How many labels can a biological oscillator carry? A quality-factor screen for proposed information carriers

arXiv:2608.10560v2 Announce Type: replace-cross Abstract: How many distinguishable labels can a biological oscillator carry? Proposals invoking collective vibrational modes, endogenous electromagnetic fields, microtubule excitations and oscillatory phase codes are each debated on grounds particular to themselves, with no shared standard for comparison. We show that spectral distinguishability alone bounds the number of labels by the quality factor, M <= Q = 2 pi nu tau. This follows from the relation between linewidth and coherence time, so it is independent of substrate, of mechanism, and of any position on quantum effects in biology, and it can be evaluated from two published quantities. Applied to a recently proposed 30 GHz intracolumnar microwave field in cortex, it gives Q = 0.19: the linewidth exceeds the carrier five-fold. The obvious rescue, that a driven emitter can be spectrally narrower than its gain medium, requires a resonant cavity, and the model's own geometry forbids one. An independent bound on metabolic power is exceeded by five to nine orders of magnitude. Six further criteria follow from the same standpoint, including a two-sided persistence window requiring a label to be both readable and rewritable. Screening eleven carriers, only the low-frequency neural rhythms pass. High-frequency molecular carriers are eliminated by brevity, not by the fragility the debate has assumed.

Abstract:How many distinguishable labels can a biological oscillator carry? Proposals invoking collective vibrational modes, endogenous electromagnetic fields, microtubule excitations and oscillatory phase codes are each debated on grounds particular to themselves, with no shared standard for comparison. We show that spectral distinguishability alone bounds the number of labels by the quality factor, M <= Q = 2 pi nu tau. This follows from the relation between linewidth and coherence time, so it is independent of substrate, of mechanism, and of any position on quantum effects in biology, and it can be evaluated from two published quantities. Applied to a recently proposed 30 GHz intracolumnar microwave field in cortex, it gives Q = 0.19: the linewidth exceeds the carrier five-fold. The obvious rescue, that a driven emitter can be spectrally narrower than its gain medium, requires a resonant cavity, and the model's own geometry forbids one. An independent bound on metabolic power is exceeded by five to nine orders of magnitude. Six further criteria follow from the same standpoint, including a two-sided persistence window requiring a label to be both readable and rewritable. Screening eleven carriers, only the low-frequency neural rhythms pass. High-frequency molecular carriers are eliminated by brevity, not by the fragility the debate has assumed.

20 pages, 7 tables, no figures. Reference implementation and verification suite at doi:https://doi.org/10.5281/zenodo.21837368. Extends and supersedes doi:https://doi.org/10.5281/zenodo.21837082. v2: adds a third scope limit to the distinguishability bound, distinguishing homogeneous from inhomogeneous linewidth, and sharpens the corresponding measurement requirement in Section 6.3. No result or conclusion changes

Neurons and Cognition (q-bio.NC); Biological Physics (physics.bio-ph); Quantum Physics (quant-ph)

arXiv:2608.10560 [q-bio.NC]

(or arXiv:2608.10560v2 [q-bio.NC] for this version)

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How many labels can a biological oscillator carry? A quality-factor screen for proposed information carriers

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