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Category: mathematics

Physics of foam strangely resembles AI training

Foams are everywhere: soap suds, shaving cream, whipped toppings and food emulsions like mayonnaise. For decades, scientists believed that foams behave like glass, their microscopic components trapped in static, disordered configurations.

Now, engineers at the University of Pennsylvania have found that foams actually flow ceaselessly inside while holding their external shape. More strangely, from a mathematical perspective, this internal motion resembles the process of deep learning, the method typically used to train modern AI systems.

The discovery could hint that learning, in a broad mathematical sense, may be a common organizing principle across physical, biological and computational systems, and provide a conceptual foundation for future efforts to design adaptive materials. The insight could also shed new light on biological structures that continuously rearrange themselves, like the scaffolding in living cells.

These Brain-Inspired Computers Are Shockingly Good at Math

New research shows that advances in technology could help make future supercomputers far more energy efficient. Neuromorphic computers are modeled after the structure of the human brain, and researchers are finding that they can tackle difficult mathematical problems at the heart of many scientif

Scientists use string theory to crack the code of natural networks

For more than a century, scientists have wondered why physical structures like blood vessels, neurons, tree branches, and other biological networks look the way they do. The prevailing theory held that nature simply builds these systems as efficiently as possible, minimizing the amount of material needed. But in the past, when researchers tested these networks against traditional mathematical optimization theories, the predictions consistently fell short.

The problem, it turns out, was that scientists were thinking in one dimension when they should have been thinking in three. “We were treating these structures like wire diagrams,” Rensselaer Polytechnic Institute (RPI) physicist Xiangyi Meng, Ph.D., explains. “But they’re not thin wires, they’re three-dimensional physical objects with surfaces that must connect smoothly.”

This month, Meng and colleagues published a paper in the journal Nature showing that physical networks in living systems follow rules borrowed from an unlikely source: string theory, the exotic branch of physics that attempts to explain the fundamental structure of the universe.

Quantum mechanics works, but it doesn’t describe reality

Physicists like Sean Carroll propose not only that quantum mechanics is not only a valuable way of interpreting the world, but actually describes reality, and that the wave function – the centre equation of quantum mechanics – describes a real object.

But, in this article, philosophers Raoni Arroyo and Jonas R. Becker Arenhart argue that the case for wave function realism is deeply confused. While it is a useful component within quantum theory, this alone doesn’t justify treating it as literally real.

Tap the link to read more.

Physicists like Sean Carroll argue not only that quantum mechanics is not only a valuable way of interpreting the world, but actually describes reality, and that the central equation of quantum mechanics – the wave function – describes a real object in the world. But philosophers Raoni Arroyo and Jonas R. Becker Arenhart warn that the arguments for wave-function realism are deeply confused. At best, they show only that the wave function is a useful element inside the theoretical framework of quantum mechanics. But this goes no way whatsoever to showing that this framework should be interpreted as true or that its elements are real. The wavefunction realists are confusing two different levels of debate and lack any justification for their realism. The real question is: does a theory need to be true to be useful?

1. Wavefunction realism

Quantum mechanics is probably our most successful scientific theory. So, if one wants to know what the world is made of, or how the world looks at the fundamental level, one is well-advised to search for the answers in this theory. What does it say about these problems? Well, that is a difficult question, with no single answer. Many interpretative options arise, and one quickly ends up in a dispute about the pros and cons of the different views. Wavefunction realists attempt to overcome those difficulties by looking directly at the formalism of the theory: the theory is a description of the behavior of a mathematical entity, the wavefunction, so why not think that quantum mechanics is, fundamentally, about wavefunctions? The view that emerges is, as Alyssa Ney puts it, that.

Continue reading “Quantum mechanics works, but it doesn’t describe reality” | >

New framework unifies space and time in quantum systems

Quantum mechanics and relativity are the two pillars of modern physics. However, for over a century, their treatment of space and time has remained fundamentally disconnected. Relativity unifies space and time into a single fabric called spacetime, describing it seamlessly. In contrast, traditional quantum theory employs different languages: quantum states (density matrix) for spatial systems and quantum channels for temporal evolution.

A recent breakthrough by Assistant Professor Seok Hyung Lie from the Department of Physics at UNIST offers a way to describe quantum correlations across both space and time within a single, unified framework. Assistant Professor Lie is first author, with Professor James Fullwood from Hainan University serving as the corresponding author. Their collaboration creates new tools that could significantly impact future studies in quantum science and beyond. The study has been published in Physical Review Letters.

In this study, the team developed a new theoretical approach that treats the entire timeline as one quantum state. This concept introduces what they call the multipartite quantum states over time. In essence, it allows us to describe quantum processes at different points in time as parts of a single, larger quantum state. This means that both spatially separated systems and systems separated in time can be analyzed using the same mathematical language.

Mathematics uncovers shifting brain connectivity in autism and aging

It is a central question in neuroscience to understand how different regions of the brain interact, how strongly they “talk” to each other. Researchers from the Max Planck Institute for Mathematics in the Sciences Leipzig, Germany, the Institute of Mathematical Sciences in Chennai, India, and colleagues demonstrate how mathematical techniques from topological data analysis (TDA) can provide a new, multiscale perspective on brain connectivity. The study was published in the journal Patterns.

With the rise of large neuroimaging datasets, scientists now work with detailed maps of brain connectivity—network representations that show how hundreds of brain regions fluctuate and coordinate their activity over time. But making sense of these enormous networks poses a challenge: What patterns matter? Which changes signal healthy aging, and which reflect differences associated with autism spectrum disorder (ASD)?

The study introduces a mathematical innovation that helps answer precisely these questions. Researchers applied persistent homology, a tool from topological data analysis (TDA), to detect how brain connectivity reorganizes during healthy aging and in ASD.

Why imaginary numbers are central to quantum physics

One of the world’s foremost philosophers of physics, Maudlin is Professor of Philosophy at NYU and Founder and Director of the John Bell Institute for the Foundations of Physics.

He is a member of the “Foundational Questions Institute” of the Académie Internationale de Philosophie des Sciences and is the recipient of a Guggenheim Fellowship, and author of ‘The Metaphysics Within Physics’, ‘Truth and Paradox: Solving the Riddles’ and ‘Quantum Non-Locality and Relativity’

Tap the link to watch his full talk now: https://iai.tv/video/tim-maudlin-why-imaginary-numbers-are-c…um-physics

Why do imaginary numbers appear at the foundation of quantum mechanics? This question, which puzzled even great physicists like Eugene Wigner, opens up deeper issues about what it means to explain features of the mathematical formalism used in physical theory. Join philosopher of science Tim Maudlin as he explores that question through the lens of quantum dynamics, arguing that the appearance of complex numbers in Schrödinger’s equation is not arbitrary, but motivated by the need for a particular kind of wave-like structure in fundamental dynamics.

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