Boltzmann Brain

Our senses are not fool proof and this is why we take the reliability of our senses as a practical assumption. It is a necessary assumption to make science work — they are essential for the application of the scientific method. The aim of our scientific venture is to use our experiences of the world to construct models. Most of the times, we have competing models. We can evaluate the validity of the models on the basis of their predictive power. But what if we were to use our experiences of the world to construct the best possible model — one that tells us how the world operates — only then to realize that the model predicts we should not trust our own experiences? Where does that leave us?

This is the kind of conundrum that modern cosmology seems to be facing — our best current cosmological model (Cosmological Constant Cold Dark Matter) — that describes the universe we live in — faces the prospect of being internally incoherent. The problem it faces? The so called Boltzmann Brain (BB) problem. The BB is a useful thought experiment that allows us to stretch things to their extreme conclusions to find its pitfalls. It is a somewhat difficult problem to describe without reviewing in full the second law of thermodynamics and revisiting Ludwig Boltzmann’s discussions with his contemporaries. I will try to make it this as simple and brief as possible.

Before Einstein came along, our understanding of the universe was based strictly in terms of Newtonian mechanics. As such, during this time, it was assumed that the universe was eternal with a fixed space-time. However, this presented a problem.
The second law of thermodynamics states that entropy increases over-time. That is to say, things tend to go from order to disorder. When we have a state of maximal entropy (disorder), then we say the given region is in thermal equilibrium. Now back to the problem: if the universe is eternal, then it is possible that the universe is in thermal equilibrium. If that is the case, how is it possible that despite the state of high entropy we have complex living organisms and other highly ordered structures (e.g. planets, stars, galaxies)?

As a response to his contemporaries, Boltzmann offered several strategies to confront this apparent contradiction. One of those strategies that is relevant to our discussion, is the notion that we exist as a result of a rare fluctuation. Given that the second law is a statistical law, meaning that we can only say X is more likely to occur than Y, then there is nothing necessarily preventing a state of high entropy to spontaneously change into a state of lower entropy. This is extremely unlikely but since we are using the language of probabilities, it is not impossible.
Thus Boltzmann reasoned, if the universe is eternal, it is possible that as a whole it is currently in thermal equilibrium. However, a random fluctuation could have caused a particular region of our space to become more ordered which led to the formation of our galaxy, stars, planets and life — highly ordered structures. This is where Boltzmann seemed to have made the first application of the anthropic argument: it is natural that we find ourselves in an atypical region of space because that part of space allows for our existence.

However, there was a fatal flaw in Boltzmann’s reasoning — anthropic reasoning doesn’t require the formation of entire galaxies let alone a single galaxy — all it requires is the existence of an intelligent observer. Given that the fluctuations that result into low entropy are extremely rare and fluctuations into even lower entropy states are exponentially rarer, the Boltzmann-fluctuation scenario seems to predict that we should be living in a universe with the highest possible entropy.
So what exactly is a Boltzmann brain? It is a configuration of matter that is as close as possible to being in thermal equilibrium with its local environment all the while still qualifying as an intelligent observer. It is in a sense the spontaneous existence of a disembodied brain.

Although such a fluctuation is rare, it is actually incredibly far less rare than an embodied observer or for that matter, a whole universe. Thus at the very minimum, a fluctuation would most likely lead to Boltzmann Brains — disembodied and alone.
What complicates the current cosmological model is that our universe is expanding. Classically, there are two outcomes: the universe will eventually collapse or it will expand forever. Given that we have evidence that the universe’s expansion is accelerating, this suggests that it will reach a time when space will empty out of particles. The BB problem is not an issue here. This is because even if a fluctuation was to occur, there are no particles that can assemble to create them. However, quantum mechanics drastically changes this picture. Even though classically the universe will evolve to zero temperature, quantum mechanically it asymptotes to a nonzero temperature (I copied this from Sean Carroll’s paper: Why Boltzmann Brains Are Bad). In other words, quantum effects such as virtual particles or entanglement will continue to exist — this is somewhat similar to the eternal universe that Boltzmann envisioned, that is, an eternal universe with random fluctuating particles.

We know we are not a BB because the world it predicts is vastly different than ours. But the problem here is that one can argue we are spontaneous BB with past memories and on and on it goes. If a model predicts there are more BB’s than ordinary observers — which is what we think we are — then there is something wrong with the model. There are some ways of resolving this problem but no one is entirely sure as to what strategy is best. Although the BB problem is extreme solipsism, I think there is a plausible way around it. I like Sean Carroll’s argument that the concept is cognitively unstable. The whole problem puts us in a predicament. If we are a BB then we cannot trust our knowledge. If then we are using our experience and reasoning skills to create a model that predicts we might be a BB, we have no reason to accept that model. Thus the randomly fluctuating universe is self-undermining. We should reject a model that predicts we are BB not because we can reasonably demonstrate we are not BB’s, but rather because such models are cognitively unstable. We can’t logically accept such models while at the same time concluding we can’t trust them. What do we make of the standard cosmological model? Perhaps at best all we can say is that it is incomplete.


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