quantum field theory in curved spacetime

Dancers on a stage with moving walls: particles in a finite quantum system collide with each other and reflect off the edges, but the walls can move according to a prescribed scenario. Physicists have long been able to describe such dances only with fixed walls or in an infinite hall. Now there is a way to account for both the motion of the walls and the reflections from them.

At the center of a neutron star, matter is compressed so tightly that a teaspoon weighs a billion tons. You'd think there's no better place to look for signs of quantum gravity. But between the laboratory and the fundamental scale lies a chasm of 10⁸⁰ in density. Three doors lead into this room.

A stone thrown at a wall bounces off. In the quantum world, a particle can pass right through, as if the wall were woven from mist. This is quantum tunneling: it lights up stars, works in microchips, and even operates in the cells of our bodies. But most particles have spin — an intrinsic rotation, like a spinning top.

Two observers, Alice and Bob, sit at opposite ends of the same lab. Between them is a source that fires off two pulses in turn. Each pulse gives birth to a wave packet flying toward its own detector. So far, this looks like an ordinary experiment with quantum particles.

In a pot of boiling water, steam bubbles appear and disappear — a similar struggle takes place in two-dimensional materials. Here, electrons both create magnetism and try to extinguish it.

A pot of boiling porridge: bubbles burst, steam escapes, and everything gets mixed up. Massive stars in giant gas clouds behave in much the same way. Their radiation and stellar winds blow out enormous cavities, molecular bubbles, scattering material all around.

The Standard Model of particle physics is a catalog of all known building blocks of the universe: electrons, quarks, and others. But it is silent about dark matter and doesn't get along with gravity.

Space is not a void but a mosaic of tiny cells. In loop quantum gravity, spacetime curvature is transferred from a smooth sheet to a network of 'atoms' of volume — spin networks. Each node of such a network is a quantum of space, and the links between them are quanta of area. But how does this mosaic change over time?

Usually, a black hole is described as a frozen frame: there's mass, there's charge, and it's all static. But real objects live in time. They radiate, lose energy, and change.

A quantum particle can be a wave, and pass through two paths at once. But if something 'peeks' at which path it took, the wave disappears. This effect is called loss of interference. Usually, photons or air molecules do the peeking.

A black hole's horizon is not a wall but rather a one-way membrane. Anything that crosses it disappears forever. Stephen Hawking showed that this boundary should glow faintly, emitting particles. But catching such radiation from a real black hole is impossible: it's too far and too dim. Physicists have found a workaround: build a "toy" black hole out of magnetic atoms.

A potter tries to measure the thickness of a jug's wall, but every time the gauge also reports the curvature of the vessel.

A light ray passing by a massive body gets deflected: this is the effect of gravitational lensing, familiar from images of distant galaxies. The astrophysicists started with a rotating black hole (Kerr spacetime) and added a tiny correction to how light itself propagates.

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.

According to Einstein's general theory of relativity Albert Einstein, a massive rotating body drags the fabric of spacetime along with it, much like a spoon twirled in a jar sets thick honey flowing.

The space we live in appears three-dimensional. But when physicists try to reconcile gravity with quantum mechanics, familiar dimensions start behaving strangely. In a new study, scientists showed that to describe a massive particle while accounting for quantum gravitational effects, it is natural to add two more dimensions.

Building a house on sand is a bad idea. In physics, it was long believed that a quantum theory of gravity could not be built on a fixed "sand"—a pre-existing spacetime.

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?

In the classical picture of the world, gravity is the smooth bending of space and time. But at the microscopic level, where quantum mechanics rules, these bends should turn into a grainy ripple. The particles of such a ripple are called gravitons. The trouble is that straightforward calculations with gravitons always run into infinities — the theory loses its meaning.

At the very beginning of the universe, when all of space was compressed into a point, the laws of physics break down. This point is called a singularity — an edge where our equations lose meaning. But what if it's not an end, but a special type of boundary? The authors of this work propose viewing the singularity as a free boundary.

Two black holes circle in a slow dance, gradually drawing closer. Their motion perturbs spacetime itself, like two heavy balls rolling on a stretched sheet, making it tremble. These tremors are what we call gravitational waves.

A black hole is not just a dark spot in space. It is a region where gravity compresses matter so intensely that even light cannot escape. Among all possible black holes, one stands out — the rotating Kerr black hole. Its description was long thought to be tied to Einstein's equations, like a recipe tied to a specific cookbook.

A billiard game would be strange if the balls had no mass. They wouldn't collide but would pass through each other, ignoring obstacles. That's roughly what it looks like to imagine light as a stream of classical particles — tiny elastic bodies flying in straight lines. A new proof puts an end to that picture.

Gravity seems simple: it keeps us on the ground and makes planets orbit. But if it were classical (described by Einstein's equations as the curvature of spacetime, while all matter follows the quantum laws of the Standard Model) then an ordinary quantum bit (qubit) falling freely…

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.

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.

The universe is not a solid monolith, but a canvas of countless quantum threads. Spacetime doesn't flow like water, but vibrates like a tapestry in the wind. For a long time, physicists only saw the overall pattern, neglecting the tremor of individual threads.

A black hole is not a frozen sphere. It's more like a soap bubble, whose walls can expand and contract. It even has two layers: the outer horizon, beyond which light cannot return, and the inner one, hidden deeper. When the hole swallows matter or loses energy, both layers shift, like the film of a bubble changing size.

If you check where an electron is every second, its quantum properties change. It's like a child playing hide-and-seek but constantly being called by name: they freeze and stop running. In the particle world, such a "caller" is a measurement. It prevents particles from freely forming a shared quantum state, or entanglement.

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.

A stone falls to the ground along the most economical route — the one that expends the least time and energy. This principle of least action governs all of classical physics. But in the microworld, everything jitters: fields fluctuate, and you can't say precisely where anything is.

Two balls suspended on threads swing side by side. Each moves on its own, but between them is an invisible thread — the attraction of masses. If gravity is quantum, it could bind them into a single whole: nudge one, and the other responds, even without contact.

A handful of sand lands on the table. The grains settle in different ways, but if the handful is large, the total volume barely changes. That's roughly how classical gravity works: space appears smooth and definite. But look closely at the individual grains, and you'll find that at the quantum level, volume itself is no longer fixed.

A tailor cuts a suit, but the seams pucker and the buttons won't align. In quantum field theory, similar glitches are called anomalies: they appear when a symmetry of the equations breaks down in the transition to a quantum description. Usually, they are fixed by sewing in extra patches, the so-called Bardeen–Wess–Zumino counterterms.

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.

If two people look at a city from different hills, their maps don't match. One sees the tower to the left of the river, the other sees it to the right. But both know: it's the same city. That's roughly how our Universe works in this new approach to quantum gravity. The authors suggest distinguishing between two "flavors" of spacetime.