Boltzmann brain

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Ludwig Boltzmann, after whom Boltzmann brains are named

A Boltzmann brain is a hypothesized self-aware entity that arises due to random fluctuations out of a state of chaos. The idea is named after the Austrian 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 idea that a disembodied brain seems to require a smaller—hence more probable—fluctuation than intelligent beings similar to humans was proposed by Lawrence Schulman (de) in 1997,[1] and the term for this idea was coined in 2004 by Andreas Albrecht and Lorenzo Sorbo.[2]

The Boltzmann brains concept is often stated as a physical paradox. It has also been called the Boltzmann babies paradox.[3] The paradox is that to contemplate the universe, intelligence is necessary; however, much of the machinery that humans use to think (complex organs, muscles, etc.) are not. 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".

Boltzmann brain paradox[edit]

The Boltzmann brain concept is a specific instance of more general problems associated with the notion of entropy in cosmology. Our observed universe is very far from statistical equilibrium: we are "living beings on a tepid planet orbiting a hot star".[4] How did it get this way?

Boltzmann proposed that the state of our observed low-entropy universe (which includes our existence) is a random fluctuation in a higher-entropy universe. Even in a near-equilibrium state, there will be stochastic fluctuations in the state of the system. 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.[5][page needed] Large fluctuations would be almost inconceivably rare, but inevitably occur if a universe lasts infinitely long. Even if the universe does not have an infinitely long past, modern cosmological theories of the Big Bang do suppose that the latter occurred via stochastic fluctuations in a larger meta-universe; the paradox is retained by incorporating our brief-but-finite past into the random fluctuation.[2]

Furthermore, there is a "selection bias": we observe our very unlikely universe because those unlikely conditions are necessary for us to be here. This is 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 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. To quote Lawrence S. Schulman:

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. It would be a smaller fluctuation, entropy-wise (recalling that entropy is extensive), not to have the tree, but to change my brain slightly and create the memory of that tree. Therefore, in terms of likely or unlikely fluctuations (and that's what entropy measures) it would be far more likely that the tree doesn't exist. You, reading this, should similarly doubt the existence of the writer.

— L. S. Schulman, "Time's Arrows and Quantum Measurement"[1]

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. This suggest a problem either with current cosmological theories or the anthropic principle.

Proposed resolutions[edit]

One class of solutions to the question 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.[6][7][8]

If we assume the many-worlds interpretation of quantum mechanics, Sean M. Carroll and colleagues have suggested that the formulation of the Boltzmann-brain problem is mistaken.[9][10] 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. Carroll's argument relies on the precise formulation of this claim: the formation of the universe was a fluctuation in systems described by quantum mechanics. Those fluctuations behave very differently from Boltzmann (entropic) fluctuations. In particular, quantum fluctuations rely on the existence of an observer: a measurement apparatus that exists in a non-thermodynamic-equilibrium state. However, the most common model for the universe before the Big Bang is empty de Sitter space in thermodynamic equilibrium, which has no such observers by definition. Hence the universe cannot be the result of purely stochastic fluctuations at equilibrium of the kind that Boltzmann assumed.[9]:3, 27 A given patch of de Sitter space can form only a small, finite number of Boltzmann brains as it approaches the vacuum.[9]:3–4 Note, however, that this argument contradicts "conventional wisdom" among cosmologists[9]:3 and is not universally agreed-upon, even among Everett cosmologists.[11]

In de Broglie–Bohm quantum mechanics, the paradox is also disallowed, for the same reason.[4] However, the paradox remains for other interpretations of quantum mechanics.[9]:29

See also[edit]

Notes[edit]

  1. ^ a b Schulman, Lawrence S. (1997). Time's Arrows and Quantum Measurement (1997 ed.). Cambridge: Cambridge University Press. p. 154. ISBN 9780511622878. 
  2. ^ a b Albrecht, Andreas; Sorbo, Lorenzo (September 2004). "Can the universe afford inflation?". Physical Review D. 70 (6). Bibcode:2004PhRvD..70f3528A. arXiv:hep-th/0405270 Freely accessible. doi:10.1103/PhysRevD.70.063528. Retrieved 16 December 2014. 
  3. ^ "Boltzmann babies in the proper time measure". eScholarship. 2008-07-14. Retrieved 2011-08-22. 
  4. ^ a b Goldstein, Sheldon; Struyve, Ward; Tumulka, Roderich. "The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations". pp. 11–12. arXiv:1508.01017 Freely accessible. 
  5. ^ Schroeder, Daniel (2000). Introduction to Thermal Physics. New York: Addison Wesley Longman. ISBN 0-201-38027-7. 
  6. ^ 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. 82. Bibcode:2010PhRvD..82f3520D. arXiv:0808.3778 Freely accessible. doi:10.1103/PhysRevD.82.063520. 
  7. ^ Andrei Linde; Vitaly Vanchurin; Sergei Winitzki (15 Jan 2009). "Stationary Measure in the Multiverse". Journal of Cosmology and Astroparticle Physics. 2009 (01): 031. Bibcode:2009JCAP...01..031L. arXiv:0812.0005 Freely accessible. doi:10.1088/1475-7516/2009/01/031. 
  8. ^ Andrei Linde; Mahdiyar Noorbala (9 Sep 2010). "Measure problem for eternal and non-eternal inflation". Journal of Cosmology and Astroparticle Physics. 2010 (09): 008. Bibcode:2010JCAP...09..008L. arXiv:1006.2170 Freely accessible. doi:10.1088/1475-7516/2010/09/008. 
  9. ^ a b c d e Kimberly K. Boddy; Sean M. Carroll; Jason Pollack (1 May 2014). "De Sitter Space Without Quantum Fluctuations". pp. 3–4. arXiv:1405.0298 Freely accessible. 
  10. ^ Grossman, Lisa (14 May 2014). "Quantum twist could kill off the multiverse". New Scientist. Retrieved 9 January 2015. 
  11. ^ Wallace, David (2012). The Emergent Multiverse: Quantum Theory according to the Everett Interpretation. Oxford University Press. 

Further reading[edit]

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