Lifeboat Foundation

A novel mathematical technique from the University of Surrey now simplifies space mission planning by mapping efficient routes, akin to a subway map, potentially revolutionizing travel to the Moon and beyond.

Just as sat-nav did away with the need to argue over the best route home, scientists from the University of Surrey have developed a new method to find the optimal routes for future space missions without the need to waste fuel.

The new method uses mathematics to reveal all possible routes from one orbit to another without guesswork or using enormous computer power.

Researchers have successfully used 40-year-old mathematics to explain quantum tunneling, providing a unified approach to diverse quantum phenomena.

Quantum mechanical effects such as radioactive decay, or more generally: ‘tunneling’, display intriguing mathematical patterns. Two researchers at the University of Amsterdam now show that a 40-year-old mathematical discovery can be used to fully encode and understand this structure.

Quantum Physics – Easy and Hard.

Quantum mechanics, the most potent theory physicists have developed, doesn’t make sense. What I mean by that statement is that quantum mechanics — which was developed to describe the microworld of molecules, atoms, and subatomic particles — leaves its users without a common-sense picture of what it describes. Full of what seem to be paradoxes and puzzles, quantum physics demands, for most scientists, an interpretation: a way of making sense of its mathematical formalism in terms of a concrete description of what exists in the world and how we interact with it. Unfortunately, after a century not one but a basketful of “quantum interpretations” have been proposed. Which one is correct? Which one most clearly understands what quantum physics has been trying to tell us these past 100 years?

In light of these questions, I’m beginning a series that explores the most radical of all the quantum interpretations, the one I think gets it right, or at least is pointed in the right direction. It is a relative newcomer to the scene, so you may not have heard of it. But it has been gaining a lot of attention recently because it doesn’t just ask us to reimagine how we view the science of atoms; it asks us to reimagine the process of science itself.

The term “QBism” was shorthand for “Quantum Bayesianism” when this idea/theory/interpretation was first proposed in the late 1990s and early 2000s. The name hit the nail on the head because “Bayesianism” is a radical way of interpreting probabilities. The Bayesianist approach to what we mean by probability differs strongly from what you learned in school about coin flips and dice rolls and how frequently a particular result can be expected to appear. Since probabilities lie at the heart of quantum mechanics, QBism zeroed in on a key aspect of quantum formalism — one that other interpretations had missed or swept under the rug — because it focused squarely on how we interpret probabilities. We’re going to dig deep into all of this as we go along in this series, but since today’s column is supposed to be the introduction, let’s start with a 10,000-foot view of what’s at stake in the great “Quantum Interpretation Wars” so we can see where QBism fits in.

Now Princeton researchers have sparked new life into static. Using millions of hours of computational time to run detailed simulations, the researchers found a way to describe static charge atom-by-atom with the mathematics of heat and work. Their paper appeared in Nature Communications on March 23.

The study looked specifically at how charge moves between materials that do not allow the free flow of electrons, called insulating materials, such as vinyl and acrylic. The researchers said there is no established view on what mechanisms drive these jolts, despite the ubiquity of static: the crackle and pop of clothes pulled from a dryer, packing peanuts that cling to a box.

“We know it’s not electrons,” said Mike Webb, assistant professor of chemical and biological engineering, who led the study. “What is it?”

Theoretical physicists employ their imaginations and their deep understanding of mathematics to decipher the underlying laws of the universe that govern particles, forces and everything in between. More and more often, theorists are doing that work with the help of machine learning.

As might be expected, the group of theorists using machine learning includes people classified as “computational” theorists. But it also includes “formal” theorists, the people interested in the self-consistency of theoretical frameworks, like string theory or quantum gravity. And it includes “phenomenologists,” the theorists who sit next to experimentalists, hypothesizing about new particles or interactions that could be tested by experiments; analyzing the data the experiments collect; and using results to construct new models and dream up how to test them experimentally.

In all areas of theory, machine-learning algorithms are speeding up processes, performing previously impossible calculations, and even causing theorists to rethink the way theoretical physics research is done.

Black holes, white holes, wormholes, anti-universes, and all kinds of awesome relativity weirdness:

Einstein was wrong about black holes, what else? Use code veritasium at the link below to get an exclusive 60% off an annual Incogni plan: https://incogni.com/veritasium.

Continue reading “Something Strange Happens When You Follow Einstein’s Math” »

1/ Researchers have found that AI models can solve complex tasks like “3SUM” by using simple dots like “…” instead of sentences.

Researchers have found that specifically trained LLMs can solve complex problems just as well using dots like “…” instead of full sentences. This could make it harder to control what’s happening in these models.

The researchers trained Llama language models to solve a difficult math problem called “3SUM”, where the model has to find three numbers that add up to zero.

Continue reading “Meaningless fillers enable complex thinking in large language models” »

Dive into RNNs, the backbone of time series, understand their mathematics, implement them from scratch, and explore their applications.

Generally, it’s advised not to compare apples to oranges. However, in the field of topology, a branch of mathematics, this comparison is necessary. Apples and oranges, it turns out, are said to be topologically the same since they both lack a hole – in contrast to doughnuts or coffee cups, for instance, which both have one (the handle in the case of the cup) and, hence, are topologically equal.

In a more abstract way, quantum systems in physics can also have a specific apple or doughnut topology, which manifests itself in the energy states and motion of particles. Researchers are very interested in such systems as their topology makes them robust against disorder and other disturbing influences, which are always present in natural physical systems.

Things get particularly interesting if, in addition, the particles in such a system interact, meaning that they attract or repel each other, like electrons in solids. Studying topology and interactions together in solids, however, is extremely difficult. A team of researchers at ETH led by Tilman Esslinger has now managed to detect topological effects in an artificial solid, in which the interactions can be switched on or off using magnetic fields. Their results, which have just been published in the scientific journal Science, could be used in quantum technologies in the future.