# I Expanding universe and the Boltzmann brain problem

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1. Jan 15, 2017

### analyst5

Hello

I have been reading Sean Carroll's book "From eternity to here" where he mentioned the concept of functioning brains emerging from random fluctuations on a quantum level due to the expansion of universe. They have been called Boltzmann brains https://en.wikipedia.org/wiki/Boltzmann_brain

I'm no physics expert but this surely sounds confusing. Do these entities exist and do scientists really believe in the reality of the scenario?

Is it possible that the low entropy beginning of the universe can explain why these or similar big fluctuations would be impossible?

Regards,
Analyst

2. Jan 15, 2017

### Staff: Mentor

They should be possible. Assuming I am not a Boltzmann brain, the universe is so young that regular brains should be much more common, but in the very distant future Boltzmann brains could dominate. Most of them will have weird inconsistent memories, but some will have a brain like we have. This is incredibly unlikely for a given place and time, but if you have a finite chance for it and infinite time and/or infinite space, it wil happen.

3. Jan 15, 2017

### analyst5

Carroll mentions something about the beginning of the universe and low entropy conditions which could eventually completely supress the creation of macroscopic fluctuations, is this a possibility? Since we really don't know why was universe in a low entropy state and can structures form in a non-typical way (starting from the big bang and not from random fluctuations). The real question is do we live inside a Boltzmann box, which is a metaphor for a universe where occasionaly there are fluctuations from the second law of thermodynamics.

4. Jan 15, 2017

### Staff: Mentor

I don't have the book.

I don't see how fluctuations could be suppressed (as in: not happen at all).

5. Jan 15, 2017

### Chronos

Energy borrowed from the vacuum must be repaid. I don't see how a Boltzmann brain could endure long enough to even be observed.

Last edited: Jan 15, 2017
6. Jan 16, 2017

### analyst5

Maybe there was something special which allowed structure formation from a low entropy state which cannot be duplicated going from a high entropy state and fluctuating. I think that's what was meant.

Could you explain with more details?

Regards.

7. Jan 16, 2017

### Staff: Mentor

There is no need to "borrow energy from the vacuum". The universe will keep a constant positive temperature due to the accelerated expansion of the universe. You can simply take energy from the cosmic microwave background (which will get typical wavelengths of the Hubble length in the distant future, making it extremely unlikely - but possible - to have a lot of energy in this observable universe).

8. Jan 16, 2017

### cosmik debris

Does dark energy play a role here since it does not dilute with expansion?

9. Jan 17, 2017

### Staff: Mentor

It is the reason for the accelerated expansion, yes.

10. Jan 17, 2017

### analyst5

Hello,

After thinking about this I came to the conclusion that this is extremely speculative stuff and that your first post sounds too optimistic (or pessimistic? - depending on the criteria) for existence of fluctuations such as Boltzmann brains or even Boltzmann earths. If a theory predicts this kind of stuff, it must be false because statistics would put us in a unexplainable position.

Therefore, there must be a way out of this mess. As I've mentioned I'm no physics expert but based on logic and scientific method I think that there must be a flaw in this kind of reasoning. Maybe there are some models in which space doesn't have a temperature or can't produce particles, or even the second law of thermodynamics has a different meaning if the universe is really not a Boltzmann box but structures can only form in the beginning when the universe is in a low entropy state.

Thanks

Analyst

11. Jan 17, 2017

### PeroK

A lot of paradoxes come from a misuse of probability theory. In this case, one flaw is in the treatment of an infinite universe. If you take an example of tossing a coin. You could say: "suppose you toss a coin an infinite number of times, then you get an infinite number of heads and an infinite numbers of tails". But, you can't. It's an experiment you can never do. What you can do is toss a coin a large, finite number of times. But not an infinite numbers of times.

If you now apply this to an infinite universe, then it's tempting to say something like: "imagine the probability of something happening in a region of space in a given time is $\epsilon > 0$ then it must already have happened an infinite number of times in an infinite universe".

But, this runs into the paradox that you are implicitly assuming the infinite universe has carried out this random experiment an infnite number of times and, in some sense, the results of the entire experiment are or can be known. And, this is where you are on shaky ground applying probability theory.

Let's instead have a thought experiment. To avoid the problem of space travel, let's assume we have a computer model that can simulate our universe. We can run this model and observe the most extreme fluctuations. If we ran this computer model for the current duration of the universe, pehaps doing one simulation every Planck time, then we would still see nothing like a Boltzmann Brain. The most extreme fluctuations would be nothing like what would be required.

In fact, if our computer model simulated tossing a coin and counted the longest run of heads (as an extreme random fluctuation), then running this model for the current duration of the universe, tossing a coin every Planck time would give an expected longest run of heads of about 200, by my calculation. But, getting 200 heads in a row is an enormous number compared to probability of quantum fluctuations producing something macroscopic.

