continuum

Surf doesn't roll onto the shore as an even front. It comes in tongues of foam that merge and split apart. Magnetic fields inside materials behave much the same way: they breathe in waves, and until now nobody had seen them whole.

In a crystal, heat travels on waves. Atoms vibrate, and these vibrations, called phonons, carry energy from the hot edge to the cold one. For a long time, it was believed that if phonons hit resonance (their frequencies exactly match) and can exchange energy, heat would flow like an avalanche. It turns out that's not the case.

In the big world, there's a simple rule: energy density can't be negative, and its flow can't outrun light. In a café, that would look like this: a waiter can't deliver orders faster than he can run. Physicists call this restriction the energy dominance condition. But in the microworld, where quanta rule and spacetime can bend, energy starts acting up.

A regular object moves along a predictable path, like a ball. In the quantum world, a particle is smeared into a probability cloud. To find order in this fog, scientists have recast Schrödinger's equation in the language of flowing water.

In the mountains, there is a saddle — a point where the trail from one valley crosses over into another. Standing exactly on it, you take a step and are already descending the new slope. In chemistry, such a place is called the transition state: a brief moment when atoms are frozen on the threshold of transformation.

Our universe isn't just expanding: it's doing so faster and faster. It's like raisin bread dough in the oven: the raisins move apart, and the farther they've already separated, the faster they continue to recede. The strange force pushing the cosmos apart is called dark energy. Most scientists think it's constant, like a permanent spring built into the very fabric of space.

A hot spoon in a cup of tea — heat runs along the metal from the hot end to the cold one. Textbooks describe this process as atoms jiggling and passing on their jolts to each other. But atoms don't just jiggle: they also spin, like tiny tops. Until now, physicists had no common language to describe both motions at once. The authors of the work built such a language.

A struck tuning fork fades: its vibrations leak into the air. But there are systems where the oscillation does not decay, even though there are plenty of free waves around, ready to carry energy away. Physicists call such 'captured' states bound states in the continuum (BIC).

A conventional antenna array is like a choir: many voices singing in unison, with the sound amplified in only one direction. To catch a signal from another side, you have to rearrange the whole choir. Now imagine a single voice that can change its timbre so that the sound itself focuses in the desired direction.

Two tiny emitters, each about the size of an atom, can together do what neither can do alone. We're talking about light scattering — when light hits particles and bounces off in all directions. Usually, a pair of particles scatters light only slightly more than a single one.

A century ago, quantum mechanics gave the world a neat picture: a particle rotating around a point can only have certain discrete amounts of angular momentum, integer multiples of Planck's constant. This rule seemed as solid as the law of gravity, and it followed from simple algebraic arguments.

A quantum state under continuous measurement is not a frozen picture but a random dance. Each measurement outcome nudges the state one way or another, and to predict the future you have to track the entire trajectory.

Light strikes a metal plate, and electrons fly out. This is the photoelectric effect, and it works only if the light has enough energy to cross the threshold that holds electrons inside.