Kopel's quality-factor bound rules out 30GHz brain microwave signals

Eran Kopel's new arXiv preprint (arXiv:2608.10560) settles a cross-disciplinary debate with a single, substrate-independent bound. The paper, "How many labels can a biological oscillator carry?", shows that the maximum number of distinguishable labels an oscillator can encode is set by its quality factor: M ≤ Q = 2πντ, where ν is the oscillation frequency and τ the coherence time. This follows directly from the relation between linewidth and coherence time, so it applies equally to collective vibrational modes, endogenous electromagnetic fields, microtubule excitations, and oscillatory phase codes—no assumptions about quantum effects in biology are needed. Only two published quantities are required to evaluate the bound, making it a practical screening tool.

Kopel applies the bound to a recent proposal of a 30 GHz intracolumnar microwave field in the cortex. The result is damning: Q = 0.19, meaning the linewidth exceeds the carrier frequency by five-fold, so the proposed field cannot carry even a single reliable label. A potential escape via driven emitters and resonant cavities is blocked by the model's own geometry, and an independent metabolic power limit is violated by five to nine orders of magnitude. Six additional criteria—including a two-sided persistence window requiring labels to be both readable and rewritable—are then used to screen eleven proposed carriers. Only low-frequency neural rhythms pass. High-frequency molecular carriers fail not because of fragility (the usual assumption), but because their coherence time is simply too short to support distinct labels.