Reality Conditions

Monday, February 06, 2006

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!


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