Witten's positive energy theorem

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.

A spotlight beam fades into the darkness, but if you trace it backward, you hit the lamp. The history of the universe might be the same: tracing its expansion backward, we run into a beginning. Physicists took the simplest model — a universe that stretches equally in all directions, like a cube with all sides growing.

The cosmological standard model is like a recipe for a cake where everything is strictly measured: dark matter is like flour without a single lump (zero pressure), and dark energy is like the perfect leavening agent (equation of state exactly minus one). But what if the flour is a bit damp and the leavening agent has lost its oomph?

A black hole is like a perfect safe: everything that falls in disappears without a trace. But quantum mechanics whispers that on the microscopic level, information is not lost but recorded on an invisible "surface." Understanding this record means unraveling the fabric of gravity.

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.

An engineering blueprint of a skyscraper always includes a number: the maximum load on the foundation — say, 500 kilopascals. Einstein's field equations in curved spacetime impose a similar limit on the 'force load' inside stars, planets, and any other clumps of matter.

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 world around us is three-dimensional, but perhaps that's just an illusion. Some theories allow for extra dimensions of space, curled up or stretched in special ways. One such model depicts a five-dimensional universe with a "diluted" dimension (called a linear dilaton).

The universe is a grand orchestra, with dark energy conducting the expansion. Ten billion years ago, the conductor changed its gesture: the negative pressure that had been holding back galaxy assembly gave way to accelerating expansion — the very phenomenon discovered by [scientist:Saul…

In the ordinary world without dark energy, the mass of any object is always positive. That seems obvious: positive mass attracts, creating gravity. But the real universe has dark energy — a mysterious force making the cosmos expand faster and faster.

In the infinite river of integers, where whirlpools of primes swirl, mathematicians have been sifting sand for centuries in search of golden nuggets — the zeros of L‑functions. These enigmatic objects, discovered by Riemann in 1859, act like an invisible hand governing the distribution of primes.

The explosion of a distant supernova told us something hard to believe: the universe is expanding faster and faster. The engine of this acceleration is dark energy — nearly 70% of everything that exists.

The void is never truly empty. In curved spacetime (for instance, in an expanding universe or near a black hole) the vacuum heats up. This is reminiscent of how acceleration makes particles appear seemingly out of nowhere: a phenomenon known as thermal vacuum radiation.

Light passing near a massive body slightly changes its path — gravity pulls even on rays. In ordinary situations, a beam of light from a distant star is squeezed as if drawn together by an invisible rubber band. This property is called the null convergence condition: gravity makes light trajectories converge rather than diverge.

At the heart of a warp drive lies Einstein's idea that massive bodies curve spacetime — the very stage on which all cosmic events unfold. Picture a bubble of such curved spacetime. Inside it, the ship floats without any G-forces, like a passenger in an airplane cabin who doesn't feel the headwind.

An empty glass on the table seems reliable. But if there's a microcrack in the bottom, one day it will break — not with a crash, but quietly, spreading in a web of lines. So too with the vacuum: it may not be the true vacuum but a false one — temporarily stable, yet ready to transition to a deeper, real state.

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.

The universe is expanding faster and faster thanks to dark energy. But measurements of the rate give contradictory results. A new explanation: in the past, dark energy acted as a brake, slowing the galaxies' recession, and then switched to acceleration. Like a car that first rolls backward and then lunges forward.

A neutron star is the leftover core of an exploded giant, compressed to the size of a city. A teaspoon of its matter weighs a billion tons. Inside such a star, particles are packed so tightly that quantum effects start to show. One of them is the intrinsic rotation of particles, or spin.

Time in physics is like a conductor setting the tempo for the whole orchestra. But in the quantum world, there's no single baton: each particle can live by its own clock. Usually, we simplify the picture and assume time flows the same for everyone.

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.

An ordinary black hole is like a stove that heats up more as its mass shrinks. A tiny hole should glow at unimaginable temperatures and evaporate in an instant. But that scenario ignores quantum corrections — what happens when the very fabric of spacetime begins to tremble.

A black hole is like a bottomless well. You can measure how much water has flowed into it by watching the level from outside. But how do you find the mass of the water itself if you're standing inside the well? That's roughly the problem the authors of a new paper tackle.

