What lies beyond all we can see? The question may seem unanswerable. Nevertheless, some cosmologists have a response: Our universe is a swelling bubble. Outside it, more bubble universes exist, all immersed in an eternally expanding and energized sea—the multiverse. The idea is polarizing. Some physicists embrace the multiverse to explain why our bubble looks […]

Let’s just check this solution real quick. What about the units? On the left, tension is in units of Newtons. On the right side of the equation, F-pull is in Newtons and the denominator is unitless (mass divided by mass). So that’s good. What about limits? What if mass B is super tiny? As the […]

In 1987, a giant star exploded right next to our own Milky Way galaxy. It was the brightest and closest supernova since the invention of the telescope some four centuries earlier, and just about every observatory turned to take a look. Perhaps most excitingly, specialized observatories buried deep underground captured shy subatomic particles called neutrinos […]

I hope that you are never in a situation in which you are in danger from a downed, but live, power line. However, if that ever happens, the recommended safety procedure is to move away with tiny, shuffled steps. This type of movement will help prevent you from getting shocked. Of course the best option […]

Have you ever wondered what life would be like if Earth weren’t shaped like a sphere? We take for granted the smooth ride through the solar system and the seamless sunsets afforded by the planet’s rotational symmetry. A round Earth also makes it easy to figure out the fastest way to get from point A […]

This data looks nice and linear. That means that the inner and outer planets orbit at a constant rotational rate (which is expected). The angular velocity is defined as the change in angular position divided by a change in time—that means the slope of angle vs. time would actually be the angular velocity (we use […]

Maybe the question isn’t why the aggregates form in disease, but why they don’t form in healthy cells. “One of the things I often ask in group meetings is: Why is the cell not scrambled eggs?” Hyman said in his talk at the cell biology meeting; the protein content of the cytoplasm is “so concentrated […]

This acceleration is for any change in velocity. It doesn’t matter if the object is increasing or decreasing in speed—it’s still an acceleration. If you know the acceleration for something, you can find the stopping distance using the following kinematic equation (here is a derivation if you want it). Illustration: Rhett Allain In this expression, […]

Hints of additional mergers have been spotted in bundles of stars known as globular clusters. Diederik Kruijssen, an astronomer at Heidelberg University in Germany, used galaxy simulations to train a neural network to scrutinize globular clusters. He had it study their ages, makeup, and orbits. From that data, the neural network could reconstruct the collisions […]

Hints of additional mergers have been spotted in bundles of stars known as globular clusters. Diederik Kruijssen, an astronomer at Heidelberg University in Germany, used galaxy simulations to train a neural network to scrutinize globular clusters. He had it study their ages, makeup, and orbits. From that data, the neural network could reconstruct the collisions […]

Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to exactly half an acre? It sounds like high school geometry, but mathematicians and math enthusiasts have been […]

On December 3, humanity suddenly had information at its fingertips that people have wanted for, well, forever: the precise distances to the stars. “You type in the name of a star or its position, and in less than a second you will have the answer,” Barry Madore, a cosmologist at the University of Chicago and […]

People are often looking for interesting things to do at night. Well, here’s a secret—you just need to go outside and look up in the sky. Trust me, there are some super awesome things to see. Just put down your phone and look up. Here, I’ll go over all the best things to look at. […]

Programmers normally want to minimize the time their code takes to execute. But in 1962, the Hungarian mathematician Tibor Radó posed the opposite problem. He asked: How long can a simple computer program possibly run before it terminates? Radó nicknamed these maximally inefficient but still functional programs “busy beavers.” Original story reprinted with permission from […]

The torque in this case depends on three variables: the magnitude of the force (F), the distance between the force and the point about which you want to calculate the torque (often called the torque-arm, r) and the angle between the force and the torque-arm (θ). In the case above, the angle between the force […]

Ever since astronomers reached a consensus in the 1980s that most of the mass in the universe is invisible—that “dark matter” must glue galaxies together and gravitationally sculpt the cosmos as a whole—experimentalists have hunted for the nonluminous particles. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation […]

How big is a proton? That might sound like a pretty simple question, but it turned out to have the potential to wreck a lot of modern physics. That’s because different methods of measuring the proton’s charge radius produced results that disagreed—and not just by a little bit. The answers were four standard deviations apart. […]

At first, “everything seemed to work,” Jerolmack said. Domokos’ mathematics had predicted that rock shards should average out to cubes. An increasing number of actual rock shards seemed happy to comply. But Jerolmack soon realized that proving the theory would require confronting rule-breaking cases, too. After all, the same geometry offered a vocabulary to describe […]

Just to be clear, 106 means 10 x 10 x 10 x 10 x 10 x 10. But what if I want to do the inverse of 10 raised to some power? It’s much easier to write big numbers by raising them to some power—this is exactly what we do with numbers in scientific notation. […]

In a secluded laboratory buried under a mountain in Italy, physicists have re-created a nuclear reaction that happened between two and three minutes after the Big Bang. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research […]