171:, eventually a very rare thermal fluctuation will occur where atoms bounce off each other in exactly such a way as to form a substructure equivalent to our entire observable universe. Boltzmann argues that, while most of the universe is featureless, humans do not see those regions because they are devoid of intelligent life; to Boltzmann, it is unremarkable that humanity views solely the interior of its Boltzmann universe, as that is the only place where intelligent life lives. (This may be the first use in modern science of the
209:, Sean M. Carroll, and Matthew C. Johnson. Rather, it would form in a sequence of smaller fluctuations that would look like the brain's decay path run in reverse. Boltzmann-style thought experiments generally focus on structures like human brains that are presumably self-aware observers. However, smaller structures that minimally meet the criteria are vastly and exponentially more common than larger structures; a rough analogy is how the odds of a single real English word showing up when one shakes a box of
278:). Quantum mechanics heavily favors smaller fluctuations that "borrow" the least amount of energy from the vacuum. Typically, a quantum Boltzmann brain would suddenly appear from the vacuum (alongside an equivalent amount of virtual antimatter), remain only long enough to have a single coherent thought or observation, and then disappear into the vacuum as suddenly as it appeared. Such a brain is completely self-contained, and can never radiate energy out to infinity.
159:; therefore, the Second Law, which is always observed to increase entropy, is unlikely to be statistical. To counter Zermelo's argument, Boltzmann advanced two theories. The first theory, now believed to be the correct one, is that the universe started for some unknown reason in a low-entropy state. The second and alternative theory, published in 1896 but attributed in 1895 to Boltzmann's assistant
500:
telescopes", "observers who have a memory of coherent experiences", or "observers who have the same series of experiences as me", also vastly outnumber "normal observers". Therefore, under most models of consciousness, it is unclear that one can reliably conclude that oneself is not such a "Boltzmann observer", in a case where
Boltzmann brains dominate the universe. Even under "
20:
438:
in less than 20 billion years, then infinite
Boltzmann nucleation is avoided. (If the average local false vacuum decay rate is over 20 billion years, Boltzmann brain nucleation is still infinite, as the universe increases in size faster than local vacuum collapses destroy the portions of the universe
356:
states "We're not arguing that
Boltzmann Brains exist—we're trying to avoid them." Carroll has stated that the hypothesis of being a Boltzmann brain results in "cognitive instability". Because, he argues, it would take longer than the current age of the universe for a brain to form, and yet it thinks
340:
years. A typical nucleated
Boltzmann brain will cool off to absolute zero and eventually completely decay, as any isolated object would in the vacuum of space. Unlike the quantum fluctuation case, the Boltzmann brain will radiate energy out to infinity. In nucleation, the most common fluctuations are
507:
As stated earlier, most
Boltzmann brains have "abnormal" experiences; Feynman has pointed out that, if one knows oneself to be a typical Boltzmann brain, one does not expect "normal" observations to continue in the future. In other words, in a Boltzmann-dominated universe, most Boltzmann brains have
126:
The
Boltzmann brain gained new relevance around 2002, when some cosmologists started to become concerned that, in many theories about the universe, human brains are vastly more likely to arise from random fluctuations; this leads to the conclusion that, statistically, humans are likely to be wrong
483:
theories, the ratio of normal observers to
Boltzmann brains depends on how infinite limits are taken. Measures might be chosen to avoid appreciable fractions of Boltzmann brains. Unlike the single-universe case, one challenge in finding a global solution in eternal inflation is that all possible
205:"heat death", given enough time, every possible structure (including every possible brain) will presumably get formed via random fluctuation, the timescale of which is related to the Poincaré recurrence time. A Boltzmann brain (or body or world) need not fluctuate suddenly into existence, argue
499:
In
Boltzmann brain scenarios, the ratio of Boltzmann brains to "normal observers" is astronomically large. Almost any relevant subset of Boltzmann brains, such as "brains embedded within functioning bodies", "observers who believe they are perceiving 3 K microwave background radiation through
421:
with a cosmological constant, and starting from any finite spatial slice, the number of "normal" observers is finite and bounded by the heat death of the universe. If the universe lasts forever, the number of nucleated
Boltzmann brains is, in most models, infinite; cosmologists such as
215:
letters are greater than the odds that a whole
English sentence or paragraph will form. The average timescale required for the formation of a Boltzmann brain is vastly greater than the current age of the universe. In modern physics, Boltzmann brains can be formed either by
378:, do not count as observers. Quantum fluctuations are easier to exclude than nucleated brains, as quantum fluctuations can more easily be targeted by straightforward criteria (such as their lack of interaction with the environment at infinity).
