Facts So Romantic

Can Many-Worlds Theory Rescue Us From Boltzmann Brains?

Boltzmann’s theory leads to a paradox, where the very scientific assumption that we can trust what we observe leads to the conclusion that we can’t trust what we observe.Image by Chaosophia218 / Tumblr

Can you trust the world to be consistent? Scientists don’t have much choice. They need to assume that objective observations of the universe can be trusted. This assumption has allowed us to develop powerful theories about the inner workings of the cosmos, but it has, paradoxically, also shown us the possibility that we might be deceived after all. It’s an idea known as “Boltzmann’s brain,” and it stems from some of the deepest questions in physics.

“The problem arises when we start with our experience of the world, use it to construct our best theory of how the world actually operates, and then realize that this theory itself predicts that our sense data are completely unreliable,” writes Sean Carroll, a Caltech theoretical physicist, in a paper published in February. He went with the title “Why Boltzmann Brains Are Bad” because the theories that predict them are, as a result, “cognitively unstable: they cannot simultaneously be true and justifiably believed.” They lead us to think that the universe could simply be our mind thinking it is part of a vast cosmos.

Ludwig Boltzmann, despite Carrol’s title, had a good brain. He is perhaps most famous for developing, in 1872, the kinetic theory of gases. Boltzmann’s theory not only explained how heat and energy are the result of molecular interactions, it gave a clear definition to a concept known as entropy. Entropy is often described as a measure of the disorder of a system, and the second law of thermodynamics states that the entropy of a system can never decrease.

A Boltzmann brain existing is more probable than a universe existing.

In physics, the pressure, temperature, and volume of a gas are known as the state of a gas. In Boltzmann’s model, any arrangement of atoms or molecules that produces this state is known as a microstate of the gas. Since the state of a gas depends on the overall motion of its atoms or molecules, many microstates can produce the same state. Boltzmann showed that entropy can be defined as the number of microstates a state has. The more microstates, the greater the entropy. This explains why the entropy of a system tends to increase. Over time, a gas is more likely to find itself in a state with lots of possible microstates than one with few microstates.

Since entropy increases over time, the early universe must have had much lower entropy. This means the Big Bang must have had an extraordinarily low entropy. But why would the primordial state of the universe have such low entropy? Boltzmann’s theory provides a possible answer. Although higher entropy states are more likely over time, it is possible for a thermodynamic system to decrease its entropy. For example, all the air molecules in a room could just happen to cram together in one corner of the room. It isn’t very likely, but, statistically, it is possible. The same idea applies to the universe as a whole: If the primordial cosmos was in thermodynamic equilibrium, there is a small chance that things came together to create an extremely low entropy state. That state then triggered the Big Bang and the universe we see around us.

However, if the low entropy of the Big Bang was just due to random chance, that leads to a problem. Infinite monkeys might randomly type out the Complete Works of Shakespeare, but they would be far more likely to type out the much shorter Gettysburg Address. Likewise, a low entropy Big Bang could arise out of a primordial state, but if the universe is a collection of microstates, then it is more likely to find itself in a conscious state that thinks it is in a universe rather than the entire physical universe itself. That is, a Boltzmann brain existing is more probable than a universe existing. Boltzmann’s theory leads to a paradox, where the very scientific assumption that we can trust what we observe leads to the conclusion that we can’t trust what we observe.

Although it’s an interesting paradox, most astrophysicists don’t think Boltzmann brains are a real possibility. (Carroll, for instance, mercilessly deems them “self-undermining and unworthy of serious consideration,” on account of their cognitive instability.) Instead they look to physical processes that would solve the paradox. The physical processes that give rise to the Boltzmann brain possibility are the vacuum energy fluctuations intrinsic to quantum theory—small energy fluctuations can appear out of the vacuum. Usually they aren’t noticeable, but under certain conditions these vacuum fluctuations can lead to things like Hawking radiation and cosmic inflation in the early universe. These fluctuations were in thermal equilibrium in the early universe, so they follow the same random Boltzmann statistics as the primordial cosmos, making them also more likely to give rise to a Boltzmann brain rather than the universe we seem to be in. 

But it turns out that, since the universe is expanding, these apparent fluctuations might not be coming from the vacuum. Instead, as the universe expands, the edge of the observable universe causes thermal fluctuations to appear, much like the event horizon of a black hole gives rise to Hawking radiation. This gives the appearance of vacuum fluctuations, from our point of view. The true vacuum of space and time isn’t fluctuating, so it cannot create a Boltzmann brain.

The idea, from Caltech physicist Kimberly Boddy, and colleagues, is somewhat speculative, and it has an interesting catch. The argument that the true vacuum of the universe is stationary relies on a version of quantum theory known as the many-worlds formulation. In this view, the wave function of a quantum system doesn’t “collapse” when observed. Rather, different outcomes of the quantum system “decohere” and simply evolve along different paths. Where once the universe was a superposition of different possible outcomes, quantum decoherence creates two definite outcomes. Of course, if our minds are simply physical states within the cosmos, our minds are also split into two outcomes, each observing a particular result.

In solving the paradox of Boltzmann brains, we might have to face the reality that each of us are not as unique as we appear. The many-worlds model could also be called the many-minds model. Throughout a many-worlds universe there would be minds very like ours, each with slightly different experiences, and each having as much right to be called “us” as we do.

Brian Koberlein is an astrophysicist and physics professor at Rochester Institute of Technology. He writes about astronomy and astrophysics on his blog One Universe at a Time. Find him on Twitter @BrianKoberlein.

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