newtonian gravity

A thrown stone arcs through the air, but a planet around the Sun follows a closed curve. Why an ellipse, and not a circle or a spiral? Kepler's first law provides the answer, but its usual proof requires heavy computation. This work offers a shorter path — through a single simple ratio of velocities.

An interpreter gets distracted by every rustle in the hall, and a one-hour meeting stretches into two. A neutron star compresses a solar mass into a sphere the size of a city, and the matter in its core is denser than an atomic nucleus. Physicists cannot probe its structure in the lab: the required pressures are unattainable.

Newton gave us a world where bodies move in a void and clocks tick the same for everyone. For three centuries, this picture worked flawlessly. But it relies on many invisible props: absolute position, the 'up-down' direction, and a single rhythm of time for the entire universe. We have never measured these directly — only through the relations between objects.

Two massive bodies frozen in a quantum superposition resemble a pair of dancers trying to keep a single rhythm while an orchestra blares around them. Each gravitational wave is a musician throwing them off beat.

The Kerr-NUT black hole is not just a cosmic vacuum cleaner. It's a solution to Einstein's equations where the hole has mass, rotation, and a strange NUT parameter. This parameter behaves like a magnetic charge for gravity: seemingly invisible, yet it alters the properties of surrounding space.

The early Universe was like a tightly coiled spring. In the first moments, it expanded at an unimaginable rate — a phase called inflation. Usually, this is attributed to a special field, but there's another idea: spacetime itself twists like a spring, and this twisting (in physics, torsion) becomes the engine of expansion.

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.

10⁻¹²⁰. That's not just a small number: it's a chasm. That's the ratio of dark energy density to the Planck density, the natural scale of quantum gravity. The colossal difference of 120 orders of magnitude has long seemed an unsolvable puzzle. But the answer might lie in a drama played out at the dawn of time.

A lead sphere hangs above another lead sphere. According to the usual laws of gravitation, they attract each other exactly along the vertical — along the line connecting their centers.

Quantum chromodynamics is the theory that describes how quarks and gluons assemble into protons and neutrons. In its equations, there is a strange angle, the parameter θ (theta).

Photographing hummingbird wings with an ordinary camera gives a blurry smudge. For a sharp picture, you take many rapid shots from different angles and piece them together: that's how a quantum 'snapshot' is made. In the lab, scientists 'feel' the vibrations of a tiny mirror with a laser beam.

In the depths of a neutron star, the remnant of an exploded star, matter is compressed so tightly that a teaspoon would weigh billions of tons. Within this superdense material, a special kind of force might be at work, one that affects only muon and tau neutrinos.

When two neutron stars circle each other, they don't remain rigid spheres. The partner's gravity stretches each star, creating tidal bulges — much like the Moon raises ocean tides on Earth. But unlike water, here it's superdense matter that deforms: a teaspoon of this stuff weighs billions of tons.

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.

When two superdense stars circle in a tight dance, the space around them shudders. This shudder, gravitational waves, is caught by giant detectors on Earth. But deciphering the signal is tricky: you need to figure out what exactly you're dealing with — a pair of black holes or neutron stars.

Two floats on the waves. Throw a stone into water, and the ripples will spread, rocking both floats one after another — not simultaneously. In the quantum world, such rocking is called entanglement: particles, like floats, begin moving in sync.

The Sun is not just a source of light but a giant laboratory where ghostly particles are born. Every second, billions of neutrinos fly through your body, barely noticing you. But inside the Sun, these particles behave differently: they change their type on the fly, like an actor playing three roles in a single play.

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.

Two massive spheres slowly drift apart in empty space. From the standpoint of ordinary mechanics, nothing special is happening. But Einstein's equations say otherwise: accelerating masses stir spacetime itself, and from them spread gravitational waves — ripples that stretch and squeeze everything in their path.

