Quantum Latin squares were quickly adopted by a community of theoretical physicists and mathematicians interested in their unusual properties. Last year, the French mathematical physicists Ion Nechita and Jordi Pillet created a quantum version of Sudoku—SudoQ. Instead of using the integers 0 through 9, in SudoQ the rows, columns, and subsquares each have nine perpendicular […]

So what if, instead of launching atop a chemical rocket, your object could just ride up on a cable that reaches all the way into space? That’s what would happen with a space elevator. Space Elevator Basics Suppose you built a giant tower that is 400 kilometers tall. You could ride an elevator up to […]

Fluids can be roughly divided into two categories: regular ones and weird ones. Regular ones, like water and alcohol, act more or less as expected when pumped through pipes or stirred with a spoon. Lurking among the weird ones—which include substances such as paint, honey, mucus, blood, ketchup, and oobleck—are a vast variety of behavioral […]

So Dwyer and his team turned to the Low Frequency Array (LOFAR), a network of thousands of small radio telescopes mostly in the Netherlands. LOFAR usually gazes at distant galaxies and exploding stars. But according to Dwyer, “it just so happens to work really well for measuring lightning, too.” When thunderstorms roll overhead, there’s little […]

There’s actually another good reason to use infrared light for the JWST: It’s difficult to get an unobstructed view of far-away celestial objects thanks to the gas and dust that are the detritus from old stars. These can scatter visible light more easily than they can infrared wavelengths. Essentially, infrared sensors are able to see […]

I like to analyze the physics of science fiction, and so I’m going to argue that the Merrie Melodies cartoon “Compressed Hare” takes place in the far future when animals rule the world. I mean, Bugs Bunny and Wile E. Coyote walk on two legs, talk, and build stuff. How would that not be science […]

Thomas Gehrmann remembers the deluge of mathematical expressions that came cascading down his computer screen one day 20 years ago. He was trying to calculate the odds that three jets of elementary particles would erupt from two particles smashing together. It was the type of bread-and-butter calculation physicists often do to check whether their theories […]

Sometimes the universe is just too complicated to analyze. Heck, if you take a tennis ball and toss it across the room, even that is practically too complicated. After it leaves your hand, the ball has a gravitational interaction with the Earth, which makes it accelerate toward the ground. The ball is spinning as it […]

The universe started out quite smooth overall, the thinking goes, but quantum wiggles imprinted space with tiny dollops of extra matter. As space expanded, these dense spots stretched out even as the tiny ripples continued to arise. When inflation stopped, the young cosmos was left with dense spots ranging from small to large, which would […]

Think of this plot in terms of area. The area on the graph covered by the blue data (to hit the 2 ball) is much greater than the area on the graph showing the velocities required to hit the 3 ball. It’s getting much more difficult to achieve a collision that involves all four balls. […]

The first detection of gravitational waves in 2016 provided decisive confirmation of Einstein’s general theory of relativity. But another astounding prediction remains unconfirmed: According to general relativity, every gravitational wave should leave an indelible imprint on the structure of spacetime. It should permanently strain space, displacing the mirrors of a gravitational wave detector even after […]

In the PYP experiment, the machine learning algorithm was given data from multiple nearly-identical proteins that had been imaged in sequence. (Researchers couldn’t reuse the same protein, because they get damaged by the x-ray.) The AI extracted the details of the process without the blurriness of the x-ray flashes, and it uncovered what the blur […]

In 1993, deep underground at Los Alamos National Laboratory in New Mexico, a few flashes of light inside a bus-size tank of oil kicked off a detective story that is yet to reach its conclusion. The Liquid Scintillator Neutrino Detector (LSND) was searching for bursts of radiation created by neutrinos, the lightest and most elusive […]

This graph says that the vertical position of the rocket increases by a (nearly) constant amount from one frame to the next. In physics, we call that “constant velocity.” Since this is a plot of position vs. time, the slope of the line will be equal to this constant vertical velocity. From the graph above, […]

The time it takes for Drake to move in the vertical direction is the exact same time it takes for him to move horizontally. This means that I can use the horizontal motion to calculate the time, and then use that amount of time in the vertical motion to find his final vertical position. When […]

The flocking of birds can also be viewed as a breaking of symmetry: Instead of flying in random directions, they align like the spins in a magnet. But there is an important difference: A ferromagnetic phase transition is easily explained using statistical mechanics because it’s a system in equilibrium. But birds—and cells, bacteria and cars […]

Drop an ice cube into a glass of water. You can probably picture the way it starts to melt. You also know that no matter what shape it takes, you’ll never see it melt into something like a snowflake, composed everywhere of sharp edges and fine cusps. Mathematicians model this melting process with equations. The […]

Cranking the numbers gives me 1,394 nails—which is actually not that many. A 40-by-40 square grid is 1,600 nails, and that’s more than you need to prevent a skin puncture. So, what if you replace the nails with a bunch of broken glass? It’s really the same thing. Sure, glass might be sharper than nails, […]

Let’s face it: Nobody likes to travel. Whether they’re traveling to get to an exotic location for vacation or traveling to work on a daily commute, nobody actually likes the part where they have to travel. The people who say they like to travel probably mean they like to arrive. That’s because being somewhere can […]

In an increasingly data-driven world, mathematical tools known as wavelets have become an indispensable way to analyze and understand information. Many researchers receive their data in the form of continuous signals, meaning an unbroken stream of information evolving over time, such as a geophysicist listening to sound waves bouncing off of rock layers underground, or […]