The other day, Habr published a translation of a long interview Sean Carroll conducted with philosopher of physics David Wallace. The conversation, as usual, was about the arrow of time: entropy, the past, memory. But toward the end Wallace delivers a passage that sends a chill down any sane person’s spine: if the Universe lasts long enough, Boltzmann brains will begin to arise spontaneously from pure thermal noise—self-aware fluctuations that “remember” a past that never existed. And there will be more such brains than all genuinely born human beings put together.
The host asks outright: is this the sort of thing that personally keeps you up at night? Wallace’s answer is a model of British restraint: “‘Keeps you up at night’ is an exaggeration, but I do think it’s a serious problem.”
The funniest part is that this hypothesis is rooted not in a Lovecraft plot, but in Ludwig Boltzmann—one of the fathers of statistical mechanics—and a 1895 paper in which he prudently attributed the idea of a “world-as-fluctuation” to “his old assistant Dr. Schuetz.” And in 2006, physicist Don Page turned this curiosity into a prediction about the Universe’s expiration date. Let’s see how a grim 19th-century joke became a test of whether the cosmos can survive.
The mystery that started it all is as old as statistical mechanics. The fundamental equations of physics are time-symmetric: replace t with −t, and the laws do not notice the switch. But the world does. Milk spills but does not flow back into the glass; an egg breaks but does not reassemble; waves crash but do not “gather themselves back together”—that whole set of examples comes straight from Scholarpedia’s overview article on the arrow of time. A video of an egg breaking, played backward, looks ridiculous—but as far as the equations are concerned, it is perfectly lawful.
Boltzmann’s contribution was to explain why this happens. For him, entropy is the logarithm of the number of microstates compatible with a given macrostate: a system “tends” toward equilibrium simply because equilibrium microstates are astronomically more numerous, and any wandering through phase space leads there with overwhelming probability. Everything is beautiful until you ask: where did the initial nonequilibrium state come from? If everything tends toward equilibrium, someone must once have created order. The answer that there was even greater order further in the past leads to infinite regress—today physicists package that regress in the rather grim term Past Hypothesis: the Universe’s initial state had monstrously low entropy, and that is simply a fact we have not yet explained.
At the end of the 19th century, two men came down hard on Boltzmann over this: Loschmidt pointed out that the laws are reversible—reverse the velocities of all molecules, and the system obediently returns to the past, so the growth of entropy cannot follow from dynamics as such; while Zermelo argued that under Poincaré’s theorem, any closed mechanical system eventually returns to its original state, meaning that its “tendency toward equilibrium” is merely a temporary phase. Wallace sums up the substance of the objection in the interview in one line: “You started with time-reversible equations, made time-reversible assumptions about those equations, and got something that distinguishes past from future. That can’t happen.”
And here Boltzmann makes a move that, a century later, will cost cosmologists their sleep. Responding to the objection from recurrence, he allows: what if the Universe as a whole has eternally remained in thermal equilibrium, while our orderly world is merely a rare but inevitable fluctuation within it? The original is a short paper, On Certain Questions of the Theory of Gases, Nature, volume 51, p. 413, 1895, and its opening line is immortal:
“I will conclude this article with an idea of my old assistant, Dr. Schuetz. We assume that the whole universe is, and rests forever, in thermal equilibrium. The probability that one (only one) part of the universe is in a certain state is the smaller the farther this state is from thermal equilibrium; but this probability is the greater the greater the universe itself.”
What follows is a picture with an H-curve: if the Universe is large enough, the probability of finding somewhere within it a corner as far from equilibrium as our world ceases to be vanishingly small. “The peaks of the curve would represent worlds in which visible motion and life exist.”
The irony is that Boltzmann hid behind his assistant. Sean Carroll, who dug up this text (along with Alex Vilenkin, Don Page, and Andy Albrecht, who retrieved a copy from a crumbling leather-bound volume in a library), notes that even Boltzmann did not want to answer for it. Blog commenters picked up on it: this was “the scientific version of a teenager’s ‘asking for a friend,’” while Albrecht proposed calling them “Schuetz’s Schmartz,” to preserve the alliteration. The great physicist’s psychological self-defense is understandable: he was proposing a Universe in which our cosmos is a statistical accident, rather than a lawful outcome.
The logical landmine inside this idea did not go off immediately. If our world is a fluctuation, which sort of fluctuation is it? An entire Universe containing a hundred billion galaxies is a monstrously large fluctuation—probabilistically “expensive.” But a single self-aware brain, with an entire Universe in its memory, is a tiny, “cheap” fluctuation. The economics here are merciless: small fluctuations happen immeasurably more often than large ones. Therefore, in a Boltzmann Universe, the typical observer is not a human being looking at the stars, but a lonely brain which, in Carroll’s words, “has time to look around and scream Aaaaaagghhh… before fading back into equilibrium.”
Worse still, this argument destroys the hypothesis itself. In 2008, Carroll carried it through to the end (“Boltzmann’s Universe”): if we are a fluctuation around eternal equilibrium, then almost all fluctuations that reach precisely our macrostate—with its hundred billion galaxies, Solar System, and a person bearing your memories—have a false past. Genuine memory means still lower entropy in the past, and thus an even more expensive fluctuation. In the overwhelming majority of realizations of a “world like ours,” both past and future have higher entropy than the present, while memories have been fabricated by noise. In other words, the Boltzmann-Universe hypothesis predicts that a typical observer sees chaos and remembers things that never happened. Yet we see a neat, cooling, ordered cosmos with a recorded history—and that is a direct empirical refutation. A hypothesis designed to explain the arrow of time itself admits that real memories are rare, while we have them.
