Water waves travel back in time to retrace their ripples

Nudge your bath tub just right and you might end up reversing time.

Don’t worry – you won’t end up wet, naked and without a towel in the Cretaceous period. Emmanuel Fort at the Langevin Institute in Paris, France, and his colleagues have developed what they call a “time mirror”, which can make water waves rewind into their past. Humans and rubber duckies are unaffected.

To understand how this works, imagine dropping a stone in a pond and watching waves ripple out from a central point in an ever-expanding circle. The equations governing the behaviour of waves say that it should also be possible for a ring of ripples to refocus back into a single point, like a reversed movie of the dropped stone. But we never actually see this happening, because it is vanishingly unlikely that an outside-in ring would form spontaneously.

Put it in reverse

Fort and others have previously shown that it is possible to engineer the situation so the waves turn back on themselves by kitting out the edge of your pond with sensors and wave generators, effectively recording and then playing back the waves in reverse. The process has been done with water, sound and even microwaves, and is used to produce clearer ultrasound images for medical uses.

But now the team has discovered that simply dropping the tub downwards is enough to send water waves scurrying in reverse, with no need for complex sensors. That’s because the velocity of water waves depends on acceleration due to gravity. “If you do a sudden jolt, you change the effective gravity, and the velocity of the wave changes,” says Fort.

The disruption essentially resets the starting point of the wave. Once normal gravity is restored, it starts to travel both backwards and forwards. “Suddenly, you freeze the wave. When you release it again, it doesn’t remember that it was going one way,” says Fort.

Déjà vu

To show that the backward-travelling waves converge exactly on their starting point, just as if you were rewinding time, the team conducted a series of experiments. In some, they simply created a circular ripple of waves by dipping a probe in the water, similar to dropping a stone in the pond. In others, they used wave emitters in the shape of France, the Eiffel Tower and a smiley face to create complex wave-fronts. In each case, the reversed waves converged to recreate their original shape.

The experiments aren’t truly reversing time, because the waves continue to travel out again once they have converged at the central point, points out Fort. “A real time-reversal would have a sink that absorbs all the waves,” he says.

Now the team hopes to conduct similar experiments with other kinds of waves, like light or sound, although it may prove more difficult to find an analogue of their time-mirror jolt in other wave mediums, he says.

“The work is spectacular,” says Geoffrey Edelmann of the US Naval Research Laboratory in Washington, D.C. “They essentially change the rules that govern how the wave propagates and, in doing so, create an entirely new way to focus waves free of spatial constraints.” He also thinks the technique could be extended to other kinds of waves, and perhaps have medical applications such as lithotripsy, which uses ultrasound waves to break up kidney stones.

Journal reference: Nature Physics, DOI: 10.1038/nphys3810