385:
in quantum mechanics would show that some vacuum states have no dynamical evolution and cannot support nucleated brains, nor any other type of observer. Some cosmologists believe that a better understanding of the degrees of freedom in the
193:. By 2004, physicists had pushed Eddington's observation to its logical conclusion: the most numerous observers in an eternity of thermal fluctuations would be minimal "Boltzmann brains" popping up in an otherwise featureless universe.
484:
string landscapes must be summed over; in some measures, having even a small fraction of universes permeated with Boltzmann brains causes the measure of the multiverse as a whole to be dominated by Boltzmann brains.
504:" models of consciousness, Boltzmann observers living in a consistent Earth-sized fluctuation over the course of the past several years outnumber the "normal observers" spawned before a universe's "heat death".
182:
pointed out that, because a large fluctuation is exponentially less probable than a small fluctuation, observers in Boltzmann universes will be vastly outnumbered by observers in smaller fluctuations. Physicist
408:
states: "I am confident that I am not a Boltzmann brain. However, we want our theories to similarly concur that we are not Boltzmann brains, but so far it has proved surprisingly difficult for them to do so".
1250:
That discrepancy means that if we truly are Boltzmann brains in an old universe, then our perceptions are befuddled, too. "We'd have no reason to believe that our memories of the past are accurate," says
86:
to spontaneously form literally any structure of any degree of complexity, including a functioning human brain. The scenario initially involved only a single brain with false memories, but physicist
1391:
Andrea De Simone; Alan H. Guth; Andrei Linde; Mahdiyar Noorbala; Michael P. Salem; Alexander Vilenkin (14 September 2010). "Boltzmann brains and the scale-factor cutoff measure of the multiverse".
508:"abnormal" experiences, but most observers with only "normal" experiences are Boltzmann brains, due to the overwhelming vastness of the population of Boltzmann brains in such a universe.
352:
The consensus amongst cosmologists is that some yet-to-be-revealed error is hinted at by the surprising calculation that Boltzmann brains should vastly outnumber normal human brains.
1797:
1288:
Boddy, Kimberly K., Sean Carroll, and Jason S. Pollack. "Why Boltzmann brains do not fluctuate into existence in the de Sitter vacuum." The philosophy of cosmology (2017): 288-240.
676:
357:
that it observes that it exists in a younger universe, and thus this shows that memories and reasoning processes would be untrustworthy if it were indeed a Boltzmann brain.
109:
seemed to predict. He offered several explanations, one of them being that the universe, even after it had progressed to its most likely spread-out and featureless state of
1807:
338:
268:
371:
journalist summarizes that "The starting point for our understanding of the universe and its behavior is that humans, not disembodied brains, are typical observers".
491:
measure that suffer from an extreme "youngness" problem, the typical observer is a "Boltzmann baby" formed by rare fluctuation in an extremely hot, early universe.
298:. In a de Sitter vacuum (but not in a Minkowski vacuum), a Boltzmann brain can form via nucleation of non-virtual particles gradually assembled by chance from the
1711:
1299:
619:
1079:
Aguirre, Anthony; Carroll, Sean M.; Johnson, Matthew C. (2012-02-17). "Out of equilibrium: understanding cosmological evolution to lower-entropy states".
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as close to thermal equilibrium overall as possible given whatever arbitrary criteria are provided for labeling a fluctuation a "Boltzmann brain".
1368:
Boddy, K. K., & Carroll, S. M. (2013). Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains?. arXiv preprint arXiv:1308.4686.
1006:
1755:
487:
The measurement problem in cosmology also grapples with the ratio of normal observers to abnormally early observers. In measures such as the
344:
Theoretically a Boltzmann brain can also form, albeit again with a tiny probability, at any time during the matter-dominated early universe.
