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A Boltzmann brain is a hypothesized self-aware entity which arises due to random fluctuations out of a state of chaos. The idea is named for the physicist Ludwig Boltzmann (1844–1906), who advanced an idea that the known universe arose as a random fluctuation, similar to a process through which Boltzmann brains might arise.

Boltzmann brain paradox

Boltzmann brains are often referred to in the context of the "Boltzmann brain paradox" or "problem". They have also been referred to as "Boltzmann babies." [1]

The concept arises from the need to explain why we observe such a large degree of organization in the universe. The second law of thermodynamics states that the entropy in the universe will always increase. We may think of the most likely state of the universe as one of high entropy, closer to uniform and without order. So why is the observed entropy so low?

Boltzmann proposed that we and our observed low-entropy world are a random fluctuation in a higher-entropy universe. Even in a near-equilibrium state, there will be stochastic fluctuations in the level of entropy. The most common fluctuations will be relatively small, resulting in only small amounts of organization, while larger fluctuations and their resulting greater levels of organization will be comparatively more rare. Large fluctuations would be almost inconceivably rare, but this can be explained by the enormous size of the universe and by the idea that if we are the results of a fluctuation, there is a "selection bias": We observe this very unlikely universe because the unlikely conditions are necessary for us to be here, an expression of the anthropic principle.

This leads to the Boltzmann brain concept: If our current level of organization, having many self-aware entities, is a result of a random fluctuation, it is much less likely than a level of organization which is only just able to create a single self-aware entity. For every universe with the level of organization we see, there should be an enormous number of lone Boltzmann brains floating around in unorganized environments. This refutes the observer argument above: the organization I see is vastly more than what is required to explain my consciousness, and therefore it is highly unlikely that I am the result of a stochastic fluctuation.

The Boltzmann brain paradox is that it is more likely that a brain randomly forms out of the chaos with false memories of its life than that the universe around us would have billions of self-aware brains. The rationale behind this being paradoxical is that, out of chaos, it is more likely for one instance of a complex structure to arise than for many instances of that thing to arise.

This ignores the possibility that the probability of a universe in which a brain pops into existence, without any prior mechanism driving towards its creation, may be dwarfed by the probability of a universe in which there are active mechanisms which lead to processes of development which (given a starting state that is unlikely but not as unlikely as the spontaneous appearance of a brain with no precursor) offer a reasonable probability of producing a species such as ourselves.

In a universe of the latter kind, the scenarios in which a brain can arise are naturally prone to produce many such brains, so the large number of such brains is an incidental detail.

Are You a Boltzmann Brain?

See also

Simulated reality
Dream argument
China Brain
Not to be confused with a brain in a vat


"Disturbing Implications of a Cosmological Constant", Lisa Dyson, Matthew Kleban, and Leonard Susskind, Journal of High Energy Physics 0210 (2002) 011 (at arXiv)
"Can the universe afford inflation?", Andreas Albrecht and Lorenzo Sorbo, Physical Review D 0 (2004) 063528 (at arXiv)
"Is Our Universe Likely to Decay within 20 Billion Years?", Don N. Page, (at arXiv)
"Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem", Andrei Linde, Journal of Cosmology and Astroparticle Physics, 0701 (2007) 022 (at arXiv)
"Spooks in Space", Mason Inman, New Scientist, Volume 195, Issue 2617, 18 August 2007, Pages 26-29
"Big Brain Theory: Have Cosmologists Lost Theirs?", Dennis Overbye, New York Times, 15 January 2008

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