The important concept isn’t “time reversal” at all, but the similar-sounding notion of reversibility–our ability to reconstruct the past from the present, as Laplace’s Demon is purportedly able to do, even if it’s more complicated than simply reversing time. And the key concept that ensures reversibility is conservation of information–if the information needed to specify the state of the world is preserved as time passes, we will always be able to run the clock backward and recover any previous state. That’s where the real puzzle concerning the arrow of time will arise.
With this chapter we begin Part Three of the book, which is the most important (and my favorite) of the four parts. Over the course of the next five chapters we’ll be exploring the statistical definition of entropy and its various implications, as well as the puzzles it raises.
But before getting to entropy, and the arrow of time that depends on it, we first have to understand life without an arrow of time. The only reason the Second Law is puzzling is because the rules of fundamental physics don’t exhibit an arrow of time on their own — they’re perfectly reversible. In this chapter we discuss what “reversible” really means, and contrast it with “time reversal invariance,” which is related by not quite the same. If a theory is both reversible and time-translation invariant (same rules at all times), it’s always possible to define time reversal so that your theory is invariant under it. (E.g. in most quantum field theories, “CPT” does the trick.)
Reversibility is a very deep idea; it implies that the state of the universe at any one moment in time is sufficient (along with the laws of physics) to precisely determine the state at any other time, past or future. But not many popular physics books spend much time explaining this idea. So we reach all the way back to very simplified models of discrete systems on a lattice (“checkerboard world”). What we’re after is an understanding of what it really means to have “laws of physics” in the first place — rules that the universe obeys as it evolves through time. That lets us explore different kinds of rules, in particular ones that are and are not reversible.
Along the way we talk about time-reversal invariance in the weak interactions of particle physics, and emphasize how this is not related to the thermodynamic arrow of time that is our concern in this book. Which gives me a good excuse to quote a touching passage from C.S. Wu. This chapter has everything, I tell you.