If you kick a ball along the ground, it will roll away from you – that's pretty basic science. But the world of quantum mechanics rarely plays by the rules we're used to, and now mathematicians have found that kicking a quantum ball might send it flying toward your foot instead. When a force is applied to them, quantum particles can move in the opposite direction, in an effect known as "backflow."

As counterintuitive as it seems for most of us, the idea of particles going against the grain like this isn't new. Earlier this year scientists created a fluid that exhibited the properties of "negative mass," meaning it also has negative force and flows backwards. Backflow operates on a similar (but different) principle, and until now, it was believed to only apply to "free" quantum particles – those with no forces acting on them.

But free quantum particles are essentially just a theoretical blank slate, used to calculate certain things without other variables messing up the results. This new study, from universities in Cardiff, York and Munich, has detected backflow in particles which do have forces acting upon them.

"The backflow effect in quantum mechanics has been known for quite a while, but it has always been discussed in regards to 'free' quantum particles, i.e., no external forces are acting on the particle," says Daniela Cadamuro, co-author of the study. "As 'free' quantum particles are an idealized, perhaps unrealistic situation, we have shown that backflow still occurs when external forces are present."

The team conducted theoretical analysis of quantum mechanical particles, and found that the backflow effect is always playing some role in quantum physics, albeit on a very small scale. That may explain why it hasn't been been measured until now.

"We have shown that backflow can always occur, even if a force is acting on the quantum particle while it travels," says Henning Bostelmann, co-author of the study. "The backflow effect is the result of wave-particle duality and the probabilistic nature of quantum mechanics, and it is already well understood in an idealized case of force-free motion."

Backflow could be caused by forces reflecting particles, but the team ruled this out by showing that the effect still occurs in a medium completely free of reflection. The researchers say that the discovery could be used to fine-tune calculations in future quantum experiments.

"These new findings allow us to find out the optimal configuration of a quantum particle that exhibits the maximal amount of backflow, which is important for future experimental verification," says Cadamuro.

The research was published in the journal Physical Review A.