Recommended paper of the day

Generalizing Quantum Mechanics for Quantum Spacetime, James B. Hartle

Not overly technical, and full of fascinating ideas and speculation. The table on page 7 is a neat summary of the relation between conceptions of spacetime and corresponding versions of quantum theory. Section 10 is a stunningly brief argument that from the "no boundary wave function of the universe" proposal of Hartle and Hawking it follows that spacetime must have signature (- + + +) instead of (- - + +) or (+ + + +). For non-physicist readers, this means that it explains why (assuming from start the world is 4 dimensional) there is one time dimension and 3 space dimensions instead of 2 and 2, or 0 and 4. Of course, the argument is based on the Hartle-Hawking proposal, which is not generally accepted and part of a speculative research program in quantum gravity. Still, interesting stuff!