Light from an ordinary bulb seems utterly chaotic: its waves oscillate out of sync, like a crowd where everyone walks in their own direction. Such light is called incoherent. For a long time, it was believed that elegant topological structures (knots, rings, links) could only be created in coherent laser light, where all waves march in step. But the authors of the new work have shown that even in 'messy' light, you can weave real optical lace.
The key turned out to be a mathematical object — the incoherent Milnor polynomial. It works like a construction set where the parts (topology) and the color of the parts (statistical coherence, i.e., the degree of light synchronization) are chosen independently. Previously, when working with lasers, you couldn't change brightness at different points without ruining the topology, as if repainting a Rubik's cube would cause it to solve itself. Now that limitation is gone.
The practical application resembles a Rubik's cube trick. The initial state of the cube is the brightness distribution that an observer sees. The rotations of the faces are topological transformations that serve as the encryption key. By changing statistical coherence, you can control how the 'cube' looks from afar, while topology sets the rules for its 'rotation.' This approach promises new methods of information encoding, where secrecy is ensured not only by mathematics but also by the physical properties of light itself.
Thus, chaotic light, which we are used to thinking of as just a source of heat and illumination, acquires hidden order and becomes a tool for transmitting and protecting data.
Knots of light are not material objects: they are regions of space where a certain characteristic (in this case, the coherence of oscillations) vanishes, forming lines or loops.
In M. John Harrison's novel 'Light,' alien entities are described as woven from coherent light structures — perhaps their distant relatives are now appearing in laboratories too.