Two dancers, each moving on their own, create a simple and symmetrical dance. But once they start adapting to each other, the movements become more complex, and the original structure is lost. Particles behave similarly in collisions: their intrinsic properties are usually highly entangled, hiding an elegant order. Scientists have discovered that if you remove this entanglement, the system reveals a grand SO(8) symmetry. In this symmetry, there are 28 independent ways to "rotate" a particle without changing its physical properties — whereas in the ordinary world, rotation has only three axes. It’s as if our dance, instead of three dimensions, suddenly acquired 28, yet remained harmonious. Just as spectroscopy breaks light down into pure colors, quantum information methods allow us to separate the entangled states of particles and see each one’s hidden dance. In the Standard Model, which describes fundamental particles, such symmetries are already used, but before we only saw a tangled ball, not a neat pattern. By limiting entanglements, it’s like turning off the noise and enjoying nature’s perfect choreography.
The SO(8) symmetry has 28 generators — that's like 28 different dance moves you can perform simultaneously, and the dance remains unchanged. In familiar rotation, we have only three such moves.