Posted:

**Dec 15, 2011 4:28 pm**OnCue wrote:"If you tried to halve a region of this volume, the result would not be two regions each with half that volume. Instead, the process would create two new regions which together would have more volume than you started with. We describe this by saying that the attempt to measure a unit of volume smaller than the minimal size alters the geometry of the space in a way that allows more volume to be created."

(Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic Books, 2001. p. 106)

Seems very ackward and removes one of the advantages of discrete space-time. One of the issues with uniting QM and relativity is that some non-Borel sets appear, which then allow Bannach-Tarski type issues. I.e. you get incongruent measures. If you have a discrete space time, then this issue goes away, simply because you donĀ“t get a BTP for countably infinite sets. Smolin here seems to introduce an incongruent meaure from the get go.