One Way Streets: Black Holes and Irreversible Processes, Part I
Note: Today and tomorrow on the BioLogos blog, join physicist Aron Wall for a look into the thermodynamics of black holes. Aron begins this two-part blog with a brief tutorial on entropy, which is helpful for understanding black holes in more detail. (If you’d like to read more from Aron Wall, visit his blog.)
A lot of things in life are irreversible: they only ever happen in one direction.
If you drop an egg on the floor, it breaks open and the yolk comes out. But eggs never reassemble themselves and leap into your hand. If you mix hot water with ice water, you get lukewarm water. But if you have a glass of water just sitting on the table, you’ll never see half of it freeze and the other half boil! Why is this?
It turns out that the answer has to do with counting possibilities. Take the example of the glass of water—let’s imagine there’s a specific glass of water in front of you. It contains a great many water molecules: in a normal sized glass there are about 1025 of them. There are a huge number of different ways to arrange these water molecules inside the glass (something roughly like 101025). But it turns out there are only a finite number of possibilities that look similar to your glass of water.
That’s because you know the temperature of your glass of water. If the molecules are moving around too quickly, they have a lot of kinetic energy and the water will be hotter than yours is. So there’s a limit as to how quickly the molecules can be moving around.
You might think that there are an infinite number of possible positions of the water molecules in the glass, since space is continuous. But if you try to measure the position of all the water molecules too precisely, you’ll run into trouble with quantum mechanics. Heisenberg’s famous uncertainty principle says that the more accurately you can determine the momentum of an object, the less accurately the position can be determined, and vice versa. Since we have a limit on how fast the water molecules can be moving, we also have a limit on how accurately their positions can be measured.*
When you work this out, you get a finite (but huge) number of different ways for the glass of water to be. Physicists describe this using a number called the entropy. Systems with a big entropy have many different possible ways they can be, while systems with smaller entropy have fewer possible ways they can be.**
The Second Law of Thermodynamics states that the entropy of the universe increases with time. Once you know that the entropy is just counting the number of ways things can be, it makes sense that it should always increase:
Imagine you have a jigsaw puzzle solved inside its box. If you vigorously shake it, the pieces will break up and it will become unsolved. However, if you shake an unsolved puzzle, it won’t solve itself. There’s no law of physics which prevents the pieces from happening to fall in just the right way to solve the puzzle. The reason is that there’s so many more different ways the puzzle can be unsolved than solved. So you wouldn’t expect it to happen.
The same thing is true for things like mixing hot and cold water. There are enormously more ways to arrange the molecules in a lukewarm glass than a glass which is half-hot and half-cold. Suppose there are X different ways to arrange the hot/cold separated water, and a much bigger number Y different ways to arrange the lukewarm water. If we start with the hot/cold water and let it sit for a few minutes, we nearly always get lukewarm water—this is possible because the X states of the hot/cold water turn into X out of the Y possible configurations of the lukewarm water. However, practically speaking we can’t tell any more which of the Y configurations the lukewarm water is in—they all look the same to us since we’re too big to see the molecules—so we say that the entropy increases.
But if we start with the lukewarm water and wait a few minutes, we are starting with Y different possibilites, and at most X of these can turn into hot/cold water. (The laws of physics require that possibilies which start out being different have to keep on being different.) The rest of the Y configurations would have to do something else, like remain lukewarm. So the probability of the water separating into hot/cold is at most X/Y. Since Y is enormously bigger than X, this probability is very, very close to zero.
So things only ever go in one direction. The odds of it going in the reverse direction are so tiny, that for all practical purposes you can bet on it as certain.
The Second Law only says that the entropy of the whole universe has to increase as time passes. If two systems interact, it’s possible to transfer entropy from one system to the other. For example, life on Earth is possible because the sunshine falling on the Earth has low entropy, while the heat radiation emitted to outer space has high entropy.***
Now let’s think about the past and the future. For the most part, the basic laws of physics don’t distinguish between the past and the future, yet the Second Law makes them quite different. Why is that? There are some mysteries here which scientists still argue about. But the best explanation seems to be that God must have started out the universe in some very special state with low entropy. From that time onward, the entropy began to increase. (If He had instead decreed that the universe would end in a low entropy state, then entropy would decrease and everything would run backwards! But we wouldn’t be able to tell, since we would go backwards too, remembering the “future” and anticipating the “past.”)
After the Big Bang, the matter in the universe was very hot, uniform, and dense. The universe expanded (increasing the range of possible positions for the particles), while the matter cooled off and slowed down (decreasing the range of possible velocities). Eventually gravity caused the matter to become clumpy, producing galaxies, stars, and planets (decreasing the entropy stored in positions), but at the same time reheating the objects (increasing the entropy stored in velocities). In all of these complicated changes, each decrease in entropy was more than compensated for by increases in the entropy of something else.If God were to continue guiding the physical universe along its current course, without any intervening changes to the regular pattern of events, it would eventually reach the maximum entropy state, which seems to be something like a universe with really tiny temperature in which all particles are separated by astronomical distances. It would then remain that way forever (except for occasional random fluctuations into more special states). Before that time, life would have to go extinct and all interesting processes come to an end. As St. Paul says, “the creation was subjected to futility” by the will of God. Although the Second Law is needed to support the beauty and life in the universe, it reminds us that this is only on the condition of inevitable decay and death.
However, Paul goes on to add that this was done in hope; hope that the creation will be “set free from slavery to decay, into the glorious freedom of God’s children.” As Christians, we expect important supernatural events (such as the Second Coming of Jesus and the Resurrection of the Dead) to take place before life goes extinct. It’s interesting to speculate on what the laws of physics might be like in the New Heaven and New Earth, but obviously we simply don’t have enough information to say.
However, in the currently existing Heavens, there are already peculiar objects which challenge our ideas about how to count possibilities. These objects are black holes, and the challenge which they present will be described in Part 2.
*A complete analysis would also have to include the orientation and rotation of the molecules, as well as the motions of the individual H and O atoms within the water molecules, but I’m not trying to be too precise here about the details…
**To be more precise, the entropy is the logarithm\ (http://en.wikipedia.org/wiki/Logarithm) of the number of possible configurations. But don’t worry if you don’t know what a logarithm is, it won’t be important to the discussion.