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A handful of rice grains falls onto a hot skillet, and they start jumping. Each grain pushes its neighbors, and the whole pile stirs without any external hand. That's active matter: a multitude of particles that draw energy on their own and convert it into motion. Until now, physicists have studied such a "dance" using Newton's laws, without invoking quantum mechanics.

But when particles become very small (say, individual molecules or cold atoms) quantum effects come to the fore. A particle ceases to be a point and smears into a probability cloud. The authors crossed a classical model of active motion with a quantum description via the Wigner function — a kind of bridge between worlds. They calculated how far a particle would travel in a given time and found a curious regime: the displacement grows not smoothly, but as the sixth or even seventh power of time. For comparison, an ordinary Brownian particle's displacement grows linearly, like a pedestrian walking at a steady pace. Here, it's as if a swimmer accelerates with each stroke.

Such steep growth occurs when a particle "remembers" its direction for a long time and receives strong kicks from active noise. Quantum jitters of the initial state do not erase this effect: they only slightly shift the moment when it kicks in. As a result, quantum active matter can move much faster than classical predictions, and now we have a map of where and when this happens.

So the jumping grains on the skillet are just a first approximation. Shrink the scale to atoms, and the familiar picture falls apart: instead of well-defined trajectories, there's a blurred cloud, and motion obeys a very different arithmetic of time.