Mathematicians have discovered an interesting property about quantum mechanical particles – they have the unique ability to move in the opposite direction to the way in which they are being pushed.

According to Newton's Laws of Motion, acceleration is produced when a force acts on a mass. Once the force acts on an object, it will travel in the same direction as its momentum, so for example, a car going forwards will travel forwards, but not backwards.

However, now mathematicians have discovered that quantum particles are able to travel in the direction opposite to their momentum, a property known as "backflow".

Researchers from the University of York, the Technical University of Munich (TUM) and Cardiff University say that this is the first time that such movement has been observed in a particle where external forces are acting on it. Previously, this behaviour had only been seen in "free" quantum particles, where no force is acting on them.

"Forces can, of course, make a particle go backwards – that is, they can reflect it – and this naturally leads to increased backflow. But we could show that even in a completely reflection-free medium, backflow occurs," said Dr Gandalf Lechner, a researcher at Cardiff University's School of Mathematics.

"In the presence of reflection, on the other hand, we found that backflow remains a small effect, and estimated its magnitude."

The discovery is a step forward in the field of quantum mechanics research, which is working towards one day making it possible to build ultra-fast quantum computers and super-high resolution-imaging solutions.

The backflow effect in quantum mechanics has been known for several years. It is the result of wave-particle duality and the probabilistic nature of quantum mechanics, but had only seemed possible in the case of force-free motion.

"As 'free' quantum particles are an idealised, perhaps unrealistic situation, we have shown that backflow still occurs when external forces are present. This means that external forces don't destroy the backflow effect, which is an exciting new discovery," said Dr Daniela Cadamuro, a researcher at TUM.

"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."

The study, entitled "Quantum backflow and scattering" is published by the American Physical Society in the journal Physical Review A.