Poynting's theorem

When physicists drive electrons through an ultrapure gallium arsenide channel at helium temperatures, they expect to see a well-behaved, almost ideal fluid.

Two-dimensional worlds never cease to amaze: here even crystal melting is not a symmetry breaking but a vortex drama discovered by Kosterlitz and Thouless. At the heart of this theater are topological сингулярности, whose energy and энтропия bargain for order. This language is common to сверхтекучести и сверхпроводимости.

Right after the Big Bang, space was a hot plasma — a mix of charged particles and light. In such a medium, electric currents couldn't flow on their own: a 'potential difference' was needed to push electrons relative to photons.

In the late 1990s, astronomers including Saul Perlmutter discovered that the universe is expanding at an accelerating rate. The cause was dubbed dark energy — an invisible force stretching the cosmos.

An ordinary magnet always carries two poles — north and south. Split it in half, and each piece immediately grows its own pair. But deep in particle theory lives a strange notion: the monopole — a particle carrying just one magnetic charge, a lone pole without a partner.

In a thin sandwich of semiconductors, light creates pairs, an electron and a positive hole, that stick together like a ball on a rubber band. Normally, such pairs, called excitons, quickly emit light and vanish. But there are others, dark ones, that live hundreds of times longer because their internal structure forbids them from easily giving off energy.

If you pour sand into a glass, it settles in a flat layer. But instead of sand, take the tiniest particles of gas: in a gravitational field they don't just fall: each particle races along its own trajectory, collides with neighbors, and all this commotion creates pressure.

A drop of water stretches in a strong electric field. The deuterium nucleus, a bound pair of a proton and a neutron, behaves the same way, except here the field comes from a passing gamma ray, and instead of just stretching, the nucleus can simply fall apart.

To uncover the proton's true size, physicists swapped the electron in a hydrogen atom for its heavy copy — the muon. Acting like a magnifying glass with thousandfold power, the muon gets right up against the nucleus and 'probes' the proton with unprecedented precision.

Run a current through a wire, and the wire heats up. Anyone who has ever touched a phone charger knows this. Physicists call this heating Joule heating, after James Joule, who in the mid-19th century measured how much heat electricity produces. Since then, the formula has been simple: the greater the resistance and the current, the hotter the wire.

The ocean is like a layered cake: warm, light water on top, cold, heavy water below. Between the layers, at the interface, invisible waves roam. They don't lift crests like a storm; instead, they slowly rock the entire water column, as if someone were shaking a giant aquarium from within.

A single photon passes through two slits and leaves an interference pattern on a screen. Quantum mechanics describes this process with a wave function, but what happens to the particle itself?