105:(1844–1906), who, in 1896, published a theory that tried to account for the fact that the universe is not as chaotic as the budding field of
1341:
541:
163:, is the "Boltzmann universe" scenario. In this scenario, the universe spends the vast majority of eternity in a featureless state of
649:
892:
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476:
One class of solutions to the Boltzmann brain problem makes use of differing approaches to the measure problem in cosmology: in
189:
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worry that this would make it seem "infinitely unlikely for us to be normal brains". One caveat is that if the universe is a
398:
152:
697:
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148:
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132:
1377:
Carlip, S. (2007). Transient observers and variable constants or repelling the invasion of the Boltzmann's brains.
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362:
236:
By one calculation, a Boltzmann brain would appear as a quantum fluctuation in the vacuum after a time interval of
164:
127:
about their memories of the past and in fact are Boltzmann brains. When applied to more recent theories about the
1792:
374:
Some argue that brains produced via quantum fluctuation, and maybe even brains produced via nucleation in the
1497:
Andrei Linde; Mahdiyar Noorbala (9 September 2010). "Measure problem for eternal and non-eternal inflation".
565:
1444:
Andrei Linde; Vitaly Vanchurin; Sergei Winitzki (15 January 2009). "Stationary Measure in the Multiverse".
459:
1144:
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443:). Proposed hypothetical mechanisms to destroy the universe within that timeframe range from superheavy
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and the development of the universe. Over a sufficiently long time, random fluctuations could cause
937:
577:
544: – Tendency for maximum complexity to increase over time, though without any overall direction
517:
382:
217:
172:
117:) state such as the universe in which we find ourselves. Boltzmann brains were first proposed as a
110:
1219:
Bousso, R., Freivogel, B., & Yang, I. S. (2008). Boltzmann babies in the proper time measure.
1035:
Linde, A. (2007). Sinks in the landscape, Boltzmann brains and the cosmological constant problem.
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that will eventually completely dissipate, then infinite Boltzmann nucleation is also avoided.
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was absolute rather than statistical. Zermelo bolstered his theory by pointing out that the
102:
23:
1550:
Bousso, R.; Freivogel, B. (2007). "A paradox in the global description of the multiverse".
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74:
thought experiments, which are about perception and thought, Boltzmann brains are used in
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90:
pointed out that, in a fluctuating universe, the scenario works just as well with entire
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1315:"Physicist Brian Greene: 'Factual information is not the right yardstick for religion'"
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106:
91:
79:
71:
286:
Current evidence suggests that the vacuum permeating the observable universe is not a
123:
response to this explanation by Boltzmann for the low-entropy state of our universe.
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402:
367:
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Matthew Davenport; Ken D. Olum (2010). "Are there Boltzmann brains in the vacuum?".
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1706:
1705:"Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem",
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Boltzmann Brains, Matrioshka Brains, Simulation Hypothesis, and a Concept of God
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54:
50:
1698:"Is Our Universe Likely to Decay within 20 Billion Years?", Don N. Page, (
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559:
477:
211:
83:
46:
306:. One estimate for the average time required until nucleation is around
1716:
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956:
885:
Anthropic Bias: Observation Selection Effects in Science and Philosophy
739:
114:
19:
1636:
1007:"Doomsday and disembodied brains? Tiny particle rules universe's fate"
95:
1735:"Big Brain Theory: Have Cosmologists Lost Theirs?", Dennis Overbye,
592: – Philosophical idea that only one's own mind is sure to exist
859:
1677:"Disturbing Implications of a Cosmological Constant", Lisa Dyson,
1511:
1458:
1405:
1182:
1093:
867:
454:
If no cosmological constant exists, and if the presently observed
155:
shows statistical entropy in a closed system must eventually be a
49:, rather than for the entire universe to come about in the manner
38:
18:
1235:"Universes that spawn 'cosmic brains' should go on the scrapheap"
1297:
Garriga, J., & Vilenkin, A. (2009). Holographic multiverse.
