Boltzbrain

Boltzbrain, a villain of the Paradox Parlour, is a lone brain that has flickered into being out of random thermal noise in the heat death of the Universe.

The Physics

In the 1890s Ludwig Boltzmann suggested that our ordered world might be a rare fluctuation in a universe otherwise in thermal equilibrium. The difficulty is that a small fluctuation is far more likely than a big one. A single brain, complete with false memories, needs a much smaller drop in entropy than a whole ordered universe, so in such a picture most observers would be lone “Boltzmann brains”. Andreas Albrecht and Lorenzo Sorbo (Phys. Rev. D 70, 063528, 2004) discussed it as the so-called “Boltzmann's brain” paradox.

P ∝ exp(ΔS/k_B)

• P: relative probability of a fluctuation
• ΔS: entropy change of the fluctuation, negative for a fluctuation into order (J/K)
• k_B: Boltzmann constant, 1.380 649 × 10⁻²³ J/K exactly in the 2019 SI

This is Einstein's fluctuation formula. Since ΔS is negative and huge compared with k_B, the probability is fantastically small, yet in an eternal universe it is never zero.

Honest caveat: Nobody claims such brains exist. The argument is a reductio: a cosmological model in which typical observers are Boltzmann brains is judged to be wrong, because it would make our own observations unreliable. Whether our Universe faces the problem is open. It depends on whether a de Sitter (dark-energy) vacuum truly has thermal fluctuations of this kind, how long it lasts, and how to count observers in an infinite universe (the measure problem). Physicists disagree on all three.

On the sticker

Boltzbrain, a glowing violet brain on a skeletal body, holds a single bright orb in a grey sea of noise. Printed text: BOLTZBRAIN with the line P ∝ exp(ΔS/k). Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.