Why speed correlations in starling flocks are scale-free
In plain words
In starling flocks, a change in one bird's flight is correlated with birds across the whole flock, however large it is. Whether flocks are tuned to a special critical state to achieve this, and how, is debated.
Precise statement
In wild starling flocks ($10^2\text{ to }10^4$ birds), connected correlation functions of velocity fluctuations have correlation length $\xi$ proportional to flock size $L$, for both orientation and speed (Cavagna and co-workers, 2010). Orientation correlations follow from Goldstone modes of broken rotational symmetry; speed correlations require tuning near a critical point or another mechanism. Determine the mechanism for scale-free speed correlations and whether it involves tuning.
What would settle it
A model with independently inferred interaction parameters that reproduces $\xi$ proportional to $L$ for speed across flock sizes, with or without tuning to a critical point.
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