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I read an article and I got curious about the topic of Boltzmann Brains.

I read some more articles and posts about the topic and it seems to me that the arguments are that BBs would outnumber us by so much that we would almost certainly be BBs. This idea has worried me quite a bit for the past week or so.

Are these arguments true?

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    Arguments can not be true or not, they can be sound or unsound. Whether they are sound depends on the truth of their premises (and validity), and Wikipedia already discusses why those are likely false. – Conifold Sep 24 '19 at 20:40
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    It's entirely ludicrous to say that it's "more likely" that we're a Boltzmann Brain than otherwise - any such probabilities can only have been pulled out of their behinds. – curiousdannii Sep 24 '19 at 21:29
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    The same way we know that the sun rises in the morning. In the end, if one is determined enough to deny the obvious they can always suggest the evil demon is deceiving us, about everything. But without positive evidence for it, it is a pointless exercise. – Conifold Sep 25 '19 at 7:59
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    You may be interested in some of the posts under the tag: simulated-universe – christo183 Sep 25 '19 at 8:01
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    @another_name I don't think it is something intrinsic to the theory, but rather in the 'why' these thought experiments were created in the first place: e.g. BBs started as a reductio ad absurdum against a theory by Ludwig Boltzmann... – christo183 Sep 26 '19 at 6:18
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The cited article references a paper by Sean M. Carroll which provides an overview of Boltzmann Brains (BB). Carroll views BBs not as a reality, but as a way to test whether a cosmological theory is plausible or not. The rule of thumb goes something like this: if the cosmological theory allows BBs then reject the cosmological theory. (page 23)

We therefore conclude that the right strategy is to reject cosmological models that would be dominated by Boltzmann Brains (or at least Boltzmann Observers among those who have data just like ours), not because we have empirical evidence against them, but because they are cognitively unstable and therefore self-undermining and unworthy of serious consideration.

Carroll's description of the "standard argument" for this rejection is straightforward: (page 16)

The standard (but not quite correct) argument that cosmologies dominated by BBs are unacceptable is fairly straightforward: in such a universe, I would probably be a Boltzmann Brain, and I’m not, therefore that’s not the universe in which we live.

Here is the question:

Is it true that we are almost certainly Boltzmann Brains?

According to Carroll the problem with BBs has to do with cosmologies dominated by BBs. If such cosmologies were correct then we would be BBs, but we aren't, and so such cosmologies can be rejected.


Carroll, S. M. Why Boltzmann Brains are Bad. (2017) Retrieved on September 24, 2019 from https://arxiv.org/pdf/1702.00850.pdf

  • Does he give an argument for why we aren't, other than that the idea seems false to him? – Ask About Monica Sep 25 '19 at 16:08
  • @frank hubeny I would also like to know this – Fimavo Sep 25 '19 at 17:27
  • @kbelder His entire paper is his argument. In particular see the introduction to section 5. He presents a dialogue between someone worrying about being a BB (W) and someone more sanguine (S) about that. S says this as to why he is not a BB: I don’t seem very brain-like. I have arms, legs, etc. The environment around me seems pretty dramatically far from equilibrium. It is OK not to agree with him and Carroll may have hidden motivations for his opposition to BBs. However an argument for BBs would have to take into account criticisms of it like those Carroll presents. – Frank Hubeny Sep 25 '19 at 17:39
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    It's similar to the way philosophers often use solipsism as a reudctio ad absurdum. If your theory only gets you the one mind of the theorizer, then something has gone wrong. This problem was constantly thrown at Husserl, for example, after 1907 when he claimed to find his transcendental Ego. You might similarly ask how people know that solipsism is false. Maybe they don't---but that doesn't make it illegitimate to hold that there is a theoretical desideratum to somehow get other minds into your theory. Likewise, getting non-Boltzmann brains into your theory is considered a desideratum. – transitionsynthesis Sep 25 '19 at 19:21
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    Yeah, the entire notion was invented to dissuade Boltzmann from his preferred cosmological theory. This answer is like answering "Is Zeno's Paradox True?" with "Choose theories of space and time that make it not true." – user9166 Oct 1 '19 at 20:38
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Only if you don't believe time started (which Boltzmann found unconvincing.)

The notion of Boltzmann Brains relies on Boltzmann's original notion that the low-entropy nature of our universe (and its tendency to therefore increase in entropy whenever possible) is part of an eternity of random fluctuations in entropy, going back and forth.

But an infinity of anything often leads to various logical problems. In this case, almost-zero-probability outcomes like functioning, disembodied brains deluded into imagining an entire lifetime would actually happen over and over again during any eternity.

In fact, statistically, very short periods dominated by almost-zero-probability outcomes would become more common than a sustained period of normal behavior when time could apparently flow forward, which results only when entropy changes continuously in the same direction for an extended period.

The extraordinarily low level of entropy that can then slide into a long-term complex-yet-organized universe would have to get past the same level of order we are currently at, on its way down, and then keep going for a very long time. And that is just not going to happen very often.

