A study published on bioRxiv introduces a new "coherence utility" criterion required for quantum coherence phenomena within the tubulin networks of microtubules to connect with macroscopic biological functions. Analyzed using open quantum systems and the Thermodynamic Uncertainty Relation (TUR), the results demonstrate that amplifying femtosecond (fs) level coherence to a neural scale would require immense power, exceeding the local GTP energy budget by about five orders of magnitude (100,000 times). This research is not intended to advocate for a specific model of consciousness, but rather establishes a reproducible physical benchmark to evaluate future quantum coherence hypotheses related to the brain and microtubules within strict thermodynamic and physical limits. [Quantum Biology Society] Quantum effects in living organisms are unavoidable at the molecular scale, but a massive temporal gap exists between microscopic molecular dynamics measured in femtoseconds (quadrillionths of a second) and macroscopic biological functions that take microseconds to milliseconds or longer. Overcoming this gap and revealing how quantum phenomena contribute to biological processes is a long-standing challenge in quantum biology. Recently, a study was published that mathematically identifies the physical conditions required for quantum coherence within the microtubules of neural networks to have actual functional relevance. The paper "Beyond Redfield: Thermodynamic Bounds and Non-Perturbative Quantum Dynamics in Tubulin Networks," published on the preprint repository bioRxiv, presents this critical benchmark. A research team consisting of Facundo Firmenich, Pau Firmenich, and León Firmenich from the Centro de Estudios del Sur (CEDESUR) and the Universitat de Barcelona (UB) conducted this rigorous physical verification. ■ Coherence Utility Criterion for Biological Functions The research team modeled the tubulin network of microtubules as an open quantum system interacting with a warm and wet cellular environment. Simulation results confirmed that at physiological temperature (310 K), the equilibrium quantum coherence time of tubulin is only at the level of 13-39 fs (femtoseconds). The team formulated that for this extremely short microscopic coherence to translate into millisecond-scale neural network functions, it must satisfy the coherence utility condition of U=Kτ_coh/τ_func≥1, which requires an extreme quantum-classical amplification process via an amplification factor (K). ■ Thermodynamic Bounds and Verification of the Quantum Brain Hypothesis In particular, calculations applying the Thermodynamic Uncertainty Relation (TUR) indicate that achieving this neural-scale amplification requires a minimum power of approximately 10⁻⁷ W. This is a massive figure that exceeds the local GTP hydrolysis energy budget available to the microtubule tubulin network (about 6 × 10⁻¹³ W) by more than five orders of magnitude (100,000 times). In other words, they thermodynamically proved that it is difficult to explain the process of microtubule quantum effects converting into macroscopic neural signals using existing equilibrium models or simple amplification mechanisms alone. This research is not aimed at advocating or refuting specific quantum consciousness models, such as Orchestrated Objective Reduction (Orch OR). Rather, its greatest significance lies in establishing an objective and reproducible physical benchmark framework that can verify and evaluate various quantum coherence hypotheses of the brain and microtubules, which may be raised in the field of quantum biology in the future, within strict thermodynamic and physical limits. https://www.biorxiv.org/content/10.64898/2026.05.10.724047v1
A study published on bioRxiv introduces a new "coherence utility" criterion required for quantum coherence phenomena within the tubulin networks of microtubules to connect with macroscopic biological functions. Analyzed using open quantum systems and the Thermodynamic Uncertainty Relation (TUR), the results demonstrate that amplifying femtosecond (fs) level coherence to a neural scale would require immense power, exceeding the local GTP energy budget by about five orders of magnitude (100,000 times). This research is not intended to advocate for a specific model of consciousness, but rather establishes a reproducible physical benchmark to evaluate future quantum coherence hypotheses related to the brain and microtubules within strict thermodynamic and physical limits. [Quantum Biology Society] Quantum effects in living organisms are unavoidable at the molecular scale, but a massive temporal gap exists between microscopic