There’s a new paper available on ArXiv, The Universe from Scratch, which provides a lay introduction to a new approach to quantum gravity, causal dynamic triangulations.
Category Archives: Physics
Div, Grad, Curl and All That
Cosmic Variance had three interesting &ldquot;greatest&rdquot; discussion threads:
In the comments to the Greatest Physics Textbook, Clifford (the original poster) joked that no self-respecting mathematician ever read Schey’s Div, Grad, Curl and All That. I don’t know about anyone else, but that’s the book I learned the subject from. The book gives incredibly hand-wavy proofs, and if I remember right it trumpets its lack of rigor, but it does a good job of giving the intuition behind the Green, Gauss, and Stokes theorems. Reading it made reading something like Spivak’s Calculus on Manifolds much easier.
Spirit Panorama
This is kinda off-topic for the site, but the Spirit rover on Mars has just crested a hill. NASA has put together a beautiful panoramic picture of the view from the top of the hill.
New Baez
John Baez has a new This Weeks Finds in Mathematical Physics up. He links to a reasonably elementary survey article about loop quantum gravity by Abhay Ashtekar, which I’m reading right now.
The bulk of his post is about operads, which aren’t something I know much about. They originally arose in algebraic topology, but have turned out to have applications in abstract algebra. Somehow there is a connection between a particular operad from algebraic topology (the little disks operad) and the deformation theory of associative algebras, but I’m murky on the details.
Dipole moment
Chad Orzel has posted two articles (This Magic Moment and When the Moment is Right) that outline how highly-precise measurements of the electric dipole moment of the electron can be used to test supersymmetry. The existing experiments already rule out the simplest supersymmetric models, and increasing precision in the experiments will allow more sophisticated models to be tested.
Via Not Even Wrong.
Exotic Probabilities
Saul Youssef has a collection of links to papers on exotic variations to probability theory. These are forms of probability theory that share many of the usual axioms of probability theory but in which the probabilities themselves lie in a set other than the non-negative reals eg. the complex numbers, the quaternions, or even the p-adics. The primary motivation is that classical mechanics plus complex probabilities looks a lot like quantum mechanics, and so if you believe in complex probabilities you no longer have to worry about things like wavefunction collapse. Unfortunately it’s all a bit confusing if you’re a frequentist.
AMS Summer Institute in Algebraic Geometry
AMS Summer Institute in Algebraic Geometry is underway in Seattle. It’s a mammoth three-week conference on algebraic geometry. The first week is dedicated to the unlikely connections that have emerged between algebraic geometry and string theory.
Smolin on Background Independence
Lee Smolin has posted a philosophical article on alternative approaches to quantum gravity: The case for background independence.
Two Cheers for String Theory
At the new group physics weblog Cosmic Variance, Sean Carroll has posted a defense of string theory, Two Cheers for String Theory. Chad Orzel and Peter Woit have also weighed in.
Igor Dolgachev
Igor Dolgachev, a mathematician at the University of Michigan, has made available lecture notes on topics in algebraic geometry and physics. The lecture notes in algebraic geometry include invariant theory and what he calls “classical algebraic geometry”. He also provides an introduction to theoretical physics for mathematicians, and as well as one on string theory.