« January 2008 | Main | March 2008 »

February 2008

February 13, 2008

Boltzmann Brain Paradox

Digital Brain
© iStockphoto.com Sebastian Kaulitzk

Random Fluctuation Created Universe

Ludwig Eduard Boltzmann was an Austrian physicist who made important contributions to the area of statistical thermodynamics. He lived in the last half of the 19th century and proposed that the low-entropy (high order) universe that we live in is the result of a random fluctuation in a larger, higher entropy (lower order) metaverse.

Quantum Fluctuations

Although Boltzmann's proposal was made in advance of quantum mechanics, his idea is similar to modern day theories that the universe arose from a quantum vacuum fluctuation. Quantum mechanics predicts that particles can spontaneously arise from the vacuum if they are short-lived. Even in a perfect vacuum, pairs of particles and anti-particles are constantly being created and destroyed. This is possible because the total energy of the particle anti-particle pairs is zero.

In fact, the total energy of the universe appears to be zero [Stephen Hawking, A Brief History of Time, chapter 8]. Particles have positive energy, and the negative energy represented by the gravitational field of the entire universe appears to be exactly enough to cancel out the positive energy of the particles.


This idea leads to the Boltzmann Brain Paradox. In a metaverse that is larger than ours, random fluctuations of the size to create a universe such as our own will happen. Due to the size and number of particles in such a universe, these fluctuations will be exceedingly rare. The anthropic principal - the fact universes will only be observed when they are hospitable to observers - makes the amount of time between such fluctuations meaningless. These fluctuations could be happening every quadrillion years, or once every googolplex number of years. Fluctuations of a much smaller magnitude that simply create one fully formed brain for a brief amount of time should be happening with enormously higher frequency than universe-creating fluctuations. Such brains would be the smallest possible creations that would give rise to a sentient observer and are called Boltzmann Brains. The fact that such brains do not appear to exist is called the Boltzmann Brain Paradox.

There are a number of ways out of this paradox. One of the base assumptions could be false. Perhaps there is no metaverse or such quantum fluctuations do not happen on large scales.

Or, it possible that the concept of the Boltzmann Brain is true and you are the only sentient observer in the universe right now, complete with false memories of a life which did not exist. False inputs to your brain only make it appear that there are other observers with you. If true, it's possible that you will cease to exist in just a ...

Suggested Posts

Are You Living in a Computer Simulation?
Why Are We Alone? The Fermi Paradox
Speculations on Gödel's Incompleteness Theorems, the Halting Problem, and the Simulation Argument

Chris K. Haley, NestedUniverse.net. Subscribe Get free RSS or email updates here.