torus universe quantum gravity

Electrons in a solid usually either run freely (metal) or are locked in place (insulator). But sometimes strong mutual repulsion locks them into a halfway state: charges stand still, while spins, tiny magnetic arrows, continue to live their own life. This is called a Mott insulator.

In the standard picture, black holes are the undisputed density champions: all their matter is squeezed into a single point. Imagine the entire mass of Mount Everest packed into a grain of salt. But physicists have found a theoretical trick.

At the center of almost every large galaxy lurks something supermassive and dark. Most often, that something is thought to be a black hole — a region where gravity is so strong that even light cannot escape. But what if it's not a black hole, but a dense ball of ultralight particles — a boson star?

A patchwork quilt where each patch is a tiny quantum knot obeying strict mathematical rules. Physicists took many identical such knots and started sewing them together in all possible ways. The result was three-dimensional shapes — from simple spheres to intricate bagels with holes.

The quantum birth of the Universe is like a game of dice, where the chance of rolling a six is catastrophically small. The formalism of Hawking and Hartle, an elegant recipe for a world born from timelessness, has spent decades predicting that a universe like ours is fantastically improbable.

An invisible film, a quantum field, is stretched over a rubber bagel. While the bagel is small, the film stays taut and doesn't sag anywhere: the vacuum remains empty. But once you stretch the bagel to a certain size, a dent spontaneously appears in the film — the field starts to be felt at every point. This dent is not random.

The law discovered by Wolfgang Pauli forbids identical particles from occupying the same spot. Hence, in cold matter, a Fermi sea is born: particles, like water, fill energy levels from bottom to top. The shape of the sea's surface — including 'islands' of emptiness — dictates the properties of the whole system.