differential geometry

cosmology / Discrete Math / Geometry / etc.

Quantum Geometry: Causal Dynamical Triangulations

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An example causal triangulation

A “quantum gravity expert” is presumably someone well acquainted with the details of our immense ignorance of the subject. I suppose I count. ~John Baez I long ago promised that I would discuss some of my own research. Here’s the first post that makes good on that promise. Today I’ll discuss a theory of quantum gravity. Why Quantum Gravity? Without a doubt, the two greatest advances in physics in the last 120 years were the advent of general relativity and quantum mechanics. These two amazing theories have totally changed the way we see the world. Quantum mechanics describes the

cosmology / Geometry / Mathematics / etc.

For There We Are Captured—The Geometry of Spacetime

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All about me there are angles— strange angles that have no counterparts on the earth. I am desperately afraid. ~Frank Belknap Long, The Hounds of Tindalos Whoever…proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured. ~Albrecht Durer I was recently asked: What does it mean when we say spacetime is “curved” or “flat?” The answer lies in the interface between differential geometry and physics. This is the latest in many articles I’ve written on Einstein’s relativity, so you might want to check out my series on faster-than-light