Exploring the Boltzman Brains Problem in Eternal Inflation Cosmological Models

[palmer eldtrich]

Boltzman Brains are considered to be a problem for for certain cosmological models especially eternal inflation.
I have a few questions.

Firstly why is this a problem for eternal inflation and not any model fo the universe which leads to a De Sitter space?
Surely any model that presumes the future of the universe will exist forever ( as i believe standard LCDM without inflation or eternal inflation does), should have the same problem?

Secondly , it seems to me amazingly unlikely that a conscious brain can fluctuate into existence and have thoughts and memories. Of course if there is an infinite amount of time , then no matter how unlikely it will still happen. However, doesn't inflation teach us that a tiny patch of false vacuum can create an entire universe? If so how do we know that the this patch isn't more likely to form than a Boltzman brain? is there any rigorous proof to show that this can't be the case? i.e if we wait long enough how can we say that a brain is more likely than a universe to fluctuate into existence, given that according to inflation all you need for a whole universe is a tiny seed of false vacuum?

 

[Chalnoth]

It is absurd, which is sort of the point. If your model predicts more Boltzmann Brains than real ones, then that model can't possibly be accurate.

The problem with eternal inflation is a bit different, however: with eternal inflation, it's actually impossible to answer the question, "What is the ratio of Boltzmann Brains to real brains?" The infinities that arise from eternal inflation make it so that there is no unique choice of probability function ("measure") with which to do the comparison. You can choose one measure which will give one answer to the ratio, and another measure which will give another answer, and there's no way to say which one is correct.

You get the same problem with a De Sitter space universe: the infinities make it impossible to answer the question. Some theorists have tried to circumvent this issue by considering a purely-finite universe, and the preliminary results have been promising. I'm not entirely sure how far that work has gone in the last couple of years, however.

 

[Simon Bridge]

Welcome to PF;
Oooh - what he said. I just have some caveats.
To understand your questions you need to make an explicit description of what you are referring to, then try to reword the questions in terms of the description you just made.

The various forms of (or ways people talk about) "the problem" depend on the assumptions that start the argument. What you are noticing is that the assumptions may not be valid. A proper answer to your questions would involve either trying to show why the assumptions were made in the first place, i.e. what is the purpose of bringing the idea up i the first place (edit: see above); or showing that the conclusion still works for a wide variation on the assumptions.

Also see the discussion:
http://blogs.discovermagazine.com/c...ard-feynman-on-boltzmann-brains/#.VPZY86h7h5Q

A lot of the discussions on this topic tend to be a bit vague about what you mean by "universe" and "the beginning of the Universe" and stuff like that so it can be a good way to iron out your ideas on these topics. Treat it as a koan.

 

[bahamagreen]

... if we wait long enough how can we say that a brain is more likely than a universe to fluctuate into existence, given that according to inflation all you need for a whole universe is a tiny seed of false vacuum?

What is the "problem" being mentioned exactly?

Although it seems unlikely that a piece of toast would form randomly, isn't that much more likely than the alternative - that there was a toaster and a piece of bread, and a manufacturer of toasters, and an electrical utility to power the toaster, and growers of wheat, and bakeries to make that into bread, and a world for upon these things to occur, including a sun, etc...?

So by comparison, the spontaneous appearance of a piece of toast vs the spontaneous emergence of a universe with the right initial conditions and a sufficiently complex history to eventually result in a piece of toast...

Is the problem that since the latter is apparent, the former implies the universe is full of pieces of toast?
Or is it that if extended to brains rather than toast, we don't know if the latter has happened, because the former might be us - Boltzmann brains ourselves?

 

[Chronos]

It's a shame we are saddled with the burden of reality. No time right now, I need to tend my garden before the fairies grow impatient.

 

[palmer eldtrich]

What is the "problem" being mentioned exactly?

Although it seems unlikely that a piece of toast would form randomly, isn't that much more likely than the alternative - that there was a toaster and a piece of bread, and a manufacturer of toasters, and an electrical utility to power the toaster, and growers of wheat, and bakeries to make that into bread, and a world for upon these things to occur, including a sun, etc...?

So by comparison, the spontaneous appearance of a piece of toast vs the spontaneous emergence of a universe with the right initial conditions and a sufficiently complex history to eventually result in a piece of toast...

Is the problem that since the latter is apparent, the former implies the universe is full of pieces of toast?
Or is it that if extended to brains rather than toast, we don't know if the latter has happened, because the former might be us - Boltzmann brains ourselves?

Not if the seed for the complex universe we see is more likely to fluctuate than piece of toast. According to inflation, all you need is a tiny speck of false vacuum and then you can get a whole complex universe.
"A remarkable consequence of this model is that, if even a pinpoint of space contained this primordial form of energy, then the pinpoint of space would expand extremely rapidly and would bring into existence more of the same kind of energy. In fact, all the matter in the universe could have arisen from a bit of primordial energy weighing no more than a pea. This amazing scenario is a consequence of applying Einstein's theory of gravity to the inflationary universe model. Thus the known laws of nature can in principle explain where the matter and energy in the universe came from, provided there was at least a tiny seed of energy to begin with."
https://www.cfa.harvard.edu/seuforum/bb_whatpowered.htm
So I still don't see why we should assume the brain is more likely to fluctuate than the universe, especially if this is so we actaully can defeat the Boltzman Brain scenario. It seems to me this has to be the case as long as we assume the universe is eternal in at least one direction of time , which current evidence implies that it it.

 

[palmer eldtrich]

It is absurd, which is sort of the point. If your model predicts more Boltzmann Brains than real ones, then that model can't possibly be accurate.

The problem with eternal inflation is a bit different, however: with eternal inflation, it's actually impossible to answer the question, "What is the ratio of Boltzmann Brains to real brains?" The infinities that arise from eternal inflation make it so that there is no unique choice of probability function ("measure") with which to do the comparison. You can choose one measure which will give one answer to the ratio, and another measure which will give another answer, and there's no way to say which one is correct.

You get the same problem with a De Sitter space universe: the infinities make it impossible to answer the question. Some theorists have tried to circumvent this issue by considering a purely-finite universe, and the preliminary results have been promising. I'm not entirely sure how far that work has gone in the last couple of years, however.

If you had a cyclic universe where the De sitter space period did not last long enough for BB to form, would that work? for example:
http://arxiv.org/abs/1307.8106
Also I have seen that many cosmologists have as you say tried to deal with the problem by choosing a measure, but I don't see how your choice of estimating probabilities affects the universe? One measure that has been proposed is the "scale factor cut off measure"
http://arxiv.org/abs/0808.3778
can anyone give a laymans explanation as to how this works?