Manifolds are spaces that look Euclidean when you zoom in on any one of their points. Introduced by Bernhard Riemann, they have become a mathematical staple in fields like geometry, physics, and data analysis.
The theoretical physicist and best-selling author finds inspiration in politics and philosophy for rethinking space and time.
Carlo Rovelli's work focuses on reconciling general relativity and quantum mechanics through **Loop Quantum Gravity (LQG)**, which proposes that spacetime is discrete and emerges from interactions, not as a pre-existing background. He also advocates for **Relational Quantum Mechanics**, asserting reality is defined by interactions and perspective – there is no objective, observer-independent reality. A key idea is that **time is not fundamental** but an emergent property linked to entropy. While promising, LQG faces challenges in making testable predictions.
Essentially, Rovelli argues for a shift from seeking absolute truths to understanding a relational, perspective-dependent universe.
Carlo Rovelli's work focuses on reconciling general relativity and quantum mechanics through **Loop Quantum Gravity (LQG)**, which proposes that spacetime is discrete and emerges from interactions, not as a pre-existing background. He also advocates for **Relational Quantum Mechanics**, asserting reality is defined by interactions and perspective – there is no objective, observer-independent reality. A key idea is that **time is not fundamental** but an emergent property linked to entropy. While promising, LQG faces challenges in making testable predictions.
Essentially, Rovelli argues for a shift from seeking absolute truths to understanding a relational, perspective-dependent universe.
This paper presents a model where gravity, through its fundamental unification with matter, explains the collapse of the wavefunction. The model is local, parameter-free, and makes testable predictions, proposing that the time evolution of quantum states deviates from the Schrödinger equation due to gravitational effects, leading to a natural explanation for why macroscopic superpositions do not occur.
This article is a survey of the history and ideas of gauge theory. It discusses the emergence of symmetry, Noether’s theorem, the gauge principle, and the role of gauge fields in mediating interactions. It also examines the electromagnetic field and generalizations to non-Abelian gauge theories, concluding with a look at the dream of total unification.
For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors.
A new method could change that.
Recent research has made a significant mathematical advance in understanding Anderson localization, the phenomenon where disorder in a material (like impurities in silicon) can stop electron flow. Researchers proved that, for a simplified model called band matrices, electrons do become trapped ("localized") with enough disorder. This breakthrough, achieved by Yan Yau and Jun Yin’s team, uses a new mathematical technique and brings us closer to fully understanding Anderson’s original model and designing materials with specific electronic properties. It’s a key step in understanding systems between order and randomness.
A new method could change that.
Recent research has made a significant mathematical advance in understanding Anderson localization, the phenomenon where disorder in a material (like impurities in silicon) can stop electron flow. Researchers proved that, for a simplified model called band matrices, electrons do become trapped ("localized") with enough disorder. This breakthrough, achieved by Yan Yau and Jun Yin’s team, uses a new mathematical technique and brings us closer to fully understanding Anderson’s original model and designing materials with specific electronic properties. It’s a key step in understanding systems between order and randomness.
This blog post details the implementation of a 'Particle Life' simulation using WebGPU. It covers the model's mechanics, the rationale for using WebGPU, the simulation loop, force computation techniques (including parallel prefix sum), rendering details, and provides a link to an interactive demo.
Recent findings using AI reveal that Sagittarius A*, the supermassive black hole at the center of the Milky Way, is rotating at near-maximum velocity with its rotation axis pointed directly toward Earth. This discovery, made possible by advanced neural networks and Bayesian statistical approaches, challenges established black hole theories and offers new insights into galactic formation.
This article explores gamma spectroscopy using a Radiacode 103G detector and Python, detailing data collection, analysis, and experiments with various objects to identify radioactive elements.
The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore.
The article details the recent proof of the geometric Langlands conjecture, a significant advancement in mathematics that validates a decades-old program aiming for a "grand unified theory" of the field. Led by Dennis Gaitsgory and Sam Raskin, the proof—spanning five papers and nearly 1,000 pages—is expected to open new avenues of research and potentially bridge connections between mathematics and theoretical physics, particularly in understanding symmetries in quantum field theory. While not a complete solution to the broader Langlands program, it provides strong evidence for its underlying principles and offers new tools for tackling complex mathematical problems.
The article details the recent proof of the geometric Langlands conjecture, a significant advancement in mathematics that validates a decades-old program aiming for a "grand unified theory" of the field. Led by Dennis Gaitsgory and Sam Raskin, the proof—spanning five papers and nearly 1,000 pages—is expected to open new avenues of research and potentially bridge connections between mathematics and theoretical physics, particularly in understanding symmetries in quantum field theory. While not a complete solution to the broader Langlands program, it provides strong evidence for its underlying principles and offers new tools for tackling complex mathematical problems.
An advanced particle life simulation, fine-tuned for maximum complexity and emergence of simulated organisms. It's a GPU-accelerated simulation where life-like behaviors emerge from raw physics, without hardcoded cells or genetic logic.