So over such an eternity a Boltzmann Brain existing for some vanishingly short period of time might happen more often than there would be a stream of ordinary time necessary for our remembered history to really occur.

But the alternative theory involved a definite start of time, and this theory was advanced before people found a beginning to time easy to imagine. Given relativity, and the new theories of spatial expansion, we now accept the Big Bang as a likely event. The Big Bang would necessarily create a case of zero entropy -- when all the energy is in the smallest space that allows for energy to be expressed, it would necessarily be perfectly packed, and therefore have zero entropy.

  • can you clarify on 'Around the turn of the millennium, people worried that theories like evolutionary cosmology put back in very long periods of time, and threatened to revive this paradox in a more limited form. But it does not work out that way' I don't quite understand what you mean by theories like evolutionary cosmology, and I don't understand why it "doesn't work out that way". – Fimavo Sep 27 '19 at 3:51
  • @Fimavo. It is not central to the argument, and for God's sake Google works! I will delete it. The answer, completely without that side-comment answers he question. And I am not a nanny. – user9166 Sep 27 '19 at 17:00
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Presumably, if there really were things like Boltzmann brains, most of them would be giving rise not to an ordered experience like ours, but rather very chaotic ones. (For the remainder of this answer, when I say "Boltzmann brains" I include things like it that would give rise to disordered experiences.) For example, even if the Boltzmann brain by extreme luck had a part that could give rise to a visual experience like ours, it would seem far more likely that that visual experience consisted of a totally disordered collection of colors than something meaningful. Thus, under the hypothesis that there are many Boltzmann brains, it would be extremely unlikely that what I see is something reasonably ordered. So it seems that we can dismiss that hypothesis.

... with the caveat that that is assuming that my experience is randomly sampled (chosen) from all brains in the universe, including any Boltzmann brains with disordered experiences. If it is sampled only from all brains with meaningful experiences, this would raise the Boltzmann brain worry again. If it is sampled only from non-Boltzmann brains (e.g., because the brain for some reason needs to persist to be sampled), then Boltzmann brains are totally irrelevant.

So which one is it? That's a hard question, connecting to the one here: Why am I this particular human being?

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    But the whole notion of the BB is that it has its whole experience programmed right up to now to mimic a real life lived up to now. But it is not actually in the environment it remembers, it is therefore about to disintegrated back into nothing. It goes well beyond the brain in a vat, it is an instantaneous delusion of living in our current reality. That is why we could be one, and not know it... – user9166 Oct 1 '19 at 20:26
  • This is a good clarifying comment. When saying BB I mean to include not only those accidental brains with an ordered experience as you describe, but also accidental brains with a disordered experience, of which presumably there would be many more. I have edited the answer to be clearer about that. Given that, the argument is: if BBs exist in large numbers, then I would be much more likely to experience a disordered experience than an ordered one. So the fact that I am experiencing an ordered one counts as evidence against the (plentiful) existence of BBs. – present Oct 2 '19 at 16:58
  • But then the odds of us currently being those brains is zero, since we share an ordered experience, or we would not be us. – user9166 Oct 2 '19 at 18:04
  • Conditionally on us having the experience we do, the probability of us being a brain with a disordered experience is zero. But if the experience was randomly drawn from all those brains, then initially it was very unlikely it would be an ordered experience. What we observe is unlikely under the theory. Compare: two theories of galaxy formation. Under one, all galaxies look roughly like the ones we see. Under another, all kinds of other types of galaxy that we have never observed are likely, as well as the ones we do see. Then, what we see favors the former theory over the latter. – present Oct 3 '19 at 0:35
  • But the question is about us. It is in the indicative and not the subjunctive. We do have the experiences we have. I am done stating the obvious. The answer is about some question other than the one the OP actually asked. – user9166 Oct 3 '19 at 0:36
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I've read about Boltzmann brains somewhere but just assumed it was another one of these speculative thought-games that physicists make up when they the real problems facing them in quantum gravity get too hard and they need to let their hair down a little. This, I think, is confirmed by the fact that the wikipedia page on this does not name who exactly came up with this idea.

In fact, an article by Sean Carroll is titled Richard Feynman on Boltzmann Brains and quotes extensively from Richard Feynmans deservedly famous lectures but nowwhere does Feynman mention Boltzmann and Brain together. He, instead, focuses on Boltzmanns achievements in beginning statistical mechanics as the correct physics of the collective properties of macroscopic disordered systems - like gases and liquids.

Are these arguments true?

The theory on which they are based on is true, and you're better learning that theory than wondering about Boltzmann brains, which is just a device to get people talking about statistical mechanics but in fact gets them talking about not much in particular in physics.

  • The theory on which they are based is lost out to the notion of the Big Bang and an initial state of zero entropy, with too little time in the past and too little energy in the future to support this idea. To say it is true is to misrepresent physics, – user9166 Oct 2 '19 at 23:55

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