# Geometry and the Quantum

**Authors:** Alain Connes  
**arXiv:** [1703.02470](https://arxiv.org/abs/1703.02470)  
**Date:** 2017-03-07  
**Summary page:** https://www.summarizepaper.com/en/paper/1703.02470v1/

## Key points

- Alain Connes and collaborators have explored how geometry emerges from quantum formalism
- They discovered a slightly noncommutative structure and a novel spectral model of gravity coupled with matter
- The theoretical framework aligns well with experimental observations
- Their findings offer a new perspective on the interplay between quantum mechanics and gravitational phenomena
- Featured in the upcoming volume "Foundations of Mathematics and Physics one century after Hilbert" edited by Joseph Kouneiher, published by Springer in 2017
- Highlights the ongoing relevance of foundational questions in mathematics and physics
- Shows the enduring impact of Hilbert's work on shaping our understanding of fundamental principles governing the universe
- Bridging concepts from quantum theory and geometry offers fresh insights into spacetime nature and interactions with matter, paving the way for further advancements in theoretical physics

## Summary

Alain Connes and his collaborators Ali Chamseddine, Slava Mukhanov, and Walter van Suijlekom have delved into the intriguing question of how geometry emerges from the quantum formalism. Through their collaborative efforts, they have discovered a slightly noncommutative structure and a novel spectral model of gravity coupled with matter. This theoretical framework has been shown to align well with experimental observations and offers a promising new perspective on the interplay between quantum mechanics and gravitational phenomena. Their groundbreaking findings will be featured in an upcoming volume titled "Foundations of Mathematics and Physics one century after Hilbert," edited by Joseph Kouneiher and published by Springer in 2017. This contribution highlights the ongoing relevance of foundational questions in mathematics and physics, showcasing the enduring impact of Hilbert's work in shaping our understanding of the fundamental principles governing the universe. By bridging concepts from quantum theory and geometry, Connes and his team offer fresh insights into the nature of spacetime and its interactions with matter, paving the way for further advancements in theoretical physics.