Where time becomes a loop, where times becomes a loop, …

As I mentioned last week, I'm reading From Eternity to Here by Sean Carroll. It's a physics book for laypeople and is about time.

Time is a funny thing when you stop to think about it. What exactly is it? How do you define it in non-temporal terms? That isn't easy to do, and you won't be getting any answers here. If I thought I was out of my league while reading medieval monotheistic philosophy, then I feel doubly so now, reading about general relativity and spacetime curvatures. But I like the book a lot. I'm not taking notes—just reading through and absorbing whatever happens to soak in.

Physicists sometimes talk about time as a fourth dimension, but time doesn't appear (at first glance) to have the same symmetries as the other three dimensions. As Sean Carroll puts it, you can turn whichever way in 3D space and maybe even get lost, but you can't make a wrong turn into yesterday. That is, time always runs forward—at least as we perceive it. Why? That's a big question the book aims to answer. At the heart is the idea of entropy and how the quantity of information in the universe has steadily increased ever since some initial high-order state, which we call the Big Bang.

A lot of people wonder where order comes from, even to the point where it affects science's credibility, such as when someone professes their skepticism that complex life could self-arrange from simpler components. The question where does order come from? is interesting, but there's a good answer for it: order comes about by making some other place even less orderly. In that sense, order isn't any more mysterious than the cold air blowing out of an air conditioner. Where does refrigerated air come from on a hot summer day? Answer: by pumping heat uphill to the outdoors—i.e., making some other place even hotter. Marvelous, yes, but straightforward nevertheless.

But the where does order come from? question leads to a compliment question that's harder to answer: where does disorder come from? Currently, no one knows. Not all disorder comes about as a result of order increasing somewhere else. Disorder is, on average, increasing in the universe, so some disorder is coming about from—well, no one knows. Whatever the answer, it appears to have something to do with the essence of time itself.

Time travel

You can't write a physics book about time for laypeople and not include a chapter about time travel, and this book dutifully has one. In it Carroll discusses qualitative features of various theoretical ideas about time travel. One idea is the closed loop of time, called a closed timelike curve in the book. A closed timelike curve is spacetime that bends enough to form a circle, thus causing events to cycle repeatedly, like in this episode of Star Trek TNG.

I'm going to spoil the plot: it appears unlikely that it's possible to create a closed timelike curve if the universe isn't set up from the get-go to produce one. This has to do with the enormous amount of energy required to bend spacetime into a circle. Nevertheless, such loops are interesting to think about as thought experiments. In particular, they necessitate what seems to us to be a problem: a choice between paradox or defying entropy's relentless march.

To explain this, Carroll uses an example of a gate that leads into yesterday. That is, if you walk through the gate at 3PM on Wednesday, you will emerge on the other side at 3PM on Tuesday. Other than this fact, there's nothing weird about the gate—no strange force field, no Hollywood-style light show. You walk through it like any ordinary gate. Someone watching you from the Wednesday side would see you pass through normally, though on the other side you would be in Tuesday. (The observer would be looking backwards in time when they see you on the other side.)

Once in Tuesday, you would walk around as though it were any other ordinary day and re-experience the previous twenty-four hours, but at the end of that time you would return to the Wednesday side of the gate and pass through again. That is the meaning of a closed loop. The paradox problem stems from the notion of freewill: what if you chose not return to the gate? What if you instead decided to board a plane headed to another continent or to shoot yourself in the head? The idea of a closed loop of ever repeating events conflicts with our sense of freewill.

We may resolve the paradox by hypothesizing there's no freewill. But without freewill we're presented with another problem: entropy. After passing through the gate, you spend the next twenty-four hours walking around, doing whatever it is you did previously, and then return to the Wednesday side the gate. However, the condition in which you return to the gate must be exactly the same as the condition you were in when you last passed through the gate. Your hair must be the same, the specks of dust and dirt on your pants must be the same. Every cell and every atom in you must be exactly the same. You must not have aged, learned anything, forgotten anything, or changed in anyway. But this sort of thing just doesn't happen over the course of any twenty-four hour period. Things wind down, and they become more disorderly. A closed timelike curve defies this.

As I said, you won't be getting any answers here.