Mathematicians at the Universities of York, Munich and Cardiff have identified a unique property of quantum mechanical particles – they can move in the opposite way to the direction in which they are being pushed.

In everyday life, objects travel in the same direction as their momentum – a car in forward motion is going forwards, and certainly not backwards.

However, this is no longer true on microscopic scales - quantum particles can partially go into reverse and travel in the direction opposite to their momentum. This unique property is known as 'backflow'.

**New discovery**

This is the first time this has been found in a particle where external forces are acting on it. Previously, scientists were only aware of this movement in "free" quantum particles, where no force is acting on them.

Using a combination of analytical and numerical methods, researchers also obtained precise estimates about the strength of this phenomenon. Such results demonstrate that backflow is always there but is a rather small effect, which may explain why it has not been measured yet.

This discovery paves the way for further research into quantum mechanics, and could be applied to future experiments in quantum technology fields such as computer encryption.

**Unique to quantum particles**

Dr Henning Bostelmann, Researcher in York's Department of Mathematics, said: "This new theoretical analysis into quantum mechanical particles shows that this 'backflow' effect is ubiquitous in quantum physics.

"We have shown that backflow can always occur, even if a force is acting on the quantum particle while it travels. 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 idealised case of force-free motion."

Dr Gandalf Lechner, Researcher in Cardiff's University's School of Mathematics, said: "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. In the presence of reflection, on the other hand, we found that backflow remains a small effect, and estimated its magnitude."

**External forces**

Dr Daniela Cadamuro, Researcher at the Technical University of Munich, said: "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.

"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."

"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."

**Explore further:**
Breaking Newton's Law: Intriguing oscillatory back-and-forth motion of a quantum particle

**More information:**
Henning Bostelmann et al. Quantum backflow and scattering, *Physical Review A* (2017). DOI: 10.1103/PhysRevA.96.012112

## Macksb

This supports my hypothesis that coupling effects among periodic oscillators (2 or many) underlie all forms of coherent matter. Including, most importantly, quantum mechanics.

This backflow or pushback increases the flow of information between and among quantum mechanical particles. The information flow runs two ways--signals flow in both directions.

I have proposed this theory, or hypothesis, in many Physorg posts to explain "unexpected" self-organization in a variety of contexts in physics. Huygens, circa 1660, noted the "odd sympathy" when two of his clocks synchronized their pendulums. Circa 1967, Art Winfree proposed a fuller theory of coupled periodic oscillators, but he applied his idea to biology, not physics.

## physman

## Dingbone

Jul 18, 2017## Dingbone

Jul 18, 2017## mrbeardy13

## MrNewTime

## Kweden

All said, in explosive forces with many particles there is always 'swirly' that pull and push particles in back flow patterns; the only explanation for this would be the pull of the void left by the explosion.

btw-this also explains the oscilation observed (as covered by another article).

## Kweden

As I illustrated above, if we constrain the motion of particle to a lower number of dimension, its pilot wave will get breathing mode of solitons so called quantum Zitterbewegung - these changes will become time reversible and as such periodic."

But, reducing to 2 dimensions makes the particle unobservable, perhaps even non-existent. If reality is actually only 2 dimensional, then it would hold true, but the observable reality is dependent on more than 2 (many more). Still, if your 2 dimensions made a brane effect upon the particle that cannot be explained in our reality, then there could be crossover effect caused by this 2 dimensional, sub-world brane.

## big_hairy_jimbo

We DO need to keep in mind Quantum Field theory, so the first post regarding oscillators isn't too bad. As to coupling of oscillators, well I'm unsure if there is a Quantum Version of that, but perhaps coupling to other fields is what we are talking about.

I can't read behind the pay wall, but I'm wondering if this is like Group vs Phase velocity for light waves, but applied to matter waves???

Or perhaps like cars on a freeway and someone out front slows down rapidly but doesn't come to a standstill. This causes all the cars behind to slow down. An overhead observer will see that ALL cars are moving FORWARD, but there is a backward travelling wave as each car in turn applies the brakes.

Anyway, individual velocity is irrelevant, it's momentum that is the important property.

## antialias_physorg

This looks like the paper on arxiv (possibly with minor differences, but the abstract an the images seem identical)

https://arxiv.org...03.04597

Note that backflow does not mean that any kind of conservation laws are broken. there is simply a chance that for small time intervals a net backflow exists (and the way I read there's an upper bound on that average time interval...and thereby also on the averaged spatial interval).

They note the effect is probably connected to Uncertainty.

## Dingbone

Jul 19, 2017## Dingbone

Jul 19, 2017## Dingbone

Jul 19, 2017## Dingbone

Jul 19, 2017## swordsman

## Dingbone

Jul 19, 2017## mcglynn_james

## Macksb

But this is not about me. The idea and the credit belong entirely to Art Winfree, as I have made clear in many posts on Physorg.

His math is well vetted (Steve Strogatz of Sync; Ian Stewart and many others). The application of his idea to biology is well established (Bard Ermentrout and many others). There is thus a reasonable basis for believing that Art's idea might extend to physics.

You are of course right to be skeptical. I appreciate your challenge.

## Dingbone

Jul 19, 2017## Dingbone

Jul 19, 2017## vfilipovic

## Da Schneib

## GeoffMelloy

A J Bracken and G F Melloy, Probability backflow and a new dimensionless quantum number, J.Phys.A 27, 2197-2211 (1994)

This was followed up by a series of further backflow-related papers, including:

G F Melloy and A J Bracken, Probability backflow for a Dirac particle, Found.Phys. 28, 505 (1998)

- this relates to a relativistic free particle

G F Melloy and A J Bracken, The velocity of probability transport in quantum mechanics, Ann.Phys.(Leipzig) 7, 726 (1998)

- this is where the case of a non-relativistic particle moving under a constant force is studied

## Dingbone

Jul 24, 2017## Dingbone

Jul 24, 2017