A burning question in theoretical physics these days is that of whether Boltzmann Brains dominate the string theory anthropic landscape. It seems that to answer this question one must study the details of how BBs nucleate and how string vacua decay. String vacua can do pretty much anything, so attention is focused on the detailed study of how to make the Brains and ad hoc choices of “measure” on the multiverse, with these issues occupying the attention of many leading figures in cosmology. While the question of BB domination of the multiverse remains open, it is becoming increasingly clear that BBs may soon dominate hep-th. Their nucleation rate is increasing, while the decay rate of the rest of the field also appears to be increasing. Doing phenomenology and extrapolating data a few years into the future, Boltzmann Brain domination of hep-th appears inevitable.
The latest hep-th arXiv postings include two new contributions to BB studies. One is from a group of three physicists at Berkeley, the second is from a large collaboration of six cosmologists on both coasts, including three of the major figures in the subject. For a third, more intellectually substantive, contribution of similar length, there’s a new posting on the subject from Lubos.
Thanks, Peter, Luboš was certainly worth reading in this case!
Well said, Peter 🙂
I’ll use the opportunity to warm up The Return of the Boltzmann Brains
I see no actual evidence that non-Boltzmann-Brainy hep-th is shrinking or dying. But with statistical methods like ‘Select 2 papers about BB’s that happen to appear on a single day, and ignore all the other papers that month’ you can prove anything.
For my sins I read almost all of Lubos’ post and he doesn’t actually produce anything relevant to the question. If you understand the BB argument, and the people who are do are hardly stupid, part of it is that there is a finite probability that any given BB has (false) memories consistent with orderly physical laws and decreasing entropy. So Lubos’ Bayesian argument using his observations of a ‘normal’ universe doesn’t work, because the correct prior might be so overwhelmingly in favour of BBs that even Lubos’ entire history of observations can’t tip the balance.
I believe the correct reason why it doesn’t make sense to worry about BBs in cosmology is philosophical: it is that the proposition ‘I am a BB’ is self-defeating. It’s the same reason why we can assume that we are not brains-in-vats or simulations. And why (if we are religious) we implicitly assume that God will not intervene tomorrow to produce a completely different state of affairs from what we expect.
Simply this:
1) Either we are ‘normal’ or BB.
2) But if we are BB, then none of our physical reasoning or theories make any sense: they are all unreal and false, based on an absolutely meaningless chance occurrence.
2a) In particular, if we are BB, the physical reasoning that led us to think we might probably be BB is also unreal and false.
3) In doing science, we proceed implicitly on the basis that our physical reasoning is not necessarily unreal or false.
And, in fact, that we are not brains in vats, or simulations, and that God (should He exist) will not intervene tomorrow to completely change the results of whatever experiment or observation we are planning.
Note that 3) doesn’t mean that theories that seem to show we are probably BBs are necessarily false: it is only necessary that we be in the minority of ‘normal’ brains.
If you understand the BB argument, and the people who are do are hardly stupid, part of it is that there is a finite probability that any given BB has (false) memories consistent with orderly physical laws and decreasing entropy.
Compared to all possible memories, most memories will be consistent with chaos, Santa Claus, the unicorn, the tooth fairy, etc., There are infinitely more contradictory memories than consistent memories.
And that is the other point – there is no “correct” prior – how do you establish it?
To me, the funniest part of LM’s performance [apart from his serious declaration that his own brain is “normal”….] is the way he shows such disrespect for people like Linde, Guth, and Vilenkin. That sits rather oddly with his constant appeals to authority, references to how many times Ed Witten has been cited etc.
What I find strange is the way that people seem to think that the existence of BBs is somehow bizarre or laughable. On the contrary, in a Universe which is [apparently] infinite in space and time, such things most certainly do/will exist. We are all taught this when we learn elementary statistical mechanics: surely all of us have done the ancient problem of computing how long one would have to wait before all of the molecules in the air in the lecture theatre will rush into one corner and asphyxiate everyone? The answer, of course, is that the time required is negligible — by the standards of an infinite universe.
