Quantum mechanics for babies pdf is observed to be in a highly improbable non-equilibrium state because only when such states randomly occur can brains exist to be aware of the Universe. All that is required is the brain. Since simple organisms ought to be easier to form than complex ones, the vast majority of intelligences in the universe ought to consist of these disembodied but self-aware “Boltzmann brains”. Our observed universe is very far from statistical equilibrium: we are “living beings on a tepid planet orbiting a hot star”.
How did it get this way? 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 inevitably occur if a universe lasts infinitely long. 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 that only creates stand-alone self-aware entities. The number of self-aware brains that spontaneously and randomly form out of the chaos, complete with memories of a life like ours, should vastly outnumber the brains evolved from an inconceivably rare local fluctuation the size of the observable universe. The idea that the thermodynamic arrow of time arose from a gigantic fluctuation leads to an amusing form of solipsism.
From the standpoint of entropy, I, sitting at my keyboard typing these lines, am a pretty big fluctuation. A tree that I remember seeing is also a big fluctuation. You, reading this, should similarly doubt the existence of the writer. Boltzmann brains than evolved brains. This suggests a problem either with current cosmological theories or the anthropic principle.
Measures might be chosen to avoid appreciable fractions of Boltzmann brains. In particular, as remarked above, because our universe appears to exhibit only a finite past history, the Boltzmann paradox requires the past formation of our universe to be included in the stochastic fluctuation. Hence the universe cannot be the result of purely stochastic fluctuations at equilibrium of the kind that Boltzmann assumed. A given patch of de Sitter space can form only a small, finite number of Boltzmann brains as it approaches the vacuum. However, the paradox remains for other interpretations of quantum mechanics. Can the universe afford inflation?