3 Links: Math and Physics

[UPDATE 13 October 2009: Edited for typos and clarity]

First, since I’m on the record as a skeptic regarding the existence of actual or concrete infinities, I’m on the lookout for discussion of this topic. Here’s a talk given by mathematician Edward Nelson (hat tip: Not Even Wrong). In it, he expresses deep skepticism not only (in passing) regarding the idea of an actual physical infinity, but also (very controversially) on the concept as used in mathematics itself. I wouldn’t think skepticism about the former need have anything to do with the latter (and I’m certainly no mathematician), but I thought this was interesting reading.

Second, I enjoyed reading this (lengthy) overview of quantum gravity research by R.P.Woodard. The main focus of the paper is a “pedagogical explanation” of just why the techniques used in creating quantum versions of classical theories didn’t work when it came to general relativity (I thought this was helpful even if one can't follow all the formalisms). There is also a short section on the state of current research. Woodard makes this comment in the section discussing Causal Dynamical Triangulations (p.67): “…exact calculations are unlikely to be unattainable for quantum gravity, so the most fruitful way of questioning perturbation theory [i.e. the QFT method which is also the basis of original string theory – Steve] is to develop better approximation techniques.” The idea of finding a theory of everything (TOE) which consists of a set of equations with exact solutions looks like it is not going to happen. Finding a well-motivated approximate description of the ultra-high energy regime from which GR and QFT matter fields co-emerge at lower energies is probably the way things will go (I fearlessly predict).

Lastly, here’s a link which is just plain cool. Experimental physicists have been trying to place larger and larger molecules in quantum superposition: here’s a proposal for designing an experiment which could achieve this for a virus. Hat tip goes to the Physics and Cake blog.