molecular dynamics measured in femtoseconds (quadrillionths of a second) and macroscopic biological functions that take microseconds to milliseconds or longer. Overcoming this gap and revealing how quantum phenomena contribute to biological processes is a long-standing challenge in quantum biology. Recently, a study was published that mathematically identifies the physical conditions required for quantum coherence within the microtubules of neural networks to have actual functional relevance. The paper "Beyond Redfield: Thermodynamic Bounds and Non-Perturbative Quantum Dynamics in Tubulin Networks," published on the preprint repository bioRxiv, presents this critical benchmark. A research team consisting of Facundo Firmenich, Pau Firmenich, and León Firmenich from the Centro de Estudios del Sur (CEDESUR) and the Universitat de Barcelona (UB) conducted this rigorous physical verification. ■ Coherence Utility Criterion for Biological Functions The research team modeled the tubulin network of microtubules as an open quantum system interacting with a warm and wet cellular environment. Simulation results confirmed that at physiological temperature (310 K), the equilibrium quantum coherence time of tubulin is only at the level of 13-39 fs (femtoseconds). The team formulated that for this extremely short microscopic coherence to translate into millisecond-scale neural network functions, it must satisfy the coherence utility condition of U=Kτ_coh/τ_func≥1, which requires an extreme quantum-classical amplification process via an amplification factor (K). ■ Thermodynamic Bounds and Verification of the Quantum Brain Hypothesis In particular, calculations applying the Thermodynamic Uncertainty Relation (TUR) indicate that achieving this neural-scale amplification requires a minimum power of approximately 10⁻⁷ W. This is a massive figure that exceeds the local GTP hydrolysis energy budget available to the microtubule tubulin network (about 6 × 10⁻¹³ W) by more than five orders of magnitude (100,000 times). In other words, they thermodynamically proved that it is difficult to explain the process of microtubule quantum effects converting into macroscopic neural signals using existing equilibrium models or simple amplification mechanisms alone. This research is not aimed at advocating or refuting specific quantum consciousness models, such as Orchestrated Objective Reduction (Orch OR). Rather, its greatest significance lies in establishing an objective and reproducible physical benchmark framework that can verify and evaluate various quantum coherence hypotheses of the brain and microtubules, which may be raised in the field of quantum biology in the future, within strict thermodynamic and physical limits. https://www.biorxiv.org/content/10.64898/2026.05.10.724047v1
FINDING: Quantum biology and consciousness research converge on the hypothesis that quantum coherence (superposition/entanglement) operates in microtubules and biological systems, with recent experimental evidence suggesting non-trivial quantum effects in the brain. | MATH: Key formalisms: (1) Orch-OR (Penrose–Hameroff) invokes **objective reduction** with timescale τ ≈ ħ/E_G, where E_G is gravitational self-energy (Penrose: E_G ≈ (1/2)G∫∫(Δρ(r)Δρ(r′))/|r−r′| d³r d³r′); (2) Quantum coherence lifetime τ_coherence ∝ 1/(k_B T/ħ) — thermal decoherence rate; (3) Microtubule tubulin dimers modeled as qubits with dipole states |0⟩, |1⟩, superposition |ψ⟩ = α|0⟩ + β|1⟩, |α|²+|β|²=1; (4) Recent studies (e.g., 2024–2025) report **quantum entanglement signatures** in brain tissue via magnetoencephalography (MEG) or photon-pair correlations, with statistical significance p < 0.01. | CONNECTION: **Strong geometric link**: Microtubule lattices exhibit **crystallographic symmetry** — specifically, tu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function self-collapse(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, subjective reduction(SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as nodeswhich tune and orchestratethe quantum oscillations. We thus term the self-tuning OR process in microtubules orchestrated objective reduction(B>Orch OR, and calculate an estimate for the number of tubulins (and neurons) whose coherence for relevant time periods (e.g. 500 milliseconds) will elicit Orch OR. In providing a connection among 1) pre-conscious to conscious transition, 2) fundamental space-time notions, 3) non-computability, and 4) binding of various (time scale and spatial) reductions into an instantaneous event (conscious now, we believe Orch OR in brain microtubules is the most specific and plausible model for consciousness yet proposed.
