Theoretical Physics: Dissecting The Boltzmann Brain Paradox

With this advancement in modern technology, we are able to replicate the cognitive abilities of our brains in artificial intelligence (AI).

So, imagine that somewhere in the universe, artificial brains are created, and everything those brains contain, from their perspective and ideas to their origin and memories, is artificially created. Yet, those brains will perceive everything they have ever known to be real.

With that being said, how would we know that we are not the same brains that are artificially made? How would we know we are not a Boltzmann brain? In this article, we will find out what the Boltzmann brain is all about and explore the Boltzmann brain paradox further.

What is the Boltzmann brain paradox?

The Boltzmann brain, named after Ludwig Boltzmann, an Austrian physicist, is a thought experiment that suggests that instead of the entire universe coming into existence just as we have always known, it might be more probable for an individual brain to emerge out of nowhere, completely equipped with memories.

Based on the theories of thermodynamics, he stated that the universe was not as chaotic as what fellow physicists thought. Even after the universe has reached a featureless and spread-out state of thermal equilibrium, it would still occasionally fluctuate to a low-entropy state. What does that mean?

The Second Law of Thermodynamics states that the disorder of a system, also known as entropy, will either increase or stay the same but never decrease. However, Boltzmann’s theory suggests otherwise.

The catch in the concept of entropy

Boltzmann’s brain paradox suggests that while the probability of the system’s entropy staying the same or increasing is definite, it does not mean that the probability of the entropy decreasing is absolute zero. It just is too small for realistic systems to realise such that it is ignored.

To put it simply, if you were told that the chances of a green ball turning blue is one in a billion and you had 20 green balls, you could only attempt 20 times to change that green ball blue. So, technically, the chances of you succeeding are probably zero. However, what if you had an infinite system? Things could be different then.

The buildup to the Boltzmann brain paradox

Physicists then realised that if the universe contains an infinite number of particles, there would be minimally one possibility that the particles would be able to make something structured rather than being in a random orientation.

Boltzmann used the example of an infinitely old universe, stating that at a single point, every randomly organised particle will have to come together to form a structured system – a.k.a. the Big Bang!

So, are we all a Boltzmann brain?

It is funny how, even before Einstein’s theory of general relativity, people were already debating about the universe’s origin. While most knew that they were not a Boltzmann’s brain, it still struck a nerve within them, sending them into disarray as they began to research the possibility of one being a Boltzmann’s brain.


Now, before we all fall into a state of existential crisis, many scientists who have studied the cosmological models that “prove” the Boltzmann brain paradox have come to the conclusion that they are highly unstable and, therefore, cannot be considered seriously.

However, one question remained. What was the universe like before the Big Bang? Was there really nothing? Or was there a dying universe that led to the coming together of randomly organised particles, causing the development of a Big Bang? At the end of the day, that sounds a whole lot like the Boltzmann brain paradox.

Nevertheless, while this indeed sounds complex, it just shows how broad physics can be and how interesting the subject can be. If that is what keeps you going, and you want to further that interest, then look no further than Physics Tuition. As one of Singapore’s leading physics tuition centres, we aim to spur our students to excel in the subject with interesting classes. Contact us to find out more!