Maxwell's equations

A sculptor looks at a block of marble and sees the figure within, waiting to be freed from excess material. Instead of adding clay, he removes everything that is not part of the form. The authors of a new study on magnetic resonance took a similar approach: rather than complicating the tissue model by adding ever more details, they stripped away the superfluous to reveal the essence.

In a pot of boiling soup, light fat droplets rise to the top, while heavy vegetable chunks sink to the bottom. Particles in the tenuous hot gas around the Sun and other stars behave much the same way — except instead of broth, there's a mixture of charged particles: electrons, protons, and alpha particles.

A carousel doesn't just spin you around in a circle — with each revolution, it also slightly screws itself into the ground. This corkscrew-like motion is the essence of the NUT charge, a special property of spacetime that physicists have been studying since the mid-20th century.

Seventy-two protoplanetary disks, swirling cocoons of cosmic dust and gas, came under the gaze of the MIRI instrument on JWST. Most of them shoot outflows into space: dense conical structures and narrow, high-speed jets. They blast like fountains. This process is not accidental.

Two hundred and eighty-nine days: that's how long one rotation of the white dwarf white dwarf WD 1532+129 takes. This is not just a record: on its surface, near the magnetic poles, scars of iron and other metals appear — silent testimony to planets it has devoured.

Spring scales in a shop show weight simply: the load presses on a spring, it compresses, and the needle moves along the scale. The relation between force and compression is direct, like Hooke's law. Now imagine a scale with a tricky platform: the force is transmitted through levers, and the reading depends not only on the weight but also on how the platform itself bends.

A pair of black holes circles in a dance, gradually drawing closer. They lose energy and spin — a process known as angular momentum radiation. In standard Einstein theory, only gravitational waves carry away angular momentum.

Gravity is the invisible glue that holds stars and planets together. But what if this glue has a tiny mass? In massive gravity, the carrier particles (called gravitons) weigh a minuscule but nonzero amount. This changes the rules near black holes. The authors of the new study built on a mathematical tool — eigenvalue decomposition.

The Sun continuously scribbles magnetic fields across its surface. These patterns are not mere ripples but a handwriting in which nature has encoded warnings of flares. A flare is an explosion that releases the energy of billions of nuclear bombs in minutes, ejecting streams of plasma and radiation into space.

An inflatable balloon with magnetic field lines drawn on it with a marker is a simple model of how a weak magnetic field behaves in an expanding universe. While the balloon is small, the lines lie obediently on the rubber and don't hinder its stretching. That's roughly how a field fills ready-made space without arguing with its geometry.

The interiors of neutron stars are a realm of degenerate matter. Here, protons condense into a superconducting condensate, threaded by quantum vortices. Imagine tiny magnetic tops: each carries a quantum of magnetic flux and glides through the electron fluid.

In a world locked in a crystal lattice and cooled nearly to absolute zero, matter knows how to hide its deepest secrets. A quantum spin liquid is a state where electron spins never freeze, even at zero temperature, remaining in an eternally flickering superposition.

Thorium-229 harbors a secret: its nucleus possesses the lowest excited state among all known nuclides — 8.35 eV.

In the conventional Heisenberg picture, spins at low temperatures are supposed to line up in a strict pattern. But there are crystals — like pyrochlore — where geometry has its own way. Each ion sits at a vertex of a tetrahedron, and the main interaction enforces a rule: two spins point inward, two outward.

Imagine a philharmonic orchestra playing, but the microphone picks up only a blended roar — a tutti where double basses, flutes, and timpani all merge. Physicists have grappled with a similar task for decades, staring at fields of density, temperature, or magnetic induction.

Neutron stars, born in the fires of supernovae, continue to amaze even nearly a century after they were first predicted.

In the early 20th century, Einstein showed that gravity is the curvature of space and time. A bit earlier, Maxwell had unified electricity and magnetism into a single theory.

A pebble drops into a pond, and ripples spread across the water. But one wave suddenly doesn't spread out: it clings to an invisible fold on the surface and runs only along it.

A flashlight beam travels straight into the dark: that's how we usually think of light. But near a massive body, like a star or a black hole, space is curved, and the beam bends smoothly, as if guided by an invisible hand. The authors of a new study have worked out exactly how gravity alters the familiar laws of electricity and magnetism.

A sunspot cools, and above it a dark filament, a prominence, hangs for weeks. Inside it, like a compressed spring, hides the magnetic field. It can be laid out in neat arches, or it can be twisted into a tight rope.

Physicists have achieved three-dimensional Anderson localization of electromagnetic waves — a phenomenon where waves become permanently entangled in a random labyrinth of metal particles and cease to propagate.

Two electrically charged spheres attract each other with a certain force. If you replace their charges with magnetic poles, a spring scale shows exactly the same force. Black holes, it turns out, behave the same way — except instead of springs, the fabric of spacetime itself does the work.

You can feel an unfamiliar object along its length, across its width, or diagonally: each time gaining new information. But what if one way of feeling tells you absolutely nothing about what another would reveal? That's exactly how mutually unbiased bases work in quantum mechanics: measuring in one of them leaves you completely in the dark about the outcome in another.

In 1867, James Clerk Maxwell proposed an image that still stirs physicists today. Two compartments of gas are separated by a door. Molecules dart about chaotically: fast and slow. A tiny gatekeeper opens the door only for fast ones, letting them through to one side, and slow ones to the other. The hot compartment gets hotter, the cold one colder.

Light isn't just straight rays; it's electromagnetic waves that can twist through space like a pair waltzing. Physicists call their total twist orbital angular momentum, and for a long time it was thought to obey the conservation law — a fundamental principle that follows from the symmetries of nature discovered by Emmy Noether.

Light, discovered by Maxwell, behaves differently in different media. In a new study, researchers simulated a two-dimensional crystal that absorbs light and has magnetic properties. In it, light waves behave like passengers on a one-way escalator: they relentlessly move toward edges and corners, where they accumulate.

Before measurement, a quantum object lives in a world of possibilities, where wave amplitudes add up like sound waves in a studio before pressing the “record” button. Crests amplify each other, troughs cancel out.

Toss a handful of sand on the floor: there are few large grains, many medium ones, and even more tiny ones. This skew, where small events are common and large ones are rare, is described by a power law. It shows up in city sizes, earthquake magnitudes, and citation counts of scientific papers.

Magnetic moments in a crystal are like compass needles fixed at lattice sites. In the normal state, they line up in neat order, but if an electromagnetic wave strikes the crystal, the needles start to sway, like wheat stalks in the wind. These oscillations are called magnons, and they carry energy without the atoms themselves moving.

In the 19th century, James Clerk Maxwell imagined a tiny demon. It knows the speed of every gas molecule and opens a door: fast ones to the left, slow ones to the right. This creates a temperature difference without expending energy, seemingly violating the laws of physics.