Boltzmann Brains
This reality is only in your head
It happened in Duino, a rustic place on the Italian coast. The village is perched high on rocky, ragged cliffs overlooking a placid sea. There’s something fairytale about this fresh sun-soaked place with its golden sandy roads and its history of castle building. The yellow Duino castle from the 1300’s is still in use by the local people. The year Ludwig Boltzmann decided to visit with his family, Duino would have been punctuated by chittering open markets where fragrant fruits where piled in wicker baskets and hand kneaded bread cooled down next to lumps of pearly white cheese. It’s 1906 and the ocean flushes up against the quiet village. The water and shore kiss, recede, and kiss again.
Boltzmann has brought his wife and daughter with him on vacation. One can imagine the 62 year old Austrian physicist making some excuse that morning to stay behind at the hotel. His thick greying beard brushes on his wife’s face as he tells her goodbye. Perhaps he holds his daughter’s smaller hands in his. Steady, squinting a little to make up for his bad eyesight. Resolute.
In the previous few years, Boltzmann had been one of the founders of thermodynamics. He made brilliant propositions regarding atomic theory and how the life of atoms affected the properties of larger matter. But Boltzmann had vision that others didn’t. Many of his colleagues refuted the idea that atoms even existed. Much of Boltzmann’s energy was spent defending his ideas and dragging himself out of frightening fits of depression. In that way he held the temperament of an artist — given to beautiful spurts of conversation and brilliance followed by long months of dreadful silence. His doctors supposed he had a nervous disease then named “neurasthenia”. It was characterized by headaches, tiredness, and crippling moments of emotional disturbance.
The windows in Boltzmann’s hotel room muffle the sound of seagulls outside. It’s early September. The wood boards creak under the man’s short and portly body as he steps around the room. While his wife and daughter venture out into the village, Ludwig Boltzmann stays behind to hang himself. There is no note to explain why. It could have been due in large part to the poor way in which his theories were received. But it could have been that Boltzmann was simply tired of having to war with himself, of feeling that rise in his heartbeat when he thought of the inevitable moments of sadness and lunacy that lay ahead. He admitted to the very real possibility of one day losing his mind during a lecture. The same year he committed suicide his doctor had proposed Boltzmann no longer pursue his scientific curiosities.
Boltzmann may not have left a note but he is inscribed forever in the Boltzmann formula for entropy.
The formula describes the second law of thermodynamics. It says that entropy in a closed system must always be increasing until it reaches an equilibrium state. This happens because there are many more ways for a system to be disordered than there are for it to be ordered. Entropy is often worded as the universe tending to be more chaotic but at its heart entropy is about statistics. There are many more disorganized configurations than organized ones so that it’s more likely molecules will be found in a disorganized state. Entropy is at work anytime an object warms up or cools down. Ice cubes melting, or steaming baked bread cooling to room temperature for example. These objects were once in an organized state — the ice cubes being colder than their surroundings and the bread being hotter — but they gradually came into equilibrium with the temperature of their environment. The higher the entropy, the higher the equilibrium. The ice cubes began in a low entropy state and descended into a high entropy one.
But this applies to something much, much grander.
The Big Bang was a moment of low entropy. All the particles of our universe were concentrated in one hot, dense point before erupting into the gargantuan cosmos they’ve become today. Ever since then we have been moving towards higher and higher entropy, meaning we are approaching more and more equilibrium — a prospect which might bring about the death of all life in the universe.
So the entropy of a system always increases. But there are exceptions to this. Statistical fluctuations do, from time to time, result in a system having lower entropy. Organization may have a much smaller chance of manifesting than disorganization does but that chance is still there all the same. Decrease in entropy is improbable, not impossible.
This is where we derive the idea of a Boltzmann brain.
It is far more likely for the universe to be in a state of high entropy. So why, then, did we emerge from a state of such low entropy? One way to solve this is to imagine that the universe is at equilibrium on a larger scale. Our Big Bang was a statistical fluctuation in a region of an otherwise older, higher entropy universe. Some particles by chance came together and created the explosive beginnings to our world. This would imply, too, the multiverse where a low entropy daughter universe arose from a mother universe of higher equilibrium. If this mother universe is infinite then any arrangement of particles capable of happening will happen eventually.
But there is a statistical problem with this. Fluctuations would most likely deviate as little as possible from the overall equilibrium. Instead of creating an entirely new universe laden with sparkling new galaxies and devilish black holes, it’s more likely that only our brains manifested.
A brain, imagining its existence and the existence of the entire universe, complete with memories of a life that never took place. According to this thought experiment it is more probable that an intelligent observer popped into existence with all its knowledge and memories than it is for an entire universe to have been born. The observer only believes it exists in this universe but this universe is merely a figment of the observer’s imagination.
All aspects of one’s self stemming from a simple chance arrangement of particles.
This is paradoxical. As physicists like Sean Carroll have pointed out, the Boltzmann brain theory is self-defeating. Our observations of the world lead us to believe that we cannot trust our observations. All our tinkering with tools and formulas leads us to a universe that’s merely a delusion of our minds. Not only are our memories false but so is our understanding of physics and the logic we use to understand the reality in which we live. It would render us in a state that Boltzmann found at the end of his life — wanting to but unable to do science.
There is also no real way to disprove the theory because any evidence we find against being a Boltzmann brain might be nothing more than part of the statistical fluctuation which generated our mind. It’s also statistically more likely that such a mind would come with pure delusions instead of having actual intelligence.
The idea of Boltzmann brains are meant more as a mental exercise on taking things to the extreme. There’s no reason to believe we are disembodied brains or that any of our memories are artificial. There’s also little reason to entertain the idea considering that we could never approach it scientifically or try to disapprove that it’s real. We are forced into an uncomfortable standstill.
These brains echo much the same feeling as the theory that we are a simulation or a hologram. They are interesting to think about and they very well may be true, but we can’t attach ourselves to these ideas and stunt the progress of our science. Even if all of this is nothing more than a delusion it is better for us to move forward.
The universe today continues its descent into a state of thermal equilibrium, a state Boltzmann likened to being “dead”. But it hasn’t reached this moment yet. Until then we place trust in our observations. There is still a life to live.
