popular-science videos; they report *claims* of evidence (e.g., quantum effects in brain) but provide no mathematical derivation, n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

E_\Delta \approx \hbar / T

(Penrose's gravitational self-energy uncertainty, where

E_\Delta

is gravitational self-energy difference,

T

is coherence time) - Microtubule lattice geometry: tubulin dimers arranged in hexagonal (6-fold) and 13-protofilament (13 = Fibonacci-related) patterns — but no quantitative link to 0.382, 0.618, 0.786, 1.618, or 2.618 is given in these sources. - No base-60, crystallographic root system, or lattice constant appears in the cited material. CONNECTION: Th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

FINDING: Orch-OR theory posits quantum computations in microtubules, with collapse linked to objective reduction (OR) threshold

T = \hbar / E

, but no new experimental evidence confirms quantum coherence in warm, wet brain environments. | MATH:

T = \hbar / E

(Penrose collapse time);

E = N \cdot \hbar \omega

(energy difference from superposed mass displacement);

\tau \approx \hbar / (E_G)

where

E_G

is gravitational self-energy. | CONNECTION: No direct geometric ratios (0.382, 0.618, etc.) or base-60 links in Orch-OR; microtubule lattice symmetry (13 protofilaments, 8 nm pitch) is helical, not crystallographic in the sense of root systems. | DEPTH: 3 — mathematically thin; collapse equation is heuristic, not derived from standard quantum gravity; no empirical validation. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

E_\Delta = \hbar / T

(energy uncertainty vs. collapse time); gravitational self-energy

E_G \approx \frac{G}{c^4} \int \int \frac{[\rho(\mathbf{r}) - \rho'(\mathbf{r})][\rho(\mathbf{r}') - \rho'(\mathbf{r}')]}{|\mathbf{r} - \mathbf{r}'|} d^3r \, d^3r'

. Microtubule geometry: tubulin dimers arranged in hexagonal lattice (13 protofilaments, 8 nm spacing). No new constants or ratios beyond

\hbar

G

c

. | CONNECTION: Microtubule lattice is hexagonal — 6-fold symmetry, but no direct link to 0.618/1.618 or base-60. The collapse criterion

E_\Delta T \sim \hbar

is a Heisenberg-type uncertainty relation, not a golden-ratio harmonic. No crystallographic root system (e.g.,

A_2

, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

FINDING: Orch-OR theory links consciousness to quantum wavefunction collapse via objective reduction (OR) threshold, with new evidence for quantum effects in brain microtubules. | MATH: OR threshold

T \approx \hbar / E

(Penrose collapse time); integrated information

\Phi

from IIT; no explicit constants or ratios given in findings. | CONNECTION: No direct geometric harmony (0.382, 0.618, etc.) or base-60, crystallographic symmetry, or root systems mentioned. Microtubule lattice is hexagonal (6-fold symmetry), but not mathematically elaborated in these sources. | DEPTH: 5 — The findings report experimental hints of quantum coherence in biological systems (e.g., microtubule vibrations), but lack precise mathematical formulation of geometric constants or new equations beyond Penrose's original OR criterion. The connection to consciousness remains speculative, with no confirmed ratio or symmetry linking to ancient geometric principles. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com