Could a specific quantum process contribute to the physical conditions of experience? We begin with a reaction we can calculate, then ask what would connect it to neural function.
AN ELECTRON SINGLETOne defined state. A question we can test.
THE RESEARCH AIM
Give the hypothesis a physical mechanism.
Our long-term aim is to develop and test a physical account of how quantum processes might contribute to conscious experience. The first task is to identify a mechanism whose contribution can be measured independently of the larger claim.
Spin-dependent chemistry offers one candidate. A magnetic interaction can change a pair of electrons’ spin dynamics and, in a suitable reaction, alter the proportions of its products. The decisive question is whether a characterized reaction produces a signal that survives the constraints of a real neural environment.
We keep two other lines of work distinct: the foundation’s circadian timing hypothesis, and the externally proposed microtubule and objective-reduction mechanisms. Similar language across these programs does not establish a shared cause.
CONCEPT GUIDE
A vocabulary for the model.
Open eight short definitions
Spin
An intrinsic quantum form of angular momentum. The arrows used to label spin states describe measurement outcomes along a chosen axis, rather than tiny rotating spheres.
Radical pair
Two radical centers, each carrying an unpaired electron, whose spin dynamics can be correlated. Whether a particular pair occurs in a cell is an experimental question.
Singlet / triplet
The two-electron sectors with total spin zero / one. The triplet sector contains three states. Here each sector feeds its own product channel at the same rate k.
Hyperfine coupling
The interaction between an electron spin and a nuclear spin. A tensor A describes its dependence on direction. Our chosen tensor has axial symmetry.
Density matrix, ρ
A representation of quantum populations and coherences. In this reaction model its trace is the fraction of pairs that have not yet reacted.
Reaction yield, Φ
The fraction of initially created pairs that end in a specified product channel. It accumulates over the entire reaction, rather than giving an instantaneous population.
Relaxation rate, Γ
A parameter describing loss of electron-spin polarization in the stipulated local-noise model. Reaction lifetime and relaxation time are different quantities.
Coherence
Relative-phase structure between specified basis states. A change in chemical yield alone does not identify entanglement or establish a role in experience.
01 / EIGHT-STATE SPIN-CHEMISTRY MODEL
Follow the spin dynamics. Count the reaction products.
Two electron spins interact with one spin-½ nucleus. Explore how field strength, orientation, reaction lifetime, and relaxation change the final singlet and triplet yields.
Loading the reproducible calculation grid…
INITIAL STATEElectron singletUnpolarized nucleus
SPIN DYNAMICSZeeman + hyperfineReaction and relaxation
ACCUMULATED PRODUCTS
Singlet Triplet
Field sweep at the selected angle, lifetime, and relaxation rate. Each point is a solved model setting; connecting segments guide the eye.Orientation sweep at the selected field. These are fixed molecular axes; a freely rotating sample needs a different treatment.
Singlet yield ΦS—
Triplet yield ΦT—
Singlet change from zero field—
ΦS + ΦT—
Specified demonstration: A/(2π) = diag(2, 2, 4) MHz. Parameters are chosen for an inspectable model, with no fit to a protein, neuron, or conscious state. The controls select calculated grid points; no interpolated values are presented as new solutions. “pp” means percentage points of product yield.
THE HAMILTONIAN / ANGULAR-FREQUENCY UNITS
Spin operators are dimensionless with eigenvalues ±½. B is in tesla; γe = 1.76085963 × 10¹¹ rad s⁻¹ T⁻¹ is the positive gyromagnetic magnitude used here. A is in rad s⁻¹, while the controls report A/(2π) in MHz. The bold I in the interaction is the nuclear-spin operator; In in the initial state is the nuclear identity. The field lies in the x–z plane.
Initial state, reaction law, and assumptions
The initial full state is ρ(0) = |S⟩⟨S| ⊗ In/2. The nucleus is unpolarized. We evolve an 8 × 8 density matrix, with equal singlet and triplet reaction rates k > 0:
σja is the Pauli operator along axis a on electron j. Under this convention an isolated electron’s Bloch vector relaxes at rate Γ. Trace decays as exp(−kt). The relaxation law is stipulated for this demonstration. Changing Γ compares regimes within one quantum model; it is not a comparison with every classical or biochemical alternative.
The calculation omits nuclear Zeeman terms, exchange, electron–electron dipolar coupling, molecular rotation, additional nuclei, escape, and back reactions. Equal reaction rates simplify the dynamics. A candidate-specific model must justify these choices or extend them. Reaction master equations also have validity conditions; Fay and colleagues analyze corrections beyond a simple treatment.
INTEGRATE THE PRODUCT FLUX
PS projects onto the electron singlet sector; PT = I − PS. Both yields use the same rate k. Their sum checks conservation within this closed, two-channel model.
02 / THE MEASUREMENT GAP
A yield is only the first number.
A fractional change in yield says little about a cell until we know how many pairs form, which product matters, how quickly it clears, and what concentration affects its target.
A CANDIDATE CONCENTRATION BALANCE
x is product concentration; FRP is pair-formation flux in concentration per unit time; kclear is a first-order clearance rate. The steady-state relation assumes that flux and clearance stay fixed while yield changes. These parameters have not been established for a native neural candidate in this proposal.
01 / COMPUTE
Product yield
A specified reaction model gives ΦS.
02 / MEASURE
Cellular concentration
Identify the product, formation flux, and clearance.
03 / CALIBRATE
Neural response
Measure its effect on a named channel or cellular target.
04 / TEST
Perceptual endpoint
Choose a defined task and separate sensory, motor, and reporting effects.
