YOU could call it shoe string theory: scientists have finally solved the knotty problem of unravelling laces.

Why and how firmly tied shoe laces free themselves has been a maddening mystery ever since humans first donned footwear.

Now experts have the answer. Their research suggests that a blend of two forces act like an invisible hand, first loosening the knot and then tugging until the laces trail on the ground and your securely held shoe becomes a wobbly slipper.

Using a slow-motion camera, scientists revealed how knot-failure happens in seconds, triggered by a complex interaction of forces.

Lead researcher Christopher Daily-Diamond, right, from the University of California at Berkeley, said: “When you talk about knotted structures, if you can start to understand the shoelace then you can apply it to other things, like DNA or microstructures, that fail under dynamic forces.

“This is the first step toward understanding why certain knots are better than others, which no-one has really done.”

The study began with co-author and graduate student Christine Gregg lacing up a pair of running shoes and jogging on a treadmill while a colleague filmed what happened next.

When running, the foot strikes the ground at seven times the force of gravity. Responding to that force, the knot stretches and then relaxes.

As the knot loosens, the swinging leg applies an inertial force on the free ends of the laces, leading to rapid unravelling in as little as two strides.

The findings, published in the journal Proceedings of the Royal Society A, revealed a high level of acceleration at the base of the knot.

Gregg said: “The interesting thing about this mechanism is that your laces can be fine for a really long time and it’s not until you get one little bit of motion to cause loosening that starts this avalanche effect, leading to knot failure.”