The story should have ended there, but in 1998 astronomers discovered the accelerating expansion of the Universe. The future of the cosmos is eternal de Sitter space: emptiness driven apart by dark energy, with an event horizon. And in the 1970s, Gibbons and Hawking showed that de Sitter space has a nonzero temperature, and therefore thermal fluctuations. Wait long enough, and structures will begin sprouting in the void. Consciousnesses among them.
In 2002, Dyson, Kleban, and Susskind published a paper with a blunt title—Disturbing Implications of a Cosmological Constant. The calculation is simple: the Universe in the distant future is a finite system, on average in thermal equilibrium and only occasionally disturbed by fluctuations; the waiting time for an “interesting event” (say, a restart of inflation from which a new world might grow) is on the order of exp(10¹²⁰) years: the equilibrium entropy is ~10¹²⁰, while the entropy of the inflationary fluctuation is ~10¹⁰. The number exp(10¹²⁰) is not merely “a very long time,” it is ludicrously long: over such spans, the typical observer of the de Sitter future is a thermal fluctuation, not a product of evolution. The section in which the authors discuss this is titled The Misanthropic Universe?—and the question mark does not save it.
In 2006, Don Page (“Return of the Boltzmann Brains”) assembled it all into one hard argument. As long as the Universe lives and expands, the vacuum continuously produces fluctuation brains—and their production rate is proportional to the growing volume. Ordinary observers, meanwhile, are a finite stock produced during the first trillions of years of existence. If the Universe is eternal, then sooner or later the brains outnumber them, and our observations become atypical. Page’s conclusion: for us to be typical observers (rather than a rare fluctuation—otherwise both our data and our memories are suspect), the Universe must decay—transition into another vacuum state—before the asymptotic growth of volume has time to produce too many brains. Plug in the measured acceleration (a linear e-folding time of around 16 billion years), and you get this: with a probability greater than half, our vacuum will decay within the next 19 billion years. A philosophical curiosity from 1895 had become the cosmos’s expiration date.
This also gave rise to an entire industry: Boltzmann brains became a test for multiverse measures. Eternal inflation produces infinite volumes, and “how many” observers there are depends on how one slices up infinity—the measure. The proper-time measure produces whole broods of “Boltzmann babies” and is discarded; the scale-factor cutoff survives. In 2006–2007, physicists Linde and Page exchanged papers on whether volume-weighted measures save the Universe from brains—and Page showed that in the “natural” version, the problem returns. Ever since, the rule has been simple: if your theory predicts more fluctuation consciousnesses than real ones, your theory is probably wrong. Or you are its product, in which case the data you rely on are fabricated.
The final nail in the coffin—and the most elegant one—is this. A theory dominated by Boltzmann brains is self-undermining. Look: if a model predicts that, with overwhelming probability, you are a fluctuation with false memories, then the data on which the model was built—your observations, experiments, memories of papers you have read—are almost certainly false. To take such a model seriously is to accept, at the same time, that you have no reason to accept it. Carroll and Albert, and in 2025 Adam Elga, call this cognitive instability: the reasoning that brought you to the conclusion “I am a Boltzmann brain” undermines its own reliability.
The Bayesian version of the same point (Carroll, 2017): a BB-dominated model receives a catastrophic penalty for being uninformative—it can “explain” any data with equal ease, because any data might have been fabricated by a fluctuation. A good theory must value evidence; a theory in which evidence is noise is not worth its prior probability.
There is, however, a wrinkle, explored in Entropy in 2025: the cognitive instability of the BB hypothesis is mirror-symmetrical to the assumption of the second law of thermodynamics. It all comes down to which moment in time you anchor your reasoning in: trusting your memories of the past is no more—or less—justified than trusting your expectations of the future. A Boltzmann brain and a “real” observer turn out to be equally legitimate—or equally illegitimate—depending on where you plant your footing. The question is not closed; it has simply been carefully reformulated in terms of what, exactly, we have decided to trust.
A Boltzmann brain does not have to exist. It has to be impossible cheaply enough—that is its job. The hypothesis that Boltzmann himself attributed to his assistant so he would not have to answer for its consequences now functions as a filter: any cosmological theory that produces fluctuation consciousnesses faster than real ones gets discarded. At the same time, as Wallace honestly admits, it is a reminder of the price of infinity: by postulating an eternal future or infinite volume, we implicitly make a “very serious and profound assumption,” and we should understand what we are doing. His colleague Porter Williams concisely captured the scale of the problem: the LHC’s main beam pipe is three meters across, so “whatever ‘at infinity’ means—it’s less than three meters.”
We are probably not a fluctuation: this configuration is too expensive—an entire Universe with galaxies, laws, and 14 billion years of coherent history. But the hypothesis that tests this is the best insurance against theories that do not respect probability. The canary in the cosmic mine keeps singing. For as long as there is someone to sing.