If is right, this interview has happened before. Not just once, but infinitely many times. In an earlier cycle of the cosmos, we met in Dublin, asked and answered these same questions and discussed the unsettling possibility that the universe is destined to repeat itself exactly.
Carroll, a quantum cosmologist and philosopher at Johns Hopkins University in Baltimore, Maryland, pursues one of physics’ deepest questions: how gravity and the familiar classical universe emerge from the strange rules of quantum mechanics. But unlike most cosmologists, who begin with the universe we observe and then try to work backwards, Carroll starts from the vast landscape of all quantum possibilities – essentially taking quantum theory itself as his guide.
Against his better judgement, this approach has led him towards a cosmos that continually expands then contracts before a new cycle begins. Cyclic universes are nothing new, but Carroll’s proposal has a peculiar twist. In most such models, each cycle differs from the last. But in contrast, his cycles are exactly the same: every galaxy reforms, every life unfolds again and every conversation is repeated word for word.
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This bizarre picture also offers a possible escape from an uncomfortable puzzle involving so-called Boltzmann brains; in many models of universes that persist for long enough, self-aware brains with false memories should pop into existence, to the point that they outnumber ordinary minds.
New Scientist caught up with Carroll at the Dealing with Time and Chance philosophy conference at Trinity College Dublin, Ireland, to ask how he landed on such a strange cosmology, how it solves the Boltzmann brain problem and what it tells us about the nature of time.
Jacklin Kwan: Your approach begins with quantum mechanics rather than the universe described by general relativity. Why?
Sean Carroll: Quantum mechanics is the single most foundational view that we have of the world. However, when you take physics classes, you are first taught classical mechanics. Then, when you’re taught quantum mechanics, you start with a classical system and learn how to turn it into a quantum system. In other words, you learn to “quantise” the theory.
That approach has worked really well for forces like electromagnetism, but it hasn’t seemed to work in any normal, straightforward way for gravity. So, my perspective is that we got lucky with the other forces of nature. The surprising thing isn’t that gravity is hard to quantise – the surprising thing is that quantisation works so well for everything else.
So, what I have been thinking about over the past decade or so is how to start with quantum mechanics and derive the observed world from it, rather than starting with the observed world and trying to quantise it. I began with the question: what if we take quantum mechanics seriously?
That sounds like a clean starting point. But when you apply ideas like this to an eternal universe, you quickly encounter a potentially serious problem: Boltzmann brains.
What are Boltzmann brains?
If you think the universe lasts forever, it spends most of its time near a state called thermal equilibrium. It is a state where energy is spread out as evenly as possible and, on the face of it, nothing much happens.
But if the temperature isn’t precisely zero, even this apparently uneventful state can still fluctuate, allowing small pockets of order to emerge. Take the air in the room you are sitting in. There is a classic undergraduate calculation asking how long it would take for all of it, through random motion, to end up in one half of the room. It will eventually happen, but only after a time vastly longer than the age of the universe.
Given enough time, the universe fluctuates into everything that is allowed. That includes a universe like ours, but it also includes observers surrounded by empty space. These spontaneously emerging brains, complete with unreliable memories of having existed in our universe, are Boltzmann brains.
In many eternal models, Boltzmann brains would be produced in overwhelmingly greater numbers than ordinary observers who evolved out of galaxies, stars and life on planets. And if your theory says that almost every observer with experiences like yours is actually a random fluctuation with unreliable memories, then you can conclude that you’re probably one of them and there’s no real connection between what you remember and what actually happened.
And that is where the idea starts to eat itself: if the theory were true, we would have no good reason to trust the observations or reasoning that led us to believe it.
Do cyclic cosmologies offer a way out?
I’m not a big fan of cyclic cosmologies, to be perfectly honest. They’ve been around for a long time, and I’ve always worried that they either don’t solve existing problems or create new ones of their own. For instance, some quantities require an infinite amount of fine-tuning [to match with the universe that we observe today]. So, I’ve never spent much time thinking about them.
But what we realised in with my collaborators at Johns Hopkins University, and , is that there is a loophole to the Boltzmann brain worry. Let’s start with a quantum description of the entire cosmos called the “wave function of the universe”. Quantum mechanics describes the universe using a mathematical space called Hilbert space. We don’t know if Hilbert space is finite- or infinite-dimensional; it could be finite, so we decided to investigate that possibility.
You’re going to have to tell us what Hilbert space is.
Hilbert space is the space of all possible quantum states, or all possible wave functions. To take the simplest example, a single electron has an intrinsic property called “spin” that is either up, down or some combination of the two: Hilbert space contains all those possibilities and combinations.
If Hilbert space is finite, we can use a famous result called the recurrence theorem, which goes back to the mathematician Henri Poincaré. He was originally thinking about planets moving around the sun. The theorem says that if a system has only a bounded range of possible states, then, given enough time, it must eventually return very close to where it began. That makes logical sense: you have an infinite amount of time, but only a finite number of states to occupy. Of course, you will eventually come back to one you have visited before.
Put those ingredients together – a finite number of possible states evolving smoothly over infinite time – and you get cycles.