A lump of dark matter drifts through the void — invisible, almost intangible. No one knows what it's made of, but a new study suggests viewing it as a drop of quantum liquid. Two kinds of fermion particles — call them "heavy" (ψ) and "light" (χ)—exchange signals via a third mediator particle (φ), like floats tied to a single line.

A taut sheet wrinkles. If you tug a corner, a smooth wave runs across; if you sharply bunch the fabric, a sharp crease forms. Space and time in Einstein's equations behave much the same way. Gravitational waves resemble the gentle ripples of the sheet, while shock fronts are like stiff folds where matter's properties change abruptly.

A heavy ball rests on a trampoline, and the fabric sags beneath it. Any rolling ball nearby inevitably rolls toward the center. This is roughly how gravity works on the scale of the entire Universe. But what if the fabric were arched upward, like a dome? Then the ball would tend to roll outward.

Imagine a giant orchestra where every musician is a particle born in the fire of the Big Bang. When time's baton gives the downbeat, these particles begin to decay into lighter ones. Each decay is accompanied by a quiet chord — the emission of gravitons, tiny quanta of gravity.

Back in the 1930s, Fritz Zwicky noticed that the speeds of galaxies in clusters were too high for the visible mass. Later, Vera Rubin confirmed this for individual galaxies.

Since time immemorial, physicists have dreamed of tunnels piercing the cosmos — wormholes, capable of connecting far-flung corners of the Universe in an instant.

When two dead stars collide in a distant galaxy, two messengers bring us the news: a shiver in space, a gravitational wave, and a flash of light. Both messengers race toward us across the entire Universe, but their paths can differ slightly. Light sometimes gets delayed by cosmic dust, while gravitational waves pass through everything almost without noticing obstacles.

A mathematical doughnut, a torus, sits on the boundary of a three-dimensional world where gravity acts. You can crumple and stretch it, and physicists decided to see how it behaves. Inside this world, space can be flat like a table, expanding like a soap bubble, or curved like a saddle. The doughnut boundary refused to stay smooth.

In physics, there's an old ache. General relativity paints the beginning of the universe as a point — a singularity where equations break down and volume shrinks to zero. Quantum mechanics hints that at the most critical moment, something goes differently than classical physics predicts.

The idea of inflation, the superfast expansion of space just after its birth, was proposed by Alan Guth in 1980. It explained why our world is so uniform. But fresh snapshots of the Big Bang from the ACT telescope showed a pattern that slightly didn't match the predictions of two leading models.

In 2015, the LIGO detectors caught the first burst of gravitational waves — astronomers heard two black holes colliding far out in space. That ripple in spacetime reached us with its signal shape intact: like the sound of a bell traveling billions of years without distortion.

A handful of rice grains falls onto a hot skillet, and they start jumping. Each grain pushes its neighbors, and the whole pile stirs without any external hand. That's active matter: a multitude of particles that draw energy on their own and convert it into motion.

The void is not as empty as it seems. In the quantum world, even in a perfect vacuum, pairs of particles constantly pop in and out of existence, like ripples on a pond's surface, invisible to the eye but measurable. If you place a thin partition in this ripple, it alters the wave pattern.

A drop of cream falls into a cup of coffee, and within a minute, the entire drink turns beige. This mixing process can be quantified: how much "stirring" is needed to transform one distribution of particles into another? In mathematics, this approach is called optimal transport, and the measure of effort is the Wasserstein distance. The authors applied this idea to quantum systems.

On the table sits a sensitive instrument — a torsion balance. Two heavy masses rotate near a suspended rod, and their attraction tends to twist the rod. But the masses are arranged so that their ordinary Newtonian attraction cancels out: one pulls one way, the other the opposite. Only a weak residual remains, which the instrument captures.

A crowd of people moves freely across a square, but suddenly freezes in place without changing their positions. Everyone stays where they were, but motion stops. This is exactly what a symmetric mass generation transition looks like: the system gains rigidity, yet its symmetry remains untouched.

A black hole shrouded in dark matter is like a whirlpool in invisible water. This substance reveals itself only through gravity.