Can Quantum Fluctuations Create a New Universe?

[This is a transcript.]

The future is dark, and I don’t mean the upcoming US elections, I mean that stars in the universe will eventually all burn out. They’ll clump together and form black holes. The black holes will evaporate, leaving behind nothing but a very thinly distributed, cold, and dark gas. And that’s how it will remain, forever. Game over.

Well, maybe not. This video was prompted by a question that came in on twitter “If you waited long enough, could quantum fluctuations in the universe create a new one at some point?” The brief answer is, maybe.

The thing is that when the universe is filled with this thinly diluted stuff and entropy is maximal, it’s not that nothing can ever happen again. It might just take a very long time.

You see, if you take, say, two boxes of gas, one with a lower and one with a higher temperature. And you mix them together, then entropy will increase until they reach a uniform temperature. But of course the atoms of the gas are still moving. So every once in a while the gas on the left side will be just a bit warmer. If you wait long enough, there’ll be a moment in which it will be a lot warmer. And if you just wait long enough, indeed it’ll reach its original temperature.

The time it takes for this to happen is called the “recurrence time”. This time is so ridiculously long for actual rooms with actual gas that we never see this happening. But you can calculate it. This is how it works without quantum effects. If you take quantum effects into account, then basically anything that isn’t forbidden by the laws of nature can happen and will eventually happen. It might just take a very long time.

At the end of the universe we have an eternity, which is indeed kind of a long time. So maybe this could happen there, that spontaneously entropy decreases.

If you have this thinly distributed soup of particles, just by chance every once in a while, a few of them will come together to form a molecule. Wait even longer and you will get an entire cell, just by chance. Wait longer still and you’ll get a brain. These are the so-called Boltzmann brains, named after … Boltzmann who first thought of this. Wait even longer and you’ll get an entire universe starting out from scratch.

But is this really what would happen? Well, the issue is that whether or not the universe has a recurrence time depends on a mathematical property of its natural laws that’s known as “ergodicity”. Not all natural laws lead to recurrences, and the examples that physicists understand well are much simpler than reality. They’re particles bouncing off each other, like those gas atoms in the box. But in reality, particles stick to each other. Indeed, all this complexity around us comes only from the sticking together.

It's currently unclear whether the laws of nature in our own universe have a recurrence time. Some people, for example Sean Carroll, claim that it can’t be the case because if it was so, then the universe would contain many more Boltzmann brains than conscious beings on planets, like some of us. The argument then goes if Boltzmann brains exist at the end of the universe, it would be extremely likely for us to be a Boltzmann brain. But since smaller fluctuations are more likely than larger ones, we should find ourselves in a very small universe. That isn’t the case - so it must be that the universe doesn’t have recurrences at all.

I don’t think this is a mathematically sound use of probabilities because no one is picking consciousnesses from a pool and distributing them over the duration of the universe, that doesn’t make any sense. Be that as it may, whether the universe has a finite recurrence time is an open problem. So if you’re looking for a PhD topic, why not pick this, in 10 to the 100 billion years or so your thesis might just fluctuate into existence.

Thanks for watching, see you tomorrow.