When I borrowed this book (from the library), my purpose/intention was to try to see whether I may learn something about the theory of loop quantum gravity. At the end, though I don’t feel that I have grasped too substantially about the theory of loop quantum gravity, the author does seem to make the readers feel very straightforward to accept that the space at the smallest level is quantized (as quanta of gravity). It seems to be the most natural thing in the world. “Of course !” one may exhale in one’s mind. Probably, only the part that the space as a sort of substratum or backdrop has disappeared is slightly more difficult to thoroughly comprehend.

The other thing that the readers would learn well from this book is that time doesn’t exist at the fundamental level. Because we never measure time in reality but only other physical variables such as how many beats for each oscillation or how many ticks of a stopwatch, and their relationship. In particular, time does not exist in the Wheeler-DeWitt equation, the solutions of which has given rise to “loops” — first found by the famous Lee Smolin together and Ted Jacobson, p.159. Which was the beginning of loop quantum gravity. In p.249-252, the author has explained quite well about “Thermal Time” by comparing time to heat as kind of an average of many variables. Time, like heat, doesn’t exist at the most fundamental level but it exists as a useful and convenient variable. In fact, the entire Chapter 12, “Information”, including “Thermal Time”, has done a good job in explaining the information theory, probably not because I have read about this subject quite a number of times.

Another distinct and interesting “tidbit” that I’ve learnt from this book is that black hole or the universe would explode or bounce back (Big Bounce) if they get squashed or contract to (presumably approaching) the level of the quanta of space/gravity due to quantum repulsion. The quantum repulsion is not explained clearly (eg. in p.207-208) as “All of this is still at an exploratory stage” (1st line of p.209). Nevertheless, it’s said that when the space is very very small, the universe is just “spread-out cloud of probabilities in which time and space wildly fluctuate” (3rd-4th lines of p.208). ( As a side note, the author still uses the word “time” here though time should not exist at the fundamental level. Maybe, the author is just using an average sense of “time” as it’s what most readers are familiar with anyway ? Or, even the author himself can’t get rid of the old habit of thinking of time ?! This is just one of the places where I might have been confused or bewildered after the idea of “time doesn’t exist” was so ingrained in my brain. ) It seems to me that these loop theorists must like some kinds of cyclic models of the Universe, contracting and bouncing back. But what if the Universe keeps expanding and even in an accelerating pace as we’re observing now, which leads to no scenario of contraction ?!

Even though the quantized space has been so well explained, the loop quantum gravity itself is not really convincingly explained. Though the readers may learn about the “spin network” as the quantum state of gravitational field and later “spinfoam” as a sort of spacetime structure, when a reader comes across the author’s 3 equations of loop quantum gravity on a T-Shirt in Fig. 7.7 on p.191, s/he probably doesn’t feel delighted or excited as those 3 equations were not really explained (not to mention derived) but they were there just to show that the theory of loop quantum gravity can be summarized in a T-Shirt 😦 By the way, the word “spin” is used only because the result involves half-integers which are like spins in quantum mechanics.

On p.187-190, the author explains that the probability of any physical event can be calculated by summing over all possible spinfoams, using the equations of loop quantum gravity (of course !). Apparently, they take advantage of the two techniques used heavily in quantum field theory and for Standard Model, Feynman diagrams and the lattice approximation — as in “lattice QCD” I guess (as the author doesn’t say explicitly). These two tools are so famous and broadly exercised and yet they haven’t helped the loop theorists produce useful results that we can verify experimentally ?! The only example that the author has mentioned is the spectrum of (cosmic) background radiation as predicted by loop quantum gravity. They are hoping that the wide-angle fluctuations they have predicted, which are different from those theoretical predictions that do not take quanta into account (p.218-219), may show up and be verified in future (satellite/space) experiments with enough precision.

One thing I don’t really share with the author’s enthusiasm is his tendency to tell us again and again that the philosophers/scientists thousands of years ago already had the same ideas of the modern dates. Once or twice may be OK or even cute but there are just too many of this kind of “forced analogy” (in my opinion) in this book. The most long-winded example is probably in p.97-106, where the author tries to tell us that Dante’s poem “Paradiso” has described 3-sphere as in Einstein’s finite universe without border. And of course, Democritus knew pretty much everything, certainly not just atoms, but even the information theory (p.242). Maybe, Italian readers would enjoy reading these frequent mentions of ancient philosophers (even though they’re not Italians). But it’s just too much for me. Sometimes it’s even given me a feeling of going to the Bible to look for answers for modern scientific problems, which is obviously opposite to the scientific and experimental spirit of this book.

In the first paragraph of p.89, on p.214-215 and p.220-221, the author apparently mentions the LIGO’s discovery of gravitational wave in 2015/2016. This is definitely an addition to the original Italian version which was first published in 2014. By the way, the author does make use of the absence of discovery of supersymmetry at LHC/CERN (or elsewhere) to his advantage, to at least give the loop quantum gravity a little “+” in comparision to (super)string theory 🙂