In anomalous transport, a particle's mean displacement under a constant force may grow too slowly to be distinguishable from noise. The mean drift is there, but measuring it requires impractical observation times. The standard diagnostic for detecting applied force — measure the mean displacement — fails when the transport is sufficiently anomalous.
The paper shifts the diagnostic from mean to variance. In strongly heterogeneous media with subdiffusive transport (anomalous exponent α < 2), the displacement variance initially follows the unbiased scaling law, indistinguishable from zero force. But at a crossover time that depends on the force strength and the anomalous exponent, the variance transitions to a force-dominated regime with different scaling.
The crossover is observation-time-induced. At any fixed measurement window, there exists a detection threshold: forces weaker than this threshold are invisible. The threshold decreases with longer observation — weaker forces become detectable if you watch long enough. In quenched disorder systems, the threshold is even lower than in simpler continuous-time random walk models, because spatial heterogeneity amplifies the force's effect on the variance.
The structural insight: the force is not hidden — it's present from the start. But the observable that reveals it changes identity over time. At short times, the variance carries no force information. At long times, it carries all of it. The measurement doesn't change; the information content of the measurement does. The same number — displacement variance at time t — transitions from uninformative to diagnostic, and the transition time itself encodes the force strength.