This is the first book I have read by Sean Carroll, and I found in it an elegant discussion on the concept of the arrow of time. I think he has done an excellent job of presenting us with an in-depth and provocative introduction to this subject. Some parts, I found, required clear, sharp thinking as I read the material; it can sometimes be a bit confusing. Nevertheless, Carroll did quite well in explaining the material in as clear and comprehensive manner as possible. I need to mention that this book packs a tremendous amount of information between it covers. Often I would read only so many pages before have to stop and digest the material.
He divides the book into four sections. In section one, we get into some talk about the concepts of the past (events near the Big Bang), the present, the future, and an introduction to the laws of thermodynamics, especially the second law which is about entropy - an important topic in our understanding of the arrow of time. We also learn about vacuum energy, time symmetry, and what is maximum entropy as he lays the foundation for what is to come.
Section two delves into concepts involving relativity, such as the speed of light and light cones, curved spacetime along with a discussion of white and black holes. Here we learn that black holes provide the strongest connection between gravitation and entropy - the two crucial ingredients in an ultimate explanation of the arrow of time according to Carroll.
Section three introduces us to something called closed time-like curves, a closed flatland universe, and something called a space of states. Microstates and macrostates play an important role in the discussion. Chapter eight involves an interesting discussion of Boltzmann's formula, which is a calculation of entropy based on the number of microscopic arrangements of a system that are macroscopically indistinguishable. For those rusty on exponentials and logarithms, Carroll provides an appendix covering the basics. Don't worry, the book is not heavy on math. We get into a number of concepts involving entropy: Liouville's Theorem, Gibb's formula, Loschmidt's reversibility objection, and the past hypothesis (referring to a boundary condition at the beginning of the universe). I also need to mention Maxwell's demon (illustrating a connection between entropy and information) and Laplace's all-knowing demon. I found chapter eleven interesting. The material delves into quantum mechanics involving such topics as the "quantum cat" and the collapse of the wave function, entanglement, and decoherence. All of the material in this section is actually quite important to building a knowledge foundation for understanding the arrow of time.
In the last section, there is a more in depth coverage of black holes, which, as I said, provides an important connection between entropy and gravity. The question of why the universe had such a low entropy at the beginning is explored in more depth, and the future state of the universe is hypothesized - possibly something called de Sitter space. Inflation and the multiverse are discussed. In this section, the concept of bubble universes is presented as a possible solution to the arrow of time. I found myself concurring with Carroll on this. It sounds plausible, if not testable.
Don't worry about all of the concepts introduced in this review. Carroll thoroughly explains and elaborates on these topics in the process of making them understandable.
If you want a good summary of the contents of the book, I suggest you use Amazon's "Look Inside" feature, and scroll down to the table of contents. Under each chapter heading, you will find a brief description of the chapter. This gives you a pretty good idea of what is being discussed.
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