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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 Universe 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. The term for this idea was then coined in 2004 by Andreas Albrecht and Lorenzo Sorbo.
The Boltzmann brains concept is often stated as a physical paradox. (It has also been called the "Boltzmann babies paradox".) The paradox states that if one considers the probability of our current situation as self-aware entities embedded in an organized environment, versus the probability of stand-alone self-aware entities existing in a featureless thermodynamic "soup", then the latter should be vastly more probable than the former.
Boltzmann brain paradox
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The Boltzmann brains concept has been proposed as an explanation for why we observe such a large degree of organization in the Universe (a question more conventionally addressed in discussions of entropy in cosmology).
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 are made possible 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.
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 only creates stand-alone self-aware entities. 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. In an infinite universe, the number of self-aware brains that spontaneously and randomly form out of the chaos, complete with false memories of a life like ours, should vastly outnumber the real brains evolved from an inconceivably rare local fluctuation the size of the observable Universe.
The Boltzmann brain paradox is that any observers (self-aware brains with memories like we have, which includes our brains) are therefore far more likely to be Boltzmann brains than evolved brains, thereby at the same time also refuting the selection-bias argument: Why should we accept the anthropic principle, or indeed any argument, if, as we appear to have argued, it just popped up randomly into our Boltzmann brain? This position is cognitively unstable, we cannot both believe it to be true and at the same time have good reasons to believe it to be true.
One class of solutions to the question of why we don't appear to be Boltzmann brains makes use of differing approaches to the measure problem in cosmology: In infinite multiverse theories, the ratio of normal observers to Boltzmann-brain observers depends on how infinite limits are taken. Measures might be chosen to avoid appreciable fractions of Boltzmann brains.
Sean M. Carroll and colleagues have suggested that the formulation of the Boltzmann-brain problem is mistaken. In particular, they claim that a quiescent de Sitter space does not actually have quantum fluctuations, because "Quantum fluctuations require time-dependent histories of out-of-equilibrium recording devices, which are absent in stationary states.":1 Given quantum field theory in curved spacetime, a patch of de Sitter space can form only a small, finite number of Boltzmann brains as it approaches the vacuum.:3–4 This argument relies on the many-worlds interpretation of quantum mechanics, and other interpretations likely would still yield Boltzmann brains.:28
- Albrecht, Andreas; Sorbo, Lorenzo (September 2004). "Can the universe afford inflation?". Physical Review D 70 (6). Bibcode:2004PhRvD..70f3528A. doi:10.1103/PhysRevD.70.063528. Retrieved 16 December 2014.
- "Boltzmann babies in the proper time measure". eScholarship. 2008-07-14. Retrieved 2011-08-22.
- Andrea De Simone; Alan H. Guth; Andrei Linde; Mahdiyar Noorbala; Michael P. Salem; Alexander Vilenkin (14 Sep 2010). "Boltzmann brains and the scale-factor cutoff measure of the multiverse". Phys. Rev. D. doi:10.1103/PhysRevD.82.063520.
- Andrei Linde; Vitaly Vanchurin; Sergei Winitzki (15 Jan 2009). "Stationary Measure in the Multiverse". Journal of Cosmology and Astroparticle Physics (01). doi:10.1088/1475-7516/2009/01/031. Retrieved 8 January 2015.
- Andrei Linde; Mahdiyar Noorbala (9 Sep 2010). "Measure problem for eternal and non-eternal inflation". Journal of Cosmology and Astroparticle Physics (09). doi:10.1088/1475-7516/2010/09/008. Retrieved 8 January 2015.
- Kimberly K. Boddy; Sean M. Carroll; Jason Pollack (1 May 2014). "De Sitter Space Without Quantum Fluctuations". Retrieved 9 January 2015.
- Grossman, Lisa (14 May 2014). "Quantum twist could kill off the multiverse". New Scientist. Retrieved 9 January 2015.
- "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