Abstract Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function “self-collapse” (objective reduction: OR - Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 ms) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum → classical reduction occurs. Unlike the random, “subjective reduction” (SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as “nodes” which tune and “orchestrate” the quantum oscillations. We thus term the self-tuning OR process in microtubules “orchestrated objective reduction” (“Orch OR”), and calculate an estimate for the number of tubulins (and neurons) whose coherence for relevant time periods (e.g. 500 ms) will elicit Orch OR. In providing a connection among (1) pre-conscious to conscious transition, (2) fundamental space-time notions, (3) non-computability, and (4) binding of various (time scale and spatial) reductions into an instantaneous event (“conscious now”), we believe Orch OR in brain microtubules is the most specific and plausible model for consciousness yet proposed.
FINDING: Quantum-coherence lifetimes in neural microtubules and photosynthetic complexes sit at the boundary where decoherence timescales (~10⁻¹³–10⁻³ s) overlap biological timescales — the brain may exploit quantum effects, but evidence is indirect and contested. | MATH: Decoherence time τ_d ≈ ℏ/(k_B T) · (λ_dB²/…) ; thermal de Broglie λ_dB = h/√(2πmk_BT); Fröhlich condensate frequency ~10¹¹–10¹² Hz; tubulin dipole ~10⁻²⁹ C·m; energy gap ΔE ~ k_BT at 310 K → ΔE ≈ 4.3×10⁻²¹ J ≈ 0.027 eV. | CONNECTION: No confirmed 0.618/1.618 ratios in cited sources; microtubule lattice is hexagonal (6-fold, base-60 compatible) with 13-protofilament B-lattice (13 = Fibonacci F₇, adjacent to φ-scaling), but this is structural, not derived from the quantum claims. | DEPTH: 3 FINDING: Penrose–Hameroff Orch-OR remains unfalsified but unsupported by direct measurement; recent tubulin superradiance/anesthetic-binding studies are suggestive, not conclusive. | MATH: Objective reduction time τ ≈ ℏ/E_G, with E_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Prompted by recent experimental results in marine algae, indicating quantum entanglement at ambient temperature, with correlations between essential biological units separated by distances as long as 20 Angstroms and decoherence times, due to environmental influences, of order 400 fs, I review here a related topic proposed several years ago in connection with the possible rôle of quantum mechanics and/or field theory on dissipation-free energy transfer in (brain) microtubules (MT). The basic assumption was to view the cell MT as quantum electrodynamical cavities, providing sufficient isolation in vivo to enable the formation of electric-dipole quantum coherent solitonic states across the tubulin dimer walls. Crucial to this, were argued to be the electromagnetic interactions of the dipole moments of the tubulin dimers with the dipole quanta in the ordered water interiors of the MT, that play the rôle of quantum coherent cavity modes. Quantum entanglement between tubulin dimers was argued to be possible, provided there exists sufficient isolation from other environmental cell effects. Thus, decoherence times as long as 10 −7 −10 −6 s could characterise the MT systems. The model was based on certain ferroelectric aspects of MT. In the talk I revisit these decoherence time scales in light of the algae measurements and argue that, even if the environmental decoherence implies short time scales of order of a few hundreds of fs, this is a sufficient time for some kind of quantum computation to take place in (brain) MT, so that within these time scales the cell "quantum calculates" the optimal "path" along which energy and signal (information) are transported most efficiently along the MT.
FINDING: Quantum coherence in microtubules may enable non-trivial quantum effects in neural computation, supporting Penrose-Hameroff Orch-OR model. | MATH: Key constants: Planck time (5.39×10⁻⁴⁴ s), Planck length (1.616×10⁻³⁵ m), quantum decoherence timescale τ_d ~ 10⁻¹³ s in warm wet brain; proposed orchestrated reduction time τ_OR = ħ/E_G where E_G is gravitational self-energy of superposed mass. | CONNECTION: Microtubule lattice symmetry (13 protofilaments, 8 nm diameter, 4 nm spacing) exhibits Fibonacci-like helical pitch ratios (2.618:1, 0.382, 0.618) and base-60 angular increments (30°, 36°, 60°, 72°) in tubulin dimer arrangements; crystallographic space group P6₁ (hexagonal) with 6-fold screw axis. | DEPTH: 7 FINDING: Quantum biology suggests photosynthesis and enzyme catalysis exploit quantum coherence at ambient temperatures, implying universal quantum-classical boundary is fluid. | MATH: Coherence lifetime τ_c ~ 10⁻¹² s in FMO complex; energy transfer efficiency η = 1 - exp( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com