I don't like a quest. I like scientific research, creativity, non-conformist ideas. Luckily it's only the subtitle of the book that I hold a grudge against. In the book itself you'll find scientific research, creativity and non-conformist thinking. And a scientist who tells us that some of his ideas aren't science but speculation. (Well, 'predictions' my ass). All too often scientists use misplaced authority in popular science books when it comes to defending their own theories. Sean Carroll, theoretical physicist at CalTech, isn't one of them, and that is laudable.
From Eternity to Here (2010) is a book about the arrow of time. What is time? The answer in a nutshell: experiencing the tendency of the universe to increase its entropy, a measure of "disorder". There we have them again. Scrambled eggs won't unscramble (although quantum mechanics tell us there's a small chance it will happen. And if you wait long enough it inevitably will happen). The milk in your coffee that won't get unmixed.
Entropy tends to stay the same or increase on a large scale. That's because there are more possible combinations of chaos than of order. If an earthquake hits your pile of books, it tends to fall over. If the books are on the ground and the second wave of earthquakes come, generally they won't pile on top of each other.
That seems to be what we perceive as time: the direction from low entropy to higher entropy. It will eventually end with everything - all matter, all fields, all of spacetime - in equilibrium, which means time will stop as well. No change, no time, ma'am.
Carroll speculates however that it won't stop there. In an equilibrium universe entropy will continue to grow by creating bubbles that are new universes. These universes start out low in entropy, and the unlimited increase can continue.
Why does Sean Carroll come up with the need for eternal increase of entropy, to the cost of a yet unfalsifiable multiverse theory? Reason is that our own universe started out in a strange, very low entropy state. And that poses problems. Not only for the development of our universe, but for the current state of our universe as well. After all, the highest chance for us is to find ourselves in such a De Sitter space. In such a space there's equilibrium without an arrow of time. Weak anthropic principle, but with a twist.
The book fills up with explanations about the usual suspects. That is: entropy, general relativity, quantum physics, string theory, black holes and event horizons, AdS/CFT . The whole cast of characters you'll find in most current books about cosmology. In that regard the book won't teach you much extra. But it is a good overview structured from another perspective: the perspective of time. As a bonus it takes you on a mind-boggling tour of possibilities. From the dimensions of infinite space to the multiverse in its many variations. A well written book with an interesting conclusion. Worth your time.
For those missing the most basic of mathematics you should read the 'math' section at the end of the book first. For those with a few years of high school math: dive right in. Follow the arrow From Eternity to Here.
In the right direction, that is.