Each transition needs its own evidence. A downstream signal alone can hide several unknown factors inside one fitted gain. Independent chemical and physiological measurements are what make the pathway testable.
EVIDENCE / PREPARATION MATTERS
What has been observed. What remains unsettled.
PURIFIED PROTEIN · 2021
Magnetic sensitivity in bird CRY4
Xu and colleagues reported magnetic sensitivity in purified European-robin cryptochrome 4. This supports investigation of the studied molecular pathway. Human CRY1/CRY2 and a neural environment require their own characterization. [1]
MOLECULAR CONSTRAINT · 2017
The cofactor cannot be presumed present
Kutta and colleagues found low FAD-binding affinity in Type II cryptochromes, challenging a simple transfer of avian photochemistry to mammals. A neural proposal needs a measurement of native cofactor occupancy and a specified formation mechanism. [2]
FLY EXPERIMENTS · 2011–2024
Positive findings and substantial null results
Human CRY2 expressed in flies supported a reported light-dependent magnetic response. Later fly work reported cellular and circadian responses under different field conditions. Large T-maze and geotaxis experiments found no behavioral effect in their tested paradigms. These studies do not measure the same endpoint or use interchangeable preparations. [3][4][5]
The behavioral dispute continued in a 2024 comment and reply. Both are included below; neither alone resolves the disagreement. [6]
EXPERIMENTAL METHODS · 2026
A more direct way to interrogate spin chemistry
Meng and colleagues reported optical detection and radio-frequency control of spin chemistry in flavoproteins. Purified or engineered proteins and controlled optical and magnetic conditions make this a methods advance to study. They do not establish an endogenous mechanism in human neural tissue. [7]
RESEARCH NOTE 01 / A QUANTITATIVE NEXT STEP
One mediator. A prediction we can challenge.
Our proposed protocol asks whether two selective perturbations producing the same reaction-yield change also produce the same current change when formation flux, clearance, and the calibrated neuronal response remain matched.
The note derives a concentration and current prediction, carries uncertainty through the calculation, and states when an upper bound would exclude a meaningful effect. Its numerical example is explicitly synthetic; a native molecular candidate has not yet been selected.
Our Circadian Gating of Temporal Integration proposal asks whether biological phase and sleep pressure alter the conditions in which neurons integrate information. The physiological theory can be tested before a spin-chemical contribution is identified.
Rodent clock-neuron experiments connect redox rhythms to excitability. Human TMS/EEG work also reports circadian variation in cortical excitability, while acknowledging incomplete separation from time awake. Neither study closes the pathway to subjective duration. [8][9]
A distinctive proposed test concerns clock alignment: does greater dispersion of local cellular phases increase timing variability under otherwise comparable conditions? Local clock alignment would first need measurement in a suitable cellular or animal preparation. A human phase marker is not a direct measure of every neural clock.
Temporal discrimination, prospective duration, remembered duration, and repeatability are separate outcomes. Increased remembered duration can occur without improved resolution in the tested task. Choose the endpoint before analyzing the data. [10]
SEPARATE HYPOTHESIS / MICROTUBULES & ORCH OR
Specify the quantum state before invoking collapse.
Hameroff and Penrose’s Orch OR proposal associates microtubule quantum processes with a proposed gravitational objective reduction and conscious events. Its physical commitments differ from the reaction model above. [11]
EG refers to gravitational self-energy associated with the difference between specified superposed mass distributions. Cellular ATP or metabolic energy cannot simply be substituted for it.
A test needs a physiologically populated candidate state, measured dynamics in its environment, a defensible mass-distribution calculation, and a signature distinguishing the proposed reduction from ordinary decoherence and cellular effects.
Work on optical behavior in isolated tubulin and microtubule preparations, and a mouse study reporting delayed anesthetic loss of righting after a microtubule-targeting intervention, warrant further study. Neither intervention uniquely selects objective reduction or explains experience. [12][13]
RESEARCH PLAN / DECISIONS THAT CHANGE THE MODEL
Build a chain of tests.
Reproduce the molecular calculation.
Check conservation and limiting cases, compare independent solvers, and reproduce a published case with documented parameters. The demonstration here is a computational starting point.
Identify a native candidate.
Name the species, cell, compartment, reaction, energy source, and relevant abundance. If no reaction exists under the proposed conditions, redirect the mechanism.
Predict a discriminating response.
Specify field, orientation, or resonance dependence before testing. Control heating, induced currents, vibration, illumination, and delivered power. An isotope effect also needs controls for ordinary chemical changes.
Measure the mediator and attempt rescue.
Calibrate the product’s physiological effect independently. A selective perturbation should remove the predicted signal; restoring its mediator should recover it. A broad cryptochrome knockout does not isolate the proposed spin reaction.
Test a defined neural or perceptual endpoint.
Preregister the main outcome, use independent biological replicates, blind conditions, and seek replication. A precise null result can exclude the specified effect. Task accuracy, synchrony, and an anesthetic reflex are not interchangeable measures of experience.
METHODS / REPRODUCIBILITY
Inspect the assumptions. Reproduce the numbers.
The browser selects from a precomputed grid of the stated eight-state model. Each point is obtained by solving the integrated density-matrix equation. The downloadable generator records parameters, checks, and numerical tolerances. A second calculation evolves the density matrix directly in time to test representative solutions.
Verification results will load with the calculation grid.
Requires Python, NumPy, and SciPy. This is an idealized demonstration of specified spin dynamics, not a fitted biological prediction or a new theory of consciousness. The evidence discussion includes 2026 work; it does not backdate those findings into the October 2025 circadian essay.