This book was written by British mathematical physicist Roger Penrose in 2016, and I've read his previous books “The Road to Reality” and “The Emperor's New Brain” before, both of which are quite difficult to read, with a lot of deep content and quite a few unique perspectives, making it suitable for people with some basic math and physics to study carefully.
The main contents of this book include the questioning of string theory, an in-depth introduction to quantum mechanics, some ideas about cosmology and an introduction to the original twistor theory.
I've seen quite a few string theory science articles and videos before, and it is indeed stylishly appealing as a possible grand unified theory, but the biggest problem is that it's hard to observe and verify experimentally, and more dimensions are largely mathematically necessary and hard to appreciate in reality.
Quantum mechanics is relatively well understood, I've read a lot of popular science articles before, and while a lot of it is counterintuitive, a lot of it can be verified with experimental observations and also has a lot of applications in life, and the idea that things aren't deterministic but probabilistic is also in line with my beliefs about the existence of free will.
Cosmology focuses on the Big Bang theory, the evolution of black holes, and the Singularity Theorem, for which Penrose won the 2020 Nobel Prize in Physics for “discovering that the formation of black holes is a robust prediction of general relativity”. General relativity theoretically allows for the existence of black holes, and Penrose proved in the framework of general relativity that under very broad conditions (the main one being the requirement that the energy of collapsing matter be non-negative), black holes can indeed form, encircling a singularity, which is known as the Singularity Theorem. In Penrose's topological proof, the captive surface need not have spherical symmetry. Once the captive surface appears, matter collapses toward the singularity and singularities and horizons are inevitable. Black holes and singularities are almost inevitable under general relativity, implying that gravitational collapse of sufficiently large masses inevitably leads to black holes in a complex reality.
Twistor theory, a mathematical tool pioneered by Penrose primarily for solving the problem of combining general relativity and quantum mechanics, is the representation of points in four-dimensional spacetime (Minkowski space or Euclidean space) as three-dimensional complex space, i.e., the complexes in the twistor space. This part is mathematically demanding beyond my understanding, and requires re-learning projective geometry and complex number theory, and there's really no way to go any deeper than that.
In general, there has been no major theoretical breakthrough in physics in recent years, more tinkering with quantum theory and general relativity. In order to have a big development, we cannot focus most of our resources on a few popular theories such as string theory, but we need more people to put forward new ideas, new questioning, and to promote the development of physics through careful calculations and meticulous experimental observatio