Rovelli 2: Spacetime is Quantum

This is my second post on Carlo Rovelli's new book, Reality Is Not What It Seems. The first post was:

• From Democritus to Relativity to Quantum Mechanics

1. My book has now been baptized in coffee, but is still readable. I suppose it was inevitable.

We now hit the problem edge of physics in chapter 5. Quantum mechanics works for things that are very small. General relativity works for things that are very big. They contradict each other.

Relativity says that spacetime is curved and continuous. Quantum mechanics says that space is flat and energy is discontinuous.

This contradiction is not a problem unless you are dealing with something that is both very small and yet has tremendous mass. In other words, black holes and the Big Bang.

2. A favorite scientist of Rovelli is clearly the Russian, Matvei Bronštejn, put to death under Stalin in 1938. He apparently suggested before his death that, following Heisenberg's uncertainty principle, the narrowness of location would require great ambiguity in momentum. The energy this would involve at a particular point would be so great as to create a black hole.

The bottom line, Bronštejn suggested that this thought experiment implied a limit to the divisibility of space. The minimum space is around:

This "Planck length" combines the three fundamental constants of nature. "H bar," as it is called, is fundamental to quantum mechanics. C is the speed of light from special relativity. And G is the gravitational constant from general relativity.

3. The next turn in the chapter is to John Wheeler, who coined the phrase black hole. It was not too long ago that many physicists were skeptical about their existence, but now it is overwhelmingly accepted.

Apparently, Wheeler and Bryce DeWitt come up with an equation for the "foaming" of space at the Planck level, the "Wheeler-DeWitt equation." Here I am beyond much acquaintance. What is most curious about the equation is that it does not have a time variable. How do you describe interactions on the most fundamental level of reality without a time component?

There will me more to come on this subject. I have some other sources that I may use to try to triangulate.

4. We are close to the birth of quantum loop gravity, the main contender with string theory for ultimate reality right now. In the late 80s, Abhay Ashtekar simplifies and rewrites the Wheeler-DeWitt equation. Lee Smolin tells the same story from his perspective in Three Roads to Quantum Gravity.

Smolin and a guy named Ted Jacobson find some solutions to this equation. The equation only has solutions when lines "loop" in space. Thus "loop quantum gravity" is born.

More to come...