People are social animals, and their relationships are complicated and change all the time. Several fields of study and theories have tried to figure out how these social networks work and how they change over time. The social balance theory was one of them. It was first put forward in the 1940s. Using statistical physics, researchers have now been able to prove it.

Just like the name says, social balance theory is based on the idea of balance. People in their networks want and try to keep relationships balanced. There should be rules to keep the system balanced. Relationships that are positive are balanced, but relationships that are negative or mixed are not. The classical model is based on the simple idea that relationships that are good are “friends” and relationships that are bad are “enemies.”

First, a friend of a friend is still a friend. Now, this is a made-up example, so don’t think right away of that friend of yours that you hate. Another rule says that a friend of an enemy is also an enemy, and of course, an enemy of a friend is also an enemy. We need to protect our friends. The last rule is a bit more subtle: a friend of an enemy is a friend of an enemy. It looks like the new analysis mostly meets this need, but the scientists had to add a lot of complexity before they could model it.

It’s finally possible to say that social networks match up with expectations that were set 80 years ago, said Bingjie Hao, the study’s lead author from Northwestern University. “Our results can also be used in many different ways in the future.” Because of how we do math, we can put limits on the connections and take into account what each entity in the system wants. That will help when making models of systems other than social networks.

Two things were very important to the new model: not everyone knows each other in real life, and some people are more positive than others. When you use both constraints, you get a social network that is exactly the same as the one Fritz Heider predicted 80 years ago.

“We always thought this social intuition worked, but we didn’t know why,” said István Kovács, who was the lead author of the study. “All that was left was to do the math.” There have been a lot of studies on this idea, but they don’t all point to the same conclusion. We kept getting it wrong for decades. It’s because real life is hard sometimes. We realized we had to deal with both problems at the same time: “who knows whom” and “some people are just friendlier than others.”

The study has been written up in the Science Advances journal.

Iron screws and other ferromagnetic materials consist of atoms with electrons that behave as miniature magnets. Typically, the magnets’ orientations are aligned within a specific region of the material, but they vary between different regions. Imagine groups of tourists in Times Square, eagerly gesturing towards the various billboards that surround them. However, with the application of a magnetic field, the spins of the magnets in the various regions align, resulting in the material becoming completely magnetized. It’s as if all the tourists suddenly synchronized their movements to point at the same sign.

The alignment of spins, however, does not occur instantaneously. Instead, when a magnetic field is present, neighboring regions, known as domains, interact with each other, causing changes to propagate unevenly throughout the material. Scientists often draw parallels between this phenomenon and the cascading of snow in an avalanche, where a single piece of snow initiates the movement, exerting force on neighboring pieces until the entire mountainside of snow is in motion, all heading in the same direction.

In 1919, Heinrich Barkhausen showcased the avalanche effect in magnets, providing a groundbreaking demonstration. Through the clever use of a coil and a magnetic material connected to a loudspeaker, it was demonstrated that these fluctuations in magnetism produce an audible crackling sound, now referred to as Barkhausen noise.

A recent study published in the journal Proceedings of the National Academy of Sciences reveals that Barkhausen noise can be generated not just by conventional methods but also by quantum mechanical phenomena.

Experimental detection of quantum Barkhausen noise is a groundbreaking achievement. This research signifies a significant breakthrough in the field of physics and holds potential for future applications in the development of quantum sensors and electronic devices.

“Barkhausen noise is the result of the small magnets flipping together,” explains Christopher Simon, the lead author of the paper and a postdoctoral scholar in the lab of Thomas F. Rosenbaum, a professor of physics at Caltech, the president of the Institute, and the Sonja and William Davidow Presidential Chair.

“We are conducting a familiar experiment, but with a twist—in a quantum material.” We are observing that quantum effects can result in significant changes at a macroscopic level.

Typically, magnetic flips occur in a classical manner, through thermal activation. In this process, particles must temporarily acquire sufficient energy to overcome an energy barrier. However, the new study reveals that these flips can also happen through a process called quantum tunneling, which operates on a quantum level.

In the phenomenon of tunneling, particles have the ability to traverse an energy barrier by seemingly bypassing it altogether. If this effect could be applied to everyday objects, such as golf balls, it would be as if the golf ball effortlessly passed through a hill instead of having to ascend it to reach the other side.