168:
586: – Hypothesis that reality could be a computer simulation
1637:"Does my total evidence support that I'm a Boltzmann Brain?"
187:
published a similar counterargument within his widely read
113:, would spontaneously fluctuate to a more ordered (or low-
718:
Dyson, Lisa; Kleban, Matthew; Susskind, Leonard (2002).
908:
Feynman, Richard P. (1963–1965). "Order and entropy".
520: – Hypothesis about sapient life and the universe
815:
Nebulous Earth: A History of Modern Planetary Physics
495:
Identifying whether oneself is a "Boltzmann observer"
312:
242:
131:, Boltzmann brain arguments are part of the unsolved
720:"Disturbing Implications of a Cosmological Constant"
381:
Carroll believes that a better understanding of the
1342:"Death by Higgs rids cosmos of space brain threat"
1145:"Big Brain Theory: Have Cosmologists Lost Theirs?"
787:"Big Brain Theory: Have Cosmologists Lost Theirs?"
332:
262:
45:, complete with a memory of having existed in our
656:(Podcast). Sean Carroll. Event occurs at 1:47:20
626:(Podcast). Sean Carroll. Event occurs at 1:01.47
447:to a heavier-than-observed top quark triggering "
270:years. This fluctuation can occur even in a true
574: – Huge computer powered by a star's energy
57:use the Boltzmann brain thought experiment as a
1203:(Cambridge: Cambridge University Press, 2005),
1060:(Podcast). Sean Carroll. Event occurs at 47:36
348:Modern reactions to the Boltzmann brain problem
1712:Journal of Cosmology and Astroparticle Physics
1499:Journal of Cosmology and Astroparticle Physics
1446:Journal of Cosmology and Astroparticle Physics
1379:Journal of Cosmology and Astroparticle Physics
1300:Journal of Cosmology and Astroparticle Physics
1081:Journal of Cosmology and Astroparticle Physics
1037:Journal of Cosmology and Astroparticle Physics
568: – Counterintuitive result in probability
1798:Philosophy of thermal and statistical physics
1265:"Quantum twist could kill off the multiverse"
851:
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847:
845:
843:
841:
839:
837:
835:
538: – Postulation about the act of dreaming
8:
1171:
1169:
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556: – Paradox relating to fate of universe
37:suggests that it might be more likely for a
302:emitted from the de Sitter space's bounded
1756:Human Brain and Universe - Similar Shapes?
1728:, Volume 195, Issue 2617, 18 August 2007,
1138:
1136:
430:that locally decays into a Minkowski or a
1808:Thought experiments in philosophy of mind
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1215:
1213:
1181:
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955:
738:
526: – Upper limit on entropy in physics
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317:
311:
252:
247:
241:
1031:
1029:
1027:
914:. Reading, Mass.: Addison-Wesley Pub. Co
607:
394:can solve the Boltzmann brain problem.
26:, after whom Boltzmann brains are named
1005:Choi, Charles Q. (13 September 2013).
1000:
998:
101:The idea is named after the physicist
1635:Dogramaci, Sinan (19 December 2019).
698:"Richard Feynman on Boltzmann Brains"
550: – Possible fate of the universe
7:
938:"Can the universe afford inflation?"
201:In the universe's eventual state of
936:; Sorbo, Lorenzo (September 2004).
785:Overbye, Dennis (15 January 2008).
598:- Philosophical thought experiment
542:Evolution of biological complexity
365:: Stop that! That's too silly!" A
63:argument for evaluating competing
14:
1201:Physical Foundations of Cosmology
274:(a flat spacetime vacuum lacking
1722:"Spooks in Space", Mason Inman,
532: – Philosophical experiment
16:Philosophical thought experiment
1313:Sample, Ian (8 February 2020).
911:The Feynman lectures on physics
1688:Journal of High Energy Physics
1608:(June 2017). "1% Skepticism".
1553:Journal of High Energy Physics
860:"Why Boltzmann brains are bad"
727:Journal of High Energy Physics
580: – Creationist hypothesis
78:to test our assumptions about
1:
1584:10.1088/1126-6708/2007/06/018
1529:10.1088/1475-7516/2010/09/008
1476:10.1088/1475-7516/2009/01/031
1111:10.1088/1475-7516/2012/02/024
757:10.1088/1126-6708/2002/10/011
439:within the collapses' future
1766:"Are You a Boltzmann Brain?"