What *is* bizarre and very much in need of explanation is the existence of *normal* observers. How did such fantastically low-entropy systems come into existence at all, given that it *didn’t* happen as the result of a Boltzmann-style fluctuation? The only strange thing about the [brilliant] papers being mocked here is that they don’t consider this question, ie the provenance of the low-entropy state at the Big Bang.
The reason why I beleive that Boltzman brains have nothing to do with our Universe is simple: if a theoretical concept leads to a conclussion that our Universe should have properties which are in sharp contrast with what is observed, that means that the assumptions are not good or incomplete.
Esornep:
We are taught it in elementary statistical mechanics, but that doesn’t mean it is relevant to reasoning about the relative improbability of the big bang versus a deluded Boltzmann Brain… It assumes that our usual understanding of, e.g., entropy in accessible macroscopic systems, applies to cosmology in something like a “multiverse” setting where anything (some people assume) can happen. Statistical mechanical reasoning requires something like a well-defined phase space within which it makes sense to talk about fluctuations, relative probabilities of different kinds of structures forming spontaneously, or even comparing energies.
No experiments have been done that can say whether a background phase space exists (even in principle) prior to the big bang, so its existence (or absence) must be regarded as an assumption. Recognizing the contingent nature of a background (why need Nature supply it to us?), it is hard to see how we can justifiably believe that Boltzmann Brain arguments and reasoning about measures over a multiverse can say anything definitive about Nature other than, “If such a background phase space can be defined, then (and only then) our conclusions are true.” That seems like a qualification worth making clear…
The only bizarre thing about Boltzmann brains is that anybody cares. Ironic science in its purest form.
Thomas L.
For Boltzmann Brains, I think a new phrase is required, this is getting way beyond “ironic science”, and into the realm of beyond even the laughable. The behavior of physicists that it has led to is really comic beyond belief, with Lubos’s meditation on whether his brain is normal just one of the priceless absurdities.
Another funny thing about all this is that here I’m in the role of expressing not a controversial position, but the consensus view of the physics community. At his public talk at the opening of the IPMU earlier this year, David Gross referred to BB papers as “totally preposterous” and said that physicists work on this “to my regret”. In private one finds that most physicists consider this to be a really bad joke. One can get a wrong impression of this from the blogosphere, where anonymous commenters describe this work as “brilliant”, and the proprietor of one of the most prominent blogs is a big BB promoter. If you think this is widely taken seriously in physics departments, try asking around…
Penrose-backwards:
On the contrary, in a Universe which is [apparently] infinite in space and time, such things most certainly do/will exist. We are all taught this when we learn elementary statistical mechanics: surely all of us have done the ancient problem of computing how long one would have to wait before all of the molecules in the air in the lecture theatre will rush into one corner and asphyxiate everyone? The answer, of course, is that the time required is negligible — by the standards of an infinite universe.
Yes, but I think it is true, and Luboš also points that out, that by whatever measure the “density” of such events is very, very low, even if they occur with probability one. It is very unlikely that we’d encounter (or be) one of those events. That our current state ensued from a preceding lower entropy state and that this is true of all visible space and all the way back to the big bang is much more probable than I being a Boltzmann brain imagining you and this blogpost and everything else. And the further back we are able to go, the larger the entropy fluctuation has to be to explain us as a Boltzmann universe. It is just a bad idea.
(penrose)^T says:
“What is bizarre and very much in need of explanation is the existence of normal observers. How did such fantastically low-entropy systems come into existence at all, given that it didn’t happen as the result of a Boltzmann-style fluctuation?”
This is bizarre only because you are in love with thermal equilibrium and want to believe that everything that is NOT in thermal equilibrium is a fluctuation. What motivation (experimental/theoretical) is there for this?
To me this is how it looks like:
(1) The universe is what it is, (2) you are imposing your equilibrium prejudice on it when building models, (3) you end up finding strange consequences like over-abundance of Boltzmann brains[1], and then (4) you use this as a selection principle between your models. Most people do not think that your initial assumption is nothing more than a prejudice to begin with, so they find your efforts to make the world safe from Boltzmann brains as cheap speculation. “Cheap”, because the papers seem to contain little more than this (seemingly simple-minded) overall philosophy. Please correct me if I am wrong about this impression about the general approach.
[1] There are some well-defined issues here, which makes me suspicious even about the details, but lets ignore them.
