In the familiar world, we have three spatial dimensions. However, theoretical physics allows for additional, hidden directions — compactified, that is, curled up to microscopic sizes. If one such dimension has the topology of a Klein bottle, a non-orientable surface with no distinction between inside and outside, the fundamental symmetries underlying the Standard Model of particle physics are broken. In particular, such geometry violates CP symmetry — the rule that the laws of physics should not change when particles are swapped with antiparticles and space is mirrored. Under normal conditions, CP symmetry dictates that matter and antimatter are produced in equal amounts, but here that equality disappears.

Inside the curved dimension, a dense layer of virtual pairs forms — quantum fluctuations resembling a fog of particles and antiparticles that continuously pop into existence and vanish. Our three-dimensional universe, like a ship, glides through this fog. The analogy simplifies: in reality, it's about the interaction of fields at the boundary of the extra dimension, but the image of friction captures the essence: this interaction pulls virtual pairs into reality, turning them into real particles. However, due to CP violation caused by the Klein bottle topology, slightly more matter than antimatter is produced. An imbalance of just one extra proton per billion pairs is enough for galaxies, stars, and everything we see around us to eventually condense from this excess.

Such a mechanism elegantly explains one of the key mysteries of the early universe: where the observed matter came from. Without this microscopic imbalance, the world would have annihilated into radiation, leaving emptiness.