Even in our computer model, therefore, there is no chance of actually ever seeing a Boltzmann Brain emerge.

So, if someone says "there are an infinite number of Boltzmann Brains in the universe", what does this actually mean? You can't know where to look for them and even if you simulate looking for one with a computer model, you can never find one.

Last edited: Jan 17, 2017
12. Jan 17, 2017

### Staff: Mentor

Where is the unexplainable position? In a universe that produces some "normal" brains and then Boltzmann brains later, the normal brains should not rule out that they live in such a universe, because they would be wrong.

There is also the probability that you are a Boltzmann brain.

Especially if both the number of normal and Boltzmann brains is infinite, probabilistic considerations stop making sense.

13. Jan 17, 2017

### Chalnoth

Boltzmann Brains are a prediction of quantum mechanics. But quantum mechanics also says that these are going to be extraordinarily rare: there likely hasn't been one in the history of the observable universe, and likely won't be one until long after all of the stars have burned out.

The only way such things can become "common" is if you wait an extraordinarily long time: if the universe is eternal, and it always has a non-zero temperature, then eventually there will be an infinite number of such brains, regardless of how absurdly rare they are.

If you take this prediction naively, then the number of Boltzmann brains in the future of our observable universe is infinite, while the number of real brains is finite (eventually heat death will prevent the survival of any life). With so many Boltzmann brains, the natural expectation would be that every brain is a Boltzmann brain. This can't be true: Boltzmann brains would generically have disordered observations. Real brains may make errors in observing their environments, but can actually perceive ordered structures that behave in sensible ways. So the fact that we can use language and can perceive objects with definite shapes demonstrates that we are real.

This is a paradox. There are a few possible resolutions to the paradox:
1. The number of Boltzmann brains in the future of our universe isn't infinite after all, because the Hawking radiation from the cosmological horizon doesn't cause excitations that could become such brains.
2. There are Boltzmann brains, but new universes are also produced. Those new universes produce an infinite number of real brains, which makes it so that Boltzmann brains are always outnumbered. This solution has the problem that there's no good way to compare an infinite number of real brains to an infinite number of Boltzmann brains: there are ways, but no single correct way.
3. It doesn't make sense to compare counts of real brains to counts of Boltzmann brains at different times.

There are other possible solutions, I'm sure, but this is what I got off the top of my head.

14. Jan 17, 2017

### Staff: Mentor

An infinite universe right now would be sufficient to get an infinite number of normal brains.
This is one of the predictions of eternal inflation.

15. Jan 17, 2017

### Chalnoth

Yup. But then due to the measure problem, you lose all ability to unambiguously measure the relative abundances in such a universe (this is why I stated above that there's no single correct way to compare). So this may be less a solution and more just muddying the waters to hide the problem.

16. Jan 18, 2017

### analyst5

The problem is in the naive consideration that every mathematically possible event must happen. This is just ignorant.

After all, we don't really know which steps must be fulfilled for a low entropy - structure to emerge and is there a way it can emerge from a high entropy state. Maybe there is something "written down" in the low entropy beginning of the universe which allows structures to emerge just in a natural way and not from fluctuations.

Sure, it's speculative, but it is also speculative to extrapolate that Boltzmann structures will exist with zero evidence supporting it.

Despite the universe being infinite, in the period before the stars burn out the ratio of brains will be massively in favor of normal brains. Right?

Last edited: Jan 18, 2017
17. Jan 18, 2017

### analyst5

Thanks for the great response Chalnoth.

My question is: why the "if" in your condition for Boltzmann brains occuring?

Isn't the eternal universe with non zero temperature a sure thing, since our cosmological constant is positive? Did you mean that there are other plausible models in which these conditions do not happen?

Thanks

Analyst

18. Jan 18, 2017

### analyst5

Also, wouldn't the number of Boltzmann brains outnumber the number of normal brains in the many-worlds interpretation of quantum mechanics?

Thanks,

Analyst

19. Jan 18, 2017

### Chalnoth

There are two issues here.

First, it is possible that dark energy is something other than a cosmological constant. In that case, it's conceivable that it will eventually dilute away.

Second, the end state of our universe with a cosmological constant, which only has a cosmological constant and no matter fields, is called de Sitter space. de Sitter is a stationary state that has no fluctuations at all. This seems to indicate that the temperature of the space is an illusion.

No. The many worlds interpretation doesn't change the expectations any, as the different parallel worlds also contain real brains.

20. Jan 18, 2017

### analyst5

Well, that's something I didn't know.
Thank you for the info.

So, according to the Born rule, the worlds where Boltzmann brains are present in a significant amount in the present would have a small amplitude and therefore would be negligible?