Coherence Time in Neural Oscillator Assemblies Sets the Speed of Thought

A fundamental insight from systems neuroscience is that cognition emerges from coherent oscillations across neural assemblies, not merely from individual spike rates. Working memory maintenance requires sustained theta-gamma phase-amplitude coupling. Attention selectively enhances inter-areal synchronization in gamma band. Perceptual binding depends on transient phase alignment across sensory cortices.

Yet despite extensive empirical characterization, the physical principles governing how fast distributed assemblies can achieve coherence—and thus how quickly cognitive operations can proceed—remain incompletely formalized. Why does perceptual binding require 30–50 ms rather than 3 ms or 300 ms? Why do larger assemblies integrating more information process more slowly?

We propose that neural processing speed is fundamentally limited by coherence time: the time required for distributed oscillators to achieve sufficient phase alignment for a collective computation to register.

We model biological temporal processing as a sequence of commits—thermodynamically irreversible events that register high-dimensional internal state as low-dimensional output. The minimum time between commits is bounded by four physical constraints:

$\tau_{\mathrm{eff}} = \max\left[\tau_{\mathrm{QSL}},\; \tau_{\mathrm{SNR}},\; \tau_{\mathrm{coh}},\; \tau_{\mathrm{power}}\right]$

where the max operation reflects that the slowest mechanism dominates:

• Quantum speed limits ($\tau_{\mathrm{QSL}}$): ~$10^{-13}$ s, relevant only for ultrafast molecular dynamics
• Signal-to-noise limit ($\tau_{\mathrm{SNR}}$): Time for signal integration above detection threshold
• Coherence time ($\tau_{\mathrm{coh}}$): Time for phase alignment across $M$ modules
• Power limit ($\tau_{\mathrm{power}}$): Metabolic constraints on commit rate

Human visual perception exhibits temporal integration windows of 30–50 ms (flicker fusion at 20–30 Hz). We apply the bound with neural parameters:

Take $M=8$ occipital modules, $r=0.7$ (attention), full tolerance $\varepsilon=\pi$ rad, and phase-exploration rate $\Delta\omega=2\pi\times 20$ rad/s. Using the coherence time formula with $\alpha=0.9$:

$\tau_{\mathrm{coh}} \approx \frac{1}{125.66}\left(\frac{2\pi}{\pi}\right)^{0.9(1-0.7)(7)} = \frac{1}{125.66} \cdot 2^{1.89} \approx 30~\mathrm{ms}$

The effective commit time is $\tau_{\mathrm{eff}} \approx 30$–$50$ ms, matching human binding windows. Coherence time dominates.

During acute stress or falls, subjects report subjective time slowing while objective reaction times remain unchanged. We propose dual commit pathways:

Perceptual loop (cortical): High-$M$ (~10–15 modules) coherent field dynamics across sensory and associative areas. Commits sparse (5–20 Hz), expensive. Arousal increases coherence $r$ and thus information rate $\mathcal{I}(t)$. Subjective duration scales as: $T_{\mathrm{subjective}} \propto \int_0^{\Delta t} \mathcal{I}(t)\,dt$

Motor loop (cerebellar/basal ganglia): Low-$M$ (~3–5 modules) primitives executing learned policies. Commits faster (50–150 ms), cheaper. Arousal modulates decision threshold/drift rate, preserving reaction time.

This dual-loop architecture explains the dissociation: perceptual commits (high $M$, modulated by arousal) proceed independently of motor commits (low $M$, threshold-compensated).

Critical flicker fusion frequency correlates with mass-specific metabolic rate across three orders of magnitude in body size:

• Flies: ~240 Hz (metabolic rate ~10 mL O₂/g/hr, mass ~10 mg)
• Humans: ~60 Hz (~0.25 mL O₂/g/hr, mass ~70 kg)
• Leatherback turtles: ~15 Hz (~0.02 mL O₂/g/hr, mass ~500 kg)

Log-log regression shows $R^2 \approx 0.6$ across three orders of magnitude in body mass, with $f_{\mathrm{CFF}} \propto P_{\mathrm{meta}}^{0.6}$.

We have established that coherence time sets the speed of thought. Key findings:

1. Speed-flexibility trade-off: Increasing $M$ exponentially slows commits but expands combinatorial flexibility. Increasing $r$ speeds commits but restricts dynamics to low-dimensional synchronized manifolds.

2. Dual-loop architecture: Separate perceptual (high-$M$ cortical) and motor (low-$M$ cerebellar) pathways explain tachypsychia dissociation.

3. Parameter sensitivity mechanism: Modest $r$ or $M$ shifts (factor of 2) produce order-of-magnitude temporal changes without proportional metabolic costs.

4. Quantitative predictions: Visual binding windows (30–50 ms), metabolic scaling ($R^2 = 0.6$), alpha entrainment linearity, dual-task dissociations under arousal.