413:In single-universe scenarios
333:{\displaystyle 10^{10^{69}}}
263:{\displaystyle 10^{10^{50}}}
149:second law of thermodynamics
133:measure problem of cosmology
1233:Ananthaswamy, Anil (2017).
472:Measure problem (cosmology)
361:has stated, "They fail the
190:Feynman Lectures on Physics
153:Poincaré recurrence theorem
147:advanced a theory that the
143:In 1896, the mathematician
1824:
1653:10.1007/s11098-019-01404-y
1423:10.1103/PhysRevD.82.063520
1054:"Sean Carroll's Mindscape"
974:10.1103/PhysRevD.70.063528
823:Cambridge University Press
675:Boltzmann, Ludwig (1896).
650:"Sean Carroll's Mindscape"
620:"Sean Carroll's Mindscape"
562: – Philosophical view
548:Heat death of the universe
469:
392:holographic string theory
41:to spontaneously form in
1143:Overbye, Dennis (2008).
1058:preposterousuniverse.com
883:(2002). "Introduction".
677:"Lectures on Gas Theory"
654:preposterousuniverse.com
624:preposterousuniverse.com
1263:Grossman, Lisa (2014).
566:Infinite monkey theorem
232:Via quantum fluctuation
167:; however, over enough
53:think it actually did.
334:
264:
27:
1641:Philosophical Studies
584:Simulation hypothesis
470:Further information:
399:theoretical physicist
335:
296:cosmological constant
265:
197:Spontaneous formation
22:
887:. Psychology Press.
696:(29 December 2008).
466:In eternal inflation
436:anti-de Sitter space
310:
304:cosmological horizon
240:
224:generally involving
178:In 1931, astronomer
139:"Boltzmann universe"
120:reductio ad absurdum
60:reductio ad absurdum
1715:, 0701 (2007) 022 (
1576:2007JHEP...06..018B
1521:2010JCAP...09..008L
1468:2009JCAP...01..031L
1415:2010PhRvD..82f3520D
1103:2012JCAP...02..024A
966:2004PhRvD..70f3528A
749:2002JHEP...10..011D
578:Omphalos hypothesis
518:Anthropic principle
502:content externalism
383:measurement problem
222:thermal fluctuation
218:quantum fluctuation
173:anthropic principle
111:thermal equilibrium
65:scientific theories
1803:Physical cosmology
1742:The New York Times
1622:10.1111/nous.12129
1606:Schwitzgebel, Eric
1350:. 15 February 2017
1150:The New York Times
554:Heat death paradox
419:de Sitter universe
330:
260:
35:thought experiment
28:
1691:0210 (2002) 011 (
1647:(12): 3717–3723.
1393:Physical Review D
1223:, 77(10), 103514.
1221:Physical Review D
943:Physical Review D
934:Albrecht, Andreas
363:Monty Python test
300:Hawking radiation
157:periodic function
1815:
1793:Ludwig Boltzmann
1683:Leonard Susskind
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618:(17 June 2019).
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572:Matrioshka brain
524:Bekenstein bound
376:de Sitter vacuum
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294:with a positive
272:Minkowski vacuum
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180:Arthur Eddington
103:Ludwig Boltzmann
24:Ludwig Boltzmann
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1052:(3 July 2023).
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648:(6 June 2022).
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292:de Sitter space
290:, but rather a
288:Minkowski space
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248:
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238:
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207:Anthony Aguirre
199:
185:Richard Feynman
141:
88:Sean M. Carroll
70:In contrast to
32:Boltzmann brain
17:
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1750:External links
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1679:Matthew Kleban
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1616:(2): 271–290.
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1320:The Observer
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481:multiverse
445:gravitinos
432:Big Crunch
359:Seth Lloyd
226:nucleation
220:, or by a
165:heat death
129:multiverse
55:Physicists
1730:pp. 26-29
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590:Solipsism
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76:cosmology
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560:Idealism
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