“In the quantum realm, the ball doesn’t need to traverse a hill as it transforms into a wave-like particle, with a portion already present beyond the hill,” explains Simon.

Furthermore, the latest research reveals a fascinating co-tunneling phenomenon, where clusters of tunneling electrons interact and coordinate to induce simultaneous flips in the direction of their spins.

“Traditionally, every individual mini avalanche, where clusters of spins flip, would occur independently,” explains co-author Daniel Silevitch, a research professor of physics at Caltech. “However, it has been discovered that, by means of quantum tunneling, two avalanches occur simultaneously.” This phenomenon arises from the interaction between two extensive collections of electrons, which communicate with each other and, as a consequence of their interactions, bring about these alterations. This unexpected co-tunneling effect quite surprised me.

Members of the team utilized a pink crystalline material known as lithium holmium yttrium fluoride, which was cooled to temperatures close to absolute zero (-273.15°C) for their experiments. They placed a coil around it, applied a magnetic field, and then observed small changes in voltage, similar to Barkhausen’s experiment in 1919.

The voltage spikes that are observed indicate the moments when clusters of electron spins change their magnetic orientations. When the groups of spins flip, one after the other, we can observe a series of voltage spikes known as the Barkhausen noise.

Through careful analysis of the noise, the researchers demonstrated the occurrence of a magnetic avalanche, even in the absence of classical effects. They demonstrated that these effects remained unaffected by variations in the material’s temperature. Through careful analysis, they reached the conclusion that quantum effects were the underlying cause of the significant transformations.

Scientists have found that these regions can hold an astonishing number of spins, far more than the rest of the crystal.

“We are observing this quantum behavior in materials containing an incredibly large number of spins.” Ensemblies of microscopic objects are all behaving in a coherent manner,” Rosenbaum says. “This work exemplifies the core focus of our lab: isolating and comprehending quantum mechanical effects.”

Researchers in Rosenbaum’s lab recently published another paper in PNAS that examines the fascinating connection between minute quantum effects and their influence on larger-scale phenomena. In the earlier study, scientists looked at the element chromium and showed how two different types of charge modulation—one involving ions and the other involving electrons—interact with each other at different length scales using quantum mechanics.

“Chromium has been a subject of study for quite some time,” remarks Rosenbaum, “yet only recently have we come to fully grasp this particular facet of quantum mechanics.” This is yet another instance of designing uncomplicated systems to uncover quantum phenomena that can be observed on a larger scale.

Elon Musk announced in a tweet that Tesla is opening up its so-called full self-driving (FSD) beta to anyone who has paid for it after gradually opening it up over the past few years. In North America, he added, “Tesla Full Self-Driving Beta is now available to anyone who requests it from the car screen, assuming you have purchased this option.”

With automated features like automated city steering, automatic parking, smart vehicle summoning, and traffic light/stop sign recognition, FSD builds on Tesla’s “Autopilot” driver-assist feature. The feature is a paid upgrade that costs $15,000 after a $3,000 price increase in September.

Tesla Full Self-Driving Beta is now available to anyone in North America who requests it from the car screen, assuming you have bought this option.

Congrats to Tesla Autopilot/AI team on achieving a major milestone!

— Elon Musk (@elonmusk) November 24, 2022

Tesla initially stated that it would introduce fully autonomous driving features in 2018, but they didn’t actually do so until July 2021, to a select group of “careful and expert drivers.” The version 9.0 beta saw a wider release, but testers could only participate in an early access program. Tesla removed the requirements for at least 100 Autopilot miles and an 80 safety score on the most recent FSD release, so now anyone can get it.

However, Tesla is widely implementing FSD at a time when regulators are closely monitoring it. In a recent expansion of its investigation into a string of Tesla crashes involving first responders, the National Highway Traffic Safety Administration (NHTSA) is now looking at most models. It is also looking into more than 30 incidents involving Autopilot in a separate investigation.

Musk has long promised fully autonomous vehicles without a human driver. Most recently, he said he believed it might come this year, but in Tesla’s most recent earnings report, he backtracked on those statements. Following Elon Musk’s $44 billion acquisition of Twitter, the price of Tesla’s stock has been falling precipitously recently.