Two pebbles drop into water, and the ripples on the surface intersect, blending their patterns. Neutrinos behave much the same way: light particles that pierce us by the billions every second. They can transform from one type to another, like an actor changing masks. Physicists call this dance oscillations.

Gravitational waves are not vibrations of matter, but tremors of spacetime itself, predicted by Albert Einstein. They travel at the speed of light and pass through objects, stretching and squeezing them.

Physicists have mastered an elegant mathematical trick that lets them translate gravitational equations into the language of electricity. This method — double copy — works like a kind of dictionary: it replaces the complex geometry of curved spacetime, described by high-dimensional tensor fields, with the simpler rules of…

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.

Stephen Hawking imagined that the universe was born not from an explosion, but by smoothly emerging from a quantum 'nothing.' In worlds with concave geometry (anti-de Sitter space), such a birth acquires a rim, like the hoop of a drum.

Quantum objects live in a world of superpositions — being here and there at the same time, with one spin and another. But as soon as they gain enough mass, this magic fades. Roger Penrose suggested that gravity itself is to blame.

A rubber band stretches and snaps back. A steel spring compresses and expands. Elasticity seems like a property of simple things — a piece of metal or a drop of gel. But the authors of this work looked deeper. They showed that the electron's spin, its own tiny rotation, can also be elastic.

The riddle of quantum gravity has troubled minds for nearly a century. A classical field that curves spacetime refuses to fit into the probabilistic world of superpositions. Can gravitation, while remaining macroscopic, give rise to microscopic entanglement?

Strike a bell, and it hums at a single pitch. But if you place a second clapper inside, and they ring without touching each other, the sound becomes more complex. That's roughly how the neutron star from the new study is built. It's not just a hot sphere: inside, two immiscible fluids can flow — for instance, superfluid neutrons and ordinary plasma.

Spacetime resembles a giant crystal. Gravitational waves, born from collisions of black holes, not only make it tremble — they leave indelible defects: edge ones, as if an extra plane of atoms was inserted into the crystal, and screw ones, where the layers twist.

A flashlight beam in a dark room can hold a dust mote almost still: that's how optical tweezers work. But light doesn't just push the particle; it also jostles it with random kicks. Each absorbed photon strikes it like an invisible hammer. The authors of the new study have devised a light trap of a special shape.

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 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 thrown stone arcs along a clean trajectory, but an electron's position in an atom is smeared out like fog. The transition from one to the other is a puzzle. New work shows that the fuzziness disappears not because of an observer, but because of the particle's own gravity.

A stone thrown into a pond creates ripples that spread far. But if you throw it into thick jelly, the waves die out almost immediately. That's roughly how an additional gravity field behaves under different mathematical descriptions. The authors built a unified approach to calculate how such a field manifests itself in the Solar System.

Take two heavy balls and place them a meter apart: they attract each other with a force that weakens by a factor of four when you double the distance. Newton discovered this law, and it works in a room, in the solar system, in a galaxy. But does it still hold when we're talking about hundreds of millions of light-years? Astronomers found a way to test this directly.

Previously, astronomers calculated galaxy mass as if they were perfect spheres. But a galaxy is a flat pancake. The new 'Lost and Found' model takes the actual shape into account: it sums up the gravitational pull from all parts of the disk, not just the central bulge. The result is stunning: many galaxies need a third less invisible dark matter than previously thought.

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.

The familiar picture: gravity always attracts. But if a mass is in quantum superposition (that is, in two places at once, like an object in a double-exposure photograph) everything flips. Quantum theory allows a particle to be both here and there in a literal sense: its position is described by a wave function smeared across space.

For a long time, physicists were certain: quantum entanglement requires direct quantum contact. A new study refutes this. Two microscopic magnetic particles, connected only by a classical spring, successfully become entangled.

A stone drops into a pond — ripples spread across the water. Do short waves outrun long ones? No, in deep water it's the opposite: long waves overtake short ones. In metal, sound of one pitch travels at one speed, another pitch at another.