This is an entertaining book about seeming paradoxes in physics. I highly recommend the book to people interested in special relativity, quantum mechanics, thermodynamics, and mathematics.
Is time travel possible? That is covered in chapter 7, "The Grandfather Paradox", where Al-Khalili explains what might happen if you went back in time to murder your grandfather. Is it possible? I won't say right here, because it is definitely a spoiler.
What about the so-called "twins paradox". One twin stays on Earth, while the other goes in a very fast space-ship near the speed of light to a nearby star. When the twin returns, he has hardly aged, while the stay-at-home twin is much older. How can this be? While the space-faring twin travelled fast compared to the stay-at-home twin, from the space-faring twin's point of view, his stay-at-home twin travelled just as fast in the opposite direction. Since everything is "relative" why did one twin age faster than the other? The situation sounds completely symmetric--but it isn't.
If the universe is infinite in extent, and the density of stars and galaxies is approximately uniform everywhere, then why is the sky dark at night? This is Olber's paradox, and it is very subtle. While more distant stars are fainter (their radiance on Earth is inversely proportion to distance-squared), their numbers increase with distance-squared. Believe it or not, the correct explanation for this conundrum was first written by Edgar Allan Poe! He was not a scientist, and most of his "science" explanations were dead-wrong, but on this topic he got it right! Again, I don't want to give away spoilers, so I will refrain from explaining the paradox here.
Suppose a runner holds a pole horizontally while running through a barn. The barn doors in the front and the back are both open. When the pole is at rest, its length is exactly the same as the distance between the front and back doors of the barn. Now, suppose the runner can reach a relativistic speed. From the point of view of someone standing at rest near the barn, the pole seems to be "squashed", so he could actually close both doors for a tiny fraction of a second, and the pole would fit in the barn. But from the runner's point of view the barn is squashed, so that when he is in the middle of the barn, both ends of his pole would stick out of the doors. How can this be? How can both points of view be correct, when you have such a symmetric scenario?
Other paradoxes explained in the book are "Maxwell's Demon", "Schrodinger's Cat', "Laplace's Demon, and "Fermi's Paradox". Ahhh--Fermi's Paradox is so interesting. If the universe is so vast, and there are intelligent life forms out there that have advanced to a high stage of technology, why haven't we heard from any alien civilizations? Simply stated, "where is everybody?"
The book goes into considerable depth, and gives all the background you need to completely understand each paradox. The style is an easy banter, so it is a fun read, as well. If you would like to put on your thinking-cap and be stimulated as well as entertained, this would be a good book for you!