A Causal Formulation of Spike-Wave Duality

Understanding the relationship between brain activity and behavior is a central goal of neuroscience. Despite significant advances, a fundamental dichotomy persists: neural activity manifests as both discrete spikes of individual neurons and collective waves of populations. Both correlate with behavior, yet correlation alone cannot decide whether waves exert causal influence or are merely epiphenomenal reflections of spiking. By the Causal Hierarchy Theorem, no amount of observational data—however extensive—can settle this question; causal conclusions require explicit assumptions or interventions.We develop a formal framework that makes this limitation precise and constructive. We define epiphenomenality in terms of invariance of interventional distributions, provide a certificate of sufficiency that identifies when variables may be collapsed without causal loss, and show how to interpret intervention results depending on the assumed causal graph structure.The purpose of this work is not to resolve the spike–wave debate, but to reformulate it. We shift the problem from asking which signal matters most to asking under what conditions any signal can be shown to matter at all. This reframing distinguishes prediction from explanation, and offers neuroscience a principled route for deciding when waves belong to mechanism and when they belong to resonance.