Rovelli 3: Quanta of Space

This is my third post on Carlo Rovelli's new book, Reality Is Not What It Seems. The first two posts were:

• From Democritus to Relativity to Quantum Mechanics
• Spacetime is Quantum

1. This chapter is not long but it is getting at the things I am interested in right now. I re-skimed chapter 10 of Lee Smolin's Three Roads to Quantum Gravity to cross-reference their material. That chapter is called "Knots, Links, and Kinks." I see Smolin's coming out with a new edition.

Because I don't know the math, because they don't fully give the math, it's hard to get more than just an impression from these chapters. But I like the basic theses.

2. We already have the first key truth. Both space and time reduce to quanta. Space is not infinitesimally continuous. Time is not infinitesimally continuous. I like it.

Now here's another biggie. Gravity reduces to quanta, discrete units of gravity. The quanta of gravity are not in space. "They are themselves space" (172). "Quanta of gravity constitute space itself."

Using another picture, space reduces to discrete packets of volume, which we might call "nodes." "Volume is a property of the gravitational field, expressing 'how much gravitational field' there is" (163-64). The imaginary lines between these nodes are called "links," and a whole set of such intersecting lines is called a "graph."

Nodes, Links, and Graph (Rovelli)

3. There is an area associated with the lines between nodes, which is roughly the square of the Planck length mentioned in the previous post (8πL² times the square root of the spin times one plus the spin, with the spin coming in half integers). When we think of a larger three dimensional volume, the volume is the sum of the volumes of the nodes. Such a volume is a "spin network."

4. After writing all that, there is a danger of thinking that these nodes are space. But Rovelli and Smolin would both want to clarify that, like the electron, it is in the interaction of these gravitational quanta that space exists. Space is not in the node nor is the node space. Space is what happens when the nodes interact, if I understand correctly.