Well, as someone who came reasonably close to going for a Ph.D. in physics, but ended up in math, all I can say is whew 🙂 My goodness, I have (vague) memories of stoned conversations about this sort of stuff when I was an undergrad, trying to work out whether the argument that using statistical mechanics anything with probability > 0 *will* occur might give a good argument for the finiteness of the universe. Of course one might get a BB even in a finite phase space, but as pointed out above one is probably unlikely to meet one on the subway. Then again, I met some pretty strange people on the subway.
Now that I think of it, maybe a physics Ph.D. would have made life easier, I mean if people post this stuff seriously on arXiv, I could churn out papers, maybe 2 a month….
No, the relative probability of a BB having ‘chaotic’ or nonsensical memories versus ‘normal’ ones is not infinite, because memories have a finite (and perhaps not very large, on cosmological scales) information content.
That’s basic. It’s why one talks of Boltzmann ‘brains’ rather than ‘planets’ or ‘galaxies’, because the information/’negentropy’ required to put a planet or galaxy into a ‘normal’ state by chance fluctuation is much much larger than for a brain, with or without ‘normal’ memories.
I think Carroll’s way to express it is neatest: the possibility that the observer who sees a ‘normal’/orderly universe is actually a BB is cognitively unstable.
As to priors, the purpose was to show that Lubos’ statistical argument, which assumed a (completely arbitrarily) prior probability of 0.5 each for normal and BB, could break down if the appropriate prior was one heavily tilted towards BBs.
In Bayesian statistics the ‘correct’ prior should come from the physical theory or theories you think are applicable. But the question we can answer with them is not ‘Are we BBs or not’. It is:
“Is Theory A, which has realistic features (eg a cosmological constant) and predicts that BBs are numerically dominant over the universe, better or worse than Theory B, which is less realistic but has few BBs?”
The correct Bayesian way to set this up is slightly tricky, because in the case where the observer is a BB, all the apparent observational evidence that she considers to make Theory A realistic is false and meaningless. So one needs to split up the hypotheses:
A1, Theory A is correct, I am a minority ‘normal’ brain living in a ‘normally’ evolving Universe, my observations are reliable
A2, Theory A is correct and I am a majority BB, my observations are utterly unreliable
B, Theory B is correct and I am a ‘normal’ brain (since there are few BB’s), my observations are reliable.
Given a set of observations seen by me, I want to know which they favour. Suppose that they favour A1 over B because A1 has a nonzero cosmological constant. Where does that leave A2? Note that A2 is compatible with *any observations whatsoever*… so any observation that apparently favours Theory A is a red herring, and we might as well have
A2′, Any of theories A, C, D, …, Z in which BBs dominate are correct, I am a BB, my observations are worthless
This is an inevitable ill-definedness of any hypothesis that includes ‘I am a BB’, and finding any prior for A2′ vs. A1 is an ugly task. But: any subsequent observation compatible with A1 will increase its posterior probability enormously relative to A2(‘), simply because A2(‘) doesn’t predict anything, or equivalently that every observation is equally likely.
Also, if we have a hypothesis
C, There are no laws of physics, God just happened to make it look that way
although our prior belief in C may be overwhelming, any observation compatible with A1 should rationally diminish our belief in C – because C doesn’t predict anything.
So just to finish the argument, A2 and C are examples of hypotheses which we usually consider ‘not scientific’ and discard instinctively. However, Bayesian statistics allows us to consider them, and gives us the reasonable answer that since they ‘predict’ all possible observations (including chaotic, ‘unphysical’ and nonsensical ones) to be equally likely, their posterior probability will decrease hugely if the actual observations are compatible with a theory which has ‘normal’ physical laws.
This leaves us in peace to consider the ‘scientific’ and ‘normal’ hypotheses A1 vs. B.
No, the relative probability of a BB having ‘chaotic’ or nonsensical memories versus ‘normal’ ones is not infinite, because memories have a finite (and perhaps not very large, on cosmological scales) information content.
The probability of ‘normal’ versus nonsensical memories likely has as an upper bound the probability of monkeys at typewriters producing Shakespeare.
BTW see this
for a differnt point of view of the Boltzmann Brains problem