Borrowing From Quantum Math, a New Framework Describes the Brain’s Evolving States

A bold new mathematical framework proposes that the brain’s shifting electrical activity can be described the way physicists describe evolving quantum states — not because the brain is quantum mechanical, but because the mathematics of wave functions offers a compact language for systems whose many components evolve together through time. The framework, published in Frontiers in Computational Neuroscience, was developed by independent researcher Madelyn Klebba and tested against electroencephalographic (EEG) recordings captured as epilepsy patients moved between quiet, seizure-approaching, and full seizure states. The result is an unusual marriage of signal processing, dynamical systems theory, and a representational idea borrowed from Hugh Everett’s relative-state formulation of quantum mechanics.

The central problem the work addresses is one of representation rather than mechanism. Modern neuroscience can measure neural activity with extraordinary precision, yet most quantitative analyses treat each observable — signal amplitude, spectral power, entropy, phase relationships, cross-frequency coupling, and recurrence structure — as an independent descriptor. No single measure captures the full evolution of large-scale brain dynamics. Klebba’s proposal is that these established observables can instead be interpreted as complementary properties of a single evolving neural state, represented mathematically by a complex-valued function in which instantaneous amplitude and phase unfold continuously over time.

The mathematical foundation is deliberately classical. Using the Hilbert transform, an oscillatory EEG signal can be converted into an analytic signal — a complex-valued representation whose magnitude gives instantaneous amplitude and whose argument gives instantaneous phase. This is a standard tool in electrophysiology, and the study is emphatic that nothing quantum is being claimed. The inspiration from Everett is strictly structural: his formalism showed how multiple evolving configurations could be represented within a single state space without requiring collapse into one physical state. The framework adopts that representational strategy, describing the neural state as a superposition of multiple simultaneously active neural configurations, each a transient pattern of coordinated activity whose relative contribution changes continuously.

Crucially, these configurations are not proposed as separate conscious entities or parallel minds. They are mathematical constructs describing the many interacting patterns of neural activity that coexist in one biological brain — sensory processing, memory retrieval, attentional control, motor planning, and predictive inference all running in parallel across distributed networks. The framework suggests, as a theoretical hypothesis rather than an empirical result, that a unified thought might correspond to the transient dominance of one configuration within this evolving landscape, while alternatives remain dynamically active outside immediate awareness. Whether that hypothesis holds is explicitly left for future investigation.

To ground the framework empirically, the study analyzed a publicly available EEG dataset collected through a collaboration between the Neurocomputing Laboratory at IIT Delhi and the Neurology & Sleep Center in New Delhi. Recordings from ten epilepsy patients, acquired at 200 Hz with standard international 10–20 electrode placement, were divided into 50 interictal, 50 preictal, and 50 ictal segments — 150 recordings in total, each 5.12 seconds long. The dataset was chosen because it contains clearly defined transitions between distinct physiological states, providing a natural testbed for asking whether multiple electrophysiological observables change in a coordinated manner.

The results were striking in their consistency. Root-mean-square amplitude increased from about 23.5 microvolts during interictal recordings to roughly 139 microvolts during seizures, one of the largest effects in the study with an effect size of ε² = 0.658. Spectral power redistributed dramatically toward lower frequencies: delta-band activity rose from 40 percent of total power to 75.4 percent during seizures, while theta, alpha, and gamma contributions fell sharply. All three entropy measures — spectral, permutation, and sample entropy — declined significantly, indicating progressively reduced signal complexity as seizures took hold, with sample entropy showing one of the largest effects at ε² = 0.586.

Temporal organization changed as well. Alpha-band phase concentration increased significantly during ictal recordings, and theta–gamma phase-amplitude coupling, quantified with the modulation index and validated against surrogate data, differed significantly between interictal and seizure-associated states. Recurrence quantification analysis, performed after reconstructing each signal’s state space through time-delay embedding, revealed that neural trajectories became more persistent and less mobile during seizures: mean diagonal line length grew from 4.05 to 7.70, determinism increased, and mean state-space displacement fell from 0.422 to 0.291. Every major analytical domain showed statistically significant differences across seizure states, assessed with Kruskal–Wallis tests, Holm-corrected post hoc comparisons, effect sizes, and bootstrap confidence intervals.

The author is careful to situate these findings relative to existing theories of consciousness. The results are broadly consistent with Integrated Information Theory’s emphasis on large-scale integration, but the framework does not attempt to compute Φ or propose an alternative measure of consciousness. It likewise differs from electromagnetic field theories such as CEMI and Susan Pockett’s formulation: the neural field here is a mathematical representation of measurable dynamics, not a claim that the brain’s physical electromagnetic field is the substrate of experience. The framework also engages the concept of metastability — the tendency of complex neural systems to occupy transiently organized configurations while retaining the capacity to reorganize — as the theoretical context in which the evolving state representation should be understood.

The study acknowledges its limitations candidly. The recordings were single-channel, so they cannot resolve the distributed cortical interactions that the proposed configurations would represent; the data come from pathological brain states that cannot be assumed to mirror healthy cognition; and neither the individual configurations nor the proposed neural coordination functional were directly estimated from the data. The empirical contribution is the demonstration that established observables change in a coordinated, multidimensional way during seizure progression — a quantitative foundation, not a validation, of the formalism.

What the work ultimately offers is a research program rather than a finished theory. Future investigations using high-density EEG, magnetoencephalography, intracranial recordings, and computational state-space reconstruction could test whether candidate neural configurations can be empirically identified, whether transitions among them correspond to changes in attention or cognition, and whether similar coordinated dynamics appear in sleep, anesthesia, meditation, and disorders of consciousness. The framework even suggests applications beyond neuroscience, potentially informing biologically inspired artificial intelligence systems that rely on dynamical representations of high-dimensional state spaces. Whether wave-function formalism proves genuinely useful for understanding the brain will depend not on its elegance but on whether it generates predictions that competing descriptions cannot — a question the author deliberately frames as open, empirical, and now, at least, formally posed.

Subject of Research: A wave-function-based mathematical framework for representing evolving neural dynamics measured with EEG during epileptic seizure states

Article Title: Wave-function formalism for evolving neural dynamics: a mathematical framework informed by EEG

Article References: Klebba, M. (2026). Wave-function formalism for evolving neural dynamics: a mathematical framework informed by EEG. Frontiers in Computational Neuroscience, 20, Article 1812909. https://doi.org/10.3389/fncom.2026.1812909

Image Credits: AI Generated

DOI: 10.3389/fncom.2026.1812909

Keywords: EEG, neural dynamics, wave-function formalism, epilepsy, computational neuroscience, Hilbert transform, entropy, phase-amplitude coupling, recurrence analysis, metastability, state space, consciousness