Are We Boltzmann Brains? Which Processes Can Prevent Boltzmann Brains Domination In Future? (Cosmology / Quantum)

So say you’ve got a universe and there’s a kinda empty chunk of it. No planets, no big dust clouds… it’s pretty boring and could be considered “empty”. A few seconds later, there’s just a human brain floating there, in the middle of the space. Of course, like any human brain, it’s got no access to anything it needs to survive, so it stops working immediately.

The main idea is that it’s more likely for a human brain — complete with memories from an entire lifetime — to spawn in the middle of space than it is for science to develop the way it did. That’s the Boltzmann brain theory.

Where This Wacky Idea Exactly Came From?

The idea originated from an argument between physicists (like there aren’t a ton of those!) about the likelihood that science would evolve in the very specific way it did. The theory came (more specifically) from a reductio ad absurdum on Ludwig Boltzmann’s published paper that tried to explain reasons for low entropy in the universe.

According to this paper, while the entropy of a system (its measure of disorder always increases (moving towards disorder), there is some tiny possibility that a fluctuation can bring a system from disorder to order. Thus, it would decrease its entropy, moving it further away from equilibrium.

From the physicists work it follows that, theoretically, after a given period of thousands of years, atoms will come together and randomly form a human brain in the middle of space. This would happen due to random fluctuations that come from thermodynamic equilibrium. Since then, there has been debate on the topic between physicists whether, “we are Boltzmann brains or not”.

How it forms?

After thinking about the possibility of Boltzmann Brains, it turns out that there are actually two options which could result in the creation of a Boltzmann Brain:

  • Through nucleation. This would work if the current, observable universe isn’t a Minkowski space but is instead a de Sitter universe (the difference is the de Sitter is just a cosmological solution to the Einstein theory of relativity, the Minkowski is a combination of the three dimensional Euclidean space and four dimensional manifold).
  • Through quantum fluctuation. This would require a Minkowski vaccuum to occur, and it would simply play upon the idea of quantum fluctuation providing small amounts of energy to isolated activity. Through this random fluctuation of quantum energy, eventually by chance it would be put into the creation of a Boltzmann brain.

We focus completely on “creation of Boltzmann brain through nucleation” and by considering recent study of Ken Olum and colleagues, we are going to discuss why, “we are Boltzmann brains” is a nonsensical conclusion and what actually prevents Boltzmann brains domination in future!

If the dark energy is playing role in expansion of our universe, it will expand forever and will soon approach de Sitter space. So, there’s a possibility that Boltzmann brains can infinitely outnumber ordinary humans, and for this reason, you can’t say that, we are Boltzmann brains.

“Believing that we are Boltzmann brains is a nonsensical conclusion because our observation on which we base this conclusion would have no connection to the actual universe in which we live”, wrote Olum and his collaborators.

But, there is a possibility that, ordinary observers may dominate Boltzmann brains. If we want to know, what to expect in such situations, we need a procedure to regulate infinities and produce a sensible probability distribution. Thus, for this purpose, K. Olum and colleagues adopted scale factor cutoff measure. In this measure, the ratio of Boltzmann brains to ordinary observers in a given vacuum is roughly given by the ratio of the Boltzmann brain nucleation rate to the total decay rate of that vacuum.

“In the scale factor measure, this disaster is avoided when the rate of Boltzmann brain nucleation is smaller than the vaccum decay rate in each vaccum”, wrote Olum and his collaborators.

They found that there are two processes that are not always considered that influence the vacuum decay rate, thereby, preventing Boltzmann brain domination.

The first is the nucleation of small black holes. This process removes volume from the vacuum, and so contributes to total decay rate of vaccum.

“The rate is largest for the smallest black holes. It is always larger than the Boltzmann brain nucleation rate, if the minimum Boltzmann brain mass is larger than the Planck mass. Thus, we should not expect to be Boltzmann brains”, wrote Olum and his collaborators.

The other process is the nucleation of small regions of higher-energy inflating false vacuum. If vacua of high enough energies exist, this process also would prevent Boltzmann brain domination.

“It would be interesting to apply the considerations of our paper to the multiverse models like the one proposed by Vilenkin and colleagues, in which eternal inflation driven by inflating domain walls may still be possible..”, concluded authors of the study.


Reference: Ken D. Olum, Param Upadhyay, and Alexander Vilenkin, “Black holes and up-tunneling suppress Boltzmann brains” Arxiv, 2021. https://arxiv.org/abs/2105.00457


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