It’s not true that we’ve figured it out by now. In fact, it’s more than a fifty-year old problem, Boltzmann understood that this was a problem, and he suggested an answer to it. Before I get to that, I should say that the reason the problem has gotten worse, rather than better, is because in 1998, we learned something crucial about the Universe, that we didn’t know before. We learned that it’s accelerating. The Universe is not only expanding, if you look at that galaxy, it’s moving away, you come back a billion years later and look at it again, it’ll be moving away faster.
Individual galaxies are speeding away from us, faster and faster, so we say the Universe is accelerating. Unlike the low entropy of the early Universe, even though we don’t know the answer for this we at least have a good theory, that can explain it if that theory is right, and that’s the theory of dark energy. It’s just the idea that empty space itself has energy, and every little cubic centimeter of space whether or not there’s stuff, whether there’s particles, matter, radiation, or whatever, there’s still energy, even in the space itself. This energy, according to Einstein, exerts a push on the Universe, it’s a perpetual impulse that pushes galaxies apart from each other. Because dark energy, unlike matter radiation, does not dilute away as the Universe expands.
The amount of energy in each cubic centimeter remains the same, even as the Universe gets bigger and bigger. This has crucial implications for what the Universe is going to do in the future. For one thing, the Universe will expand forever. Back when I was your age, we didn’t know what the Universe was going to do, some people thought it would recollapse in the future, Einstein was fond of this idea. But if there’s dark energy and the dark energy does not go away, the Universe is just going to keep expanding for ever and ever.
14 billion years in the past, a hundred billion dog years, but an infinite number of years into the future. Meanwhile, for all intents and purposes, space looks finite to us. Space may be finite or infinite, but because the Universe is accelerating there are parts of it we cannot see and never will see. There’s a finite region of space that we have access to, surrounded by a horizon, so even though time goes on forever, space is limited to us. Finally, empty space has a temperature.
In the 1970s, Stephen Hawking told us that a black hole, even though you think it’s black, it actually emits radiation when you take into account quantum mechanics. The curvature of space-time around the black hole brings to life the quantum mechanical fluctuation that the black hole radiates. A precisely similar calculation by Hawking and Gary Gibbons shows that if you have dark energy in empty space, then the whole Universe radiates. The energy in empty space brings to life quantum fluctuations, so even though the Universe will last forever, and ordinary matter radiation will dilute away, there will always be some radiation, some thermal fluctuations, even in empty space. So what this means is that, the Universe is like a box of gas that lasts forever.
What are the implications of that? That implication was studied by Boltzmann, back in the 19th century. He said, well, entropy increases because there are many many more ways for the Universe to be high entropy rather than low entropy. But that’s a probabilistic statement. It will probably increase, and the probability is enormously huge, it’s not something you have to worry about, the air in this room all gathering over one part of the room, and suffocating us, it’s very, very unlikely. Except if they lock the doors and kept us here, literally forever, that would happen.
Everything that is allowed, every configuration that is allowed to be attained by the molecules in this room, would eventually be attained. So Boltzmann says, you can start with a Universe in thermal equilibrium, he didn’t know about the Big Bang or the expansion of the Universe, he thought that space and time were explained by Isaac Newton, they were absolutely, just stuck there forever. So his idea that natural Universe was one in which the air molecules were just spread out evenly everywhere, everything molecules. But if you’re Boltzmann, you know that if you wait long enough, the random fluctuations of those molecules will occasionally bring them into lower energy, lower entropy configurations. And then of course, in the natural course of things, they will expand back.
So it’s not that entropy must always increase, you can get fluctuations into lower entropy, more organized situations. Boltzmann then goes on to invent two very modern-sounding ideas, the multiverse and the entropic principle. He says, the problem with thermal equilibrium is that we can’t live there. Remember, life itself depends on the arrow of time. We would not be able to process information, to metabolize, walk and talk if we lived in thermal equilibrium.
So, if you imagine a very big Universe, an infinitely big Universe, with randomly bumping into each other particles, there will occasionally be small fluctuations to lower entropy states and then they would relax back. But there would also be large fluctuations, occasionally you’ll make a planet, or a star, or a galaxy, or a hundred billion galaxies. So Boltzmann says, we will only live in the part of the multiverse, the part that has an infinitely big set of fluctuating particles, where life is possible, that’s the regions where entropy is low, maybe our Universe is just one of those things that happens, from time to time.