curved space

In a mountain range, there are trails that can be contracted to a point if you walk through a flat valley. But there are also loop routes that cannot be shrunk without crossing a ridge.

When a fluid flows around an obstacle, it spawns vortices and shock waves. Describing their behavior means solving a nonlinear equation in which the flow velocity depends on itself. Classical supercomputers spend days on this, while quantum computers have barely been used: their native language is linear operations, but fluids are inherently nonlinear.

A thrown stone arcs through the air and falls. A planet orbiting a star is the same stone, but it falls forever, looping around the star in a closed curve. In Newton's world, that curve is a perfect ellipse, and the planet returns to the same point each orbit. In reality, the orbit slowly rotates: its closest point to the star, the perihelion, shifts.

In a two-dimensional universe, a black hole looks like a funnel in spacetime. But the authors of the new work went further: they proposed that the space where particle momenta 'live' is also curved, like a saddle.

Forget the flat sheet: embryonic tissue is a dynamic landscape of hills and folds. On convexities, cells stretch; in concavities, they compress, as if performing a dance governed by laws eerily similar to spacetime curvature.

Two light rays meet at a point and then diverge. Their paths form two intersecting surfaces in spacetime — null hypersurfaces (boundaries along which light propagates). It is on such a pair of surfaces that physicists can set initial data for Einstein's equations. This is called the characteristic Cauchy problem.

Two synchronized swimmers dive into the sea. One hits calm water, the other a whirlpool. Their movements, perfectly coordinated at the start, diverge. Something similar happens to two quantum particles when one moves in flat space and the other in curved space.

In the quantum world, there is its own dance. Two superconducting toroids, each comfortably holding its quantized magnetic flux, whirl in a synchronous waltz. Between them is a vacuum, not a single field line, yet they mirror each other’s moves without fail.

A translator who translates not words but the very structure of a conversation runs into trouble when the chat moves beyond a quiet room. In a familiar simulation on a spatial lattice, everything follows a strict script. But the moment the interlocutors find themselves in a noisy square, where sound is distorted by echoes and the crowd keeps changing direction, the script falls apart.

In the ocean, a whirlpool pulls everything into a closed loop, just as a gravitational wave in empty space twists time into a loop. Gravitational wave — a ripple in the fabric of spacetime, and its special shape can turn the usual flow of events into a closed cycle. In such a zone, an object can return to its own past without violating the laws of physics.

In mathematics there is a sieve that sifts not dust, but infinity itself. It’s called a Q-space: here any subset turns out to be a Gδ set — a countable intersection of open sets, as if sifted through an unimaginably fine mesh.

A builder checks the strength of an arch not by running through all possible shapes in their head, but by mentally nudging it and seeing how much force is expended. That's essentially how the principle of virtual work works in mechanics. The authors of a new study have applied this approach to the very geometry of spacetime. They constructed a covariant framework of virtual work for the metric.

Toss a handful of phosphorus into silicon, and at a certain impurity concentration the material suddenly starts conducting electricity. This is a metal-insulator phase transition, and it happens abruptly. But what exactly changes in the electron wave functions when an insulator becomes a metal?

Time is a fickle thing. Inside a massive star, it flows calmly, like sand in an old clock on a mantelpiece. Outside, on the scale of the entire universe, it stretches along with space, as if the same clock were in an elevator that speeds up and slows down. For a long time, physicists puzzled over whether these two worlds could be glued together without visible seams.

Usually, a wormhole is imagined as a tunnel in space, whose walls are held open by something unusual — matter with negative energy. Like the supports in a mine that keep the ceiling from collapsing. But in this work, the physicists did without supports.

Imagine a library where instead of books, you have every conceivable combination of a few dozen quantum particles. The number of combinations grows like a snowball: add one particle, and the volume doubles. For fifty particles, there are more shelves than atoms in the visible universe.

For nearly a century, astronomers have watched galaxies spin as if held together by invisible mass. Fritz Zwicky first noticed it, and Vera Rubin precisely measured the speeds of stars at the edges.

In the mid-20th century, Roger Penrose described a black hole using the concept of a “trapped surface” – a region where even a light ray directed outward inevitably falls inward. A situation familiar to everyone: water in a sink’s vortex is irretrievably sucked down the drain.

Sunlight hits a silicon wafer, and a current flows in the circuit. That's the familiar work of a solar cell: light knocks out electrons, and a p–n junction (the boundary between two layers with different conductivities) forces them to move in one direction. But in some crystals, current arises differently — without any junctions, purely from the material's internal structure.

Holography is the idea that everything happening inside a volume can be encoded on its boundary, like an image on a hologram. In physics, this helps connect gravity to the quantum world. But sometimes, the holographic rules fail to assemble familiar spacetime, and scientists are looking for where exactly the mechanism breaks down.

In a superconductor, electrons pair up like dancers holding hands. Usually, the distance between them, the pair size, depends on how fast they move and how strongly they are bound. But sometimes the dance floor almost disappears, and there's nowhere to move. This happens in materials with flat electronic bands: electrons nearly freeze, and the usual rules stop working.

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.

According to Einstein, spacetime is a flexible fabric, curved by matter. But in the quantum world, everything is different: particles are smeared over a probability cloud, governed by a rigid rule discovered by Max Born.

A laser beam holds a single ion in a vacuum, and that ion behaves like a ball trapped between two cups. The cups aren't pits in the ground but regions where the ion energetically prefers to be. In the classical world, a ball would roll into one cup and stay there.

Science is like a city where residents pave the streets themselves. Where paths are already worn, new houses go up, while untouched vacant lots go unnoticed — not because building there is impossible, but because no one ever looks.

Each qubit has its own little ring, freely sliding on the doughnut. All quantum logic boils down to smooth movements: shift, flip, connect. Entanglement, for example, is when two doughnuts stick together, and the rings on them begin to spin synchronously, like figure skaters in pairs skating. The key insight: the geometry of the surface dictates the rules of the game.

Two seemingly incompatible mathematical languages describe a single quantum reality. The first is the language of quantum walks: here, a particle (such as an electron or even a quasiparticle in a condensed medium) takes a stroll on a graph, simultaneously exploring all possible paths — much like a pedestrian in an unfamiliar city instantly finding…

An ordinary black hole is a trap from which nothing escapes. But a rotating black hole is structured differently: at its center is not a point, but a ring of infinitely compressed matter. Space here is curved to the limit, and light rays trace unimaginable loops.

Open systems exchange energy with their surroundings, like a guitar string fading into the air. Scientists built such a system out of light, twisting the beams into corkscrews and forming an artificial lattice — a maze where losses can be controlled at every step. Light in this maze always moves at the maximum possible speed, but its energy can fade or grow.

In 2019, the Event Horizon Telescope gave humanity the first image of a black hole's shadow. Since then, astrophysicists have dreamed of more: seeing how matter moves in the very funnel of spacetime. One of the mysteries is chaos.

An electron gliding over invisible hills and valleys created by a spin texture: that is the picture behind a new chapter in condensed matter physics. In quantum materials where the direction of localized spins varies smoothly (a spin texture), an electron is no longer just a particle flying through the lattice.