Carlo Rovelli is a big fan of loop quantum gravity, and of physics in general, and this book recaps the whole history of modern physics, at least partly in order to show how elegantly loop quantum gravity fits into place as a reasonable extrapolation. It’s an interesting and believable history, and the case for the plausibility of loop quantum gravity looks convincing to me. But then, I think I was an easy mark — since I already agreed with a series of strange (from the layperson’s point of view, at least) assertions Rovelli makes about known physics.

Rovelli inserts helpful diagrams every so often to summarize the history (and sometimes potential future) of “what there is” in the physical world according to physics. I can’t quite do justice to them so I use a table (please read it as one table).

Newton | Space | Time | Particles | |

Faraday Maxwell | Space | Time | Fields | Particles |

Einstein 1905 | Spacetime | Fields | Particles | |

Einstein 1915 | Covariant fields | Particles | ||

Quantum mech. | Spacetime | Quantum fields |

Quantum gravity | Covariant quantum fields |

In the transition from special relativity (1905) to general (1915), fields and spacetime are absorbed into “covariant fields”. This is because spacetime, Rovelli asserts (and I instinctively agree), *is* the gravitational field. So other fields like the electromagnetic field are covariant fields – fields that relate to each other in circumscribed ways. The curvature of spacetime depends on the energy (e.g. electromagnetic) present, and the behavior of electromagnetic fields depends on that curvature.

Rovelli likes to sum up some key features of each theory, and these summaries are very helpful. For QM, Rovelli lists three key principles:

- Information is finite;
- There is an elementary indeterminacy to the quantum state;
- Reality is relational (QM describes
*interactions*).

As a fan of Everettian QM, I don’t think we really need the indeterminacy principle. But it’s still true that we face an inevitable uncertainty every time we do a quantum experiment (it’s just that this is a kind of self-locating uncertainty).

Loop quantum gravity refines the “information is finite” principle to include spacetime as well. Not only are energy levels discrete; spacetime is also discrete. There is a smallest length and time scale. Rovelli identifies this as the Planck length (and time).

Rovelli explains loop quantum gravity as the quantization of gravity, deriving from the Wheeler-DeWitt equation. This equation can only be satisfied on closed lines aka loops. Where loops intersect, the points are called nodes, and the lines between nodes are called links. The entire network is called a graph, and also a “spin network” because the links are characterized by math familiar from the QM treatment of spin. Loop quantum gravity identifies the *nodes with discrete indivisible volumes*, and *each link with the area of the surface* dividing the two linked volumes.

Rovelli is at pains to point out that the theory really says what it’s saying. For example: “photons exist in space, whereas the quanta of gravity constitute space itself. … Quanta of space have no place to be *in*, because they are themselves that place.” This warning might seem too obvious to be necessary, but that’s because I didn’t reproduce the graphs of spin networks in Rovelli’s book. (I lack the artistic talent and/or internet skillz.) You know, graphs that sit there *in space* for you to look at.

OK, that’s space, but what about time (and aren’t these still a spacetime)? This deserves a longish excerpt:

Space as an amorphous container of things disappears from physics with quantum gravity. Things (the quanta) do not inhabit space; they dwell one over the other, and space is the fabric of their neighboring relations. As we abandon the idea of space as an inert container, similarly we must abandon the idea of time as an inert flow, along which reality unfurls.

[…] As evidenced with the Wheeler-DeWitt equation, the fundamental equations no longer contain the time variable. Time emerges, like space, from the gravitational field.

Rovelli, chapter 7

Rovelli says loop quantum gravity hews closely to QM and relativity, so I assume we get a four-dimensional spacetime which obeys the laws of general relativity at macroscopic scales.

In a section of Chapter 11 called **Thermal Time**, Rovelli uses thermodynamics and information theory to explain why time seems to have a preferred direction, just as “down” seems to be a preferred direction in space near a massive body. When heat flows from a hot zone into the environment, entropy increases. Since entropy reductions of any significant size are absurdly improbable, these heat flows are irreversible processes. And since basically everything in the macroscopic world (and even cellular biology) involves irreversible processes, time “flows” for us. Nevertheless, at the elementary quantum level, where entropy is undefined (or trivially defined as zero – whichever way you want to play it) time has no preferred direction. All of this will be familiar to readers of my blog who slogged through my series on free will. This is the key reason scientific determinism isn’t the scary option-stealing beast that people intuitively think it is.

There was one small section in Chap. 10 on black holes that seemed to fail as an explanation. Or maybe I’m just dense. Since spacetime is granular and there is a minimal possible size, loop quantum gravity predicts that matter inside the event horizon of a black hole must bounce. The time dilation compared to the outside universe is very long, so an observer would see no effect for a very long time, but then the black hole would “explode”. But surely “explode” is not the right word? Intuitively it would seem that any bouncing energy should emerge at a comparable rate to that at which it entered, at least for matter entering during a period of relatively stable Schwarzschild radius. Maybe by “explode” Rovelli just means the black hole would “give off substantially more energy than the usual Hawking radiation”?

A lot of people seem captivated with Rovelli’s ideas, but from a distance they never seem to grab me. Maybe I’m just not familiar enough with them.

I do think the idea that black holes exploding (for us in very slow motion) is an interesting one.

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I don’t know how many explanations I’ve read of relativity but Rovelli seemed to explain it still in a way that gave me new insight.

It’s odd but I didn’t note much the references to the Wheeler-DeWitt equations and the disappearance of time. That seems to correspond a great deal with Julian Barbour and so I may want to return to the book again.

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I reread that brief section about black hole bounce in the book, and also read a Nature article from 2014 about the phenomenon. The Nature article says that it predicts the black hole turning into a “white hole,” but as I understood it, a white hole was the time reversal of a black hole, which would – just as you say – release its energy in the opposite way it fell in (more or less), the horizon becoming a surface from which anything can exit but which nothing can enter. However, Rovelli’s description in the book makes it seem that he really does expect this to be a rapid process, from the outside, once it finally reaches the outside, and he speculates about the “fast radio bursts” being primordial black holes just now “bouncing” all the way out. This feels contradictory to me, but since it’s all very cutting edge and even speculative physics, I think it’s not as refined as it might be.

I’ve long wanted to understand this much better than I do, preferably with the math, and I even have a copy each of Thorne, Wheeler, et al’s “Gravitation”, Sean Carrol’s “Spacetime and Geometry” and Gibbons and Hawking’s “Euclidean Quantum Gravity” sitting behind me in my office. But I haven’t yet gotten beyond the first few pages in any of them, mainly because time – ironically – is limited, as is energy, more metaphorically. Had I but world enough, and time…

Somewhat tangentially, I’ve also wondered about the NEED to predict a singularity in which everything compresses to zero size in the center of a black hole…it seems to me that, from a mathematical point of view, the zero point would never be reached even classically, just that infinite density would be approached as a limit. It feels to me that, though the effective radius of a gravity well might head toward zero, the LENGTH of the sort of cylinder that the tube forms could extend endlessly, assuming spacetime is infinitely deformable. But I assume that the many highly gifted mathematicians who have dealt with GR and with attempts at quantum gravity have dealt with this and it doesn’t work, but I’ve never heard a good explanation that actually addresses it. Thus, my three big, intimidating books, which I may never finish in my lifetime.

Sigh.

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