Typically, each cycle visits all the allowed states, many of which include Boltzmann brains. But if you choose the evolution of the universe precisely, the wave function need not visit every possible state. Imagine tuning all the atoms, all the little billiard balls bumping into one another, so that they don’t explore every possible arrangement. They move along one path and eventually just bounce back – they just retrace it. If that path never passes through states containing Boltzmann brains, those brains are never produced. Or at least they are sufficiently rare that they don’t make up most observers in the universe.
That is what we argue can happen in our model. It isn’t enough for the universe to be cyclic in a loose sense. Its quantum evolution has to be exactly periodic.
So, we don’t just see a succession of broadly similar universes, but the same history repeats exactly?
Yeah, so you still get a big bang, the universe expands and cools, and it empties out into empty space. This is just what’s happening in the universe we observe – galaxies are moving farther apart, photons in the cosmic background radiation are diluting and cooling down. Eventually, there will be nothing left but empty space. And the universe stays in empty space for a very, very long time.
Then, in our picture, you play the big bang backwards. Just as the expansion involved everything moving apart and growing more dilute, particles getting further away and photons getting stretched out so that they redshift, you gradually see photons coming in and becoming increasingly compressed and blue-shifted. Particles pop into existence and become more numerous. Instead of forming black holes, you form white holes, which continually spew matter and energy outward.
The whole story plays backwards, going down to a crunch exactly like the big bang played backwards in time. That crunch hits a bounce point, then you get the ordinary big bang and repeat the cycle again.
So far, this sounds the same as most cyclic cosmologies, but in our model, the universe isn’t merely cyclic, it is truly periodic. Think of a pendulum – after a fixed interval, it returns to exactly the same state and retraces the same motion. You just have to wait an extraordinarily long time. Our universe is about 10¹⁰ years old, whereas we are talking about an incomprehensibly bigger number of years called a googolplex.
It takes so long because there are so many different parts of the universe’s quantum state evolving at once, and the whole thing only repeats when they all line up again. But wait long enough and the entire history of the universe repeats exactly. And it does so an infinite number of times.
So, even our current conversation would have already happened in previous iterations and will always happen in future ones. How do you feel about there being nothing special at all about the present moment?
I don’t have very strong feelings about it. As we say , it is a matter of taste. You can think of this as a cyclic cosmology in which history repeats over and over. Or you can treat it as a single universe that happens once and then eats its own tail, like the ouroboros – the ancient symbol of a serpent eating its own tail.
What does an eternally repeating cosmos mean for free will?
If the absence of free will bothers you, then what should really bother you is the existence of laws of physics. If you know what happens at one time, then you can say what is going to happen at all the other times.
Even if the laws of physics aren’t deterministic, as in some interpretations of quantum theory, there are no implications for free will; all that matters is that there are laws in the first place. Adding a random-number generator to the laws of physics isn’t the same as saying that your willpower has the ability to determine what happens. No known version of quantum mechanics says that.
Other than banishing Boltzmann brains, what else can this eternally repeating universe help with?
These models might help us to make better sense of how time works. In the real world, time has an arrow that points from the past to the future. I can do things today that exert a causal impact on the future, but I can’t do anything now that affects the past. But in our best understanding of the fundamental laws of physics, time doesn’t have a direction.
We kind of know how to resolve this tension using a concept called entropy. Entropy is really a way of counting. Take a cup of coffee. It is made of atoms and molecules, but I never see the individual atoms, and I can’t tell you where each one is or which direction it is moving in.
Then, I can ask: given what I can observe about the cup of coffee, how many different arrangements of atoms would look the same? That is entropy. If cream is mixing into coffee, at first they are separate. There aren’t many ways to arrange the atoms while keeping the cream in one place and the coffee in another. There are many, many more ways for them to be mixed together, so that is the direction things go in – entropy increases. And this tendency for entropy to increase gives time its arrow.
But if entropy always increases, it means that, in the early universe, near the big bang, the universe was in a very, very special, low-entropy configuration. Why did it start very low? Nobody knows. But we hoped that building a cosmos from the fundamentals of quantum mechanics would offer some pointers.
What did you find?
Unfortunately, we haven’t solved the low-entropy problem here, at least in our current state of the art. If anything, this model makes the problem worse. We make little computer simulations that start the wave function of the universe in a very, very low-entropy state. Why? Because we said so. That is the only reason why.
Maybe there will be an explanation down the road. This is how science works: you make little, incremental improvements.
Does time behave differently in this cyclic universe?
In our model, once the universe has expanded and cooled, you hit thermal equilibrium. The stars burn out, they fall into black holes, the black holes evaporate and you are left with nothing but empty space. Time still exists. Time is fine. But the arrow of time doesn’t exist for most of the history of the universe.
But that isn’t really a problem for the intuition of any observers because there are no observers around. All we have at this point is just empty space.
When time does have an arrow, it always points away from the bounce. The arrow points in opposite directions on one side of the bounce compared with the other side. There will be people living in what you and I call the big crunch. But what we call the big crunch, they would call the big bang.
Where do you hope these insights into entropy and time can take us?
Ultimately, we’re trying to understand quantum gravity. One big obstacle is that there is no detailed experimental data. For instance, we haven’t found the hypothetical particles of gravity called gravitons.
The fact that our universe started in such a low-entropy state is one of the most powerful and informative pieces of data we have. Just by trying to understand how that can possibly arise in a universe governed by the rules of quantum mechanics, we stand to learn an enormous amount about gravity, quantum theory, cosmology and why time works the way it does.
