# I Boltzmann brains

1. Nov 26, 2016

### durant35

Hi guys

I recently read a lot about Boltzmann brains and their possibility of existence. Are there any models in cosmology which exclude them and make them a physical impossibility? How can we safely conclude that we are not Boltzmann brains which last for a moment and then vanish? Are the Boltzmann brains seriously taken by the scientific community?

Thanks

2. Nov 26, 2016

### Bandersnatch

3. Nov 26, 2016

### stevendaryl

Staff Emeritus
As I understand it, cosmologist Sean Carrol originally thought they were a problem, and then later convinced himself that they were not.

Here's my take on why some people worry about Boltzmann brains. On the one hand, it's obviously a stupid thing to worry about, because the assumption that the universe is real seems necessary for the scientific method to work. If I'm just a brain in a vat being fed false sensory data by a mad scientist, what hope is there for ever figuring out what's going on? So certain assumptions seem necessary to make any progress at all in science. Everybody makes those assumptions, and it's sort of useless to speculate about the possibility that they are false.

That being said, it's still a logical puzzle---a scientific brain teaser---and it would be nice to have a satisfying answer.

Here's my understanding of the original (non-quantum, non-relativistic) version of the puzzle. Suppose that you put our entire galaxy into an impenetrable box that no energy or matter can flow into or out of. Now wait a billion years, a trillion years, $10^{10^10}$ years, whatever the number is, and the box will approach thermal equilibrium, where everything is run down and used up and at its highest entropy state. Very sad...the end of history. But no! Wait even longer... Even though the box is at thermal equilibrium, that doesn't mean absolutely nothing ever happens, because thermal equilibrium is a state in which the particles are still bouncing around and colliding and interchanging energy. By far, the most likely outcome of one of these microscopic events is to return the system to the highest entropy state again. But every once in a while, the system entropy will dip lower by a microscopic amount, for a tiny amount of time. And the size and duration of these dips is itself statistically distributed. Wait long enough (I mean, a REALLY long time), and the entropy will dip arbitrarily low. Wait long enough, and there will once again be life and humans and shining stars. So heat death is not forever...

Now, suppose you are a "second generation" human--one that popped up after the heat death of the galaxy. By far, the most likely situation is that you are the ONLY human in an otherwise dead galaxy. If you are relying on random thermal fluctuations to lower the entropy, it's enormously more likely that the entropy is lowered only in a small region of space, than that it is lowered everywhere. But what if this second generation human has memories of a childhood, of parents, of visiting the big city teeming with hundreds of thousands of people? Well, the odds are still greater that those memories are fakes---the accidental artifact of random fluctuations--than that all those things actually happened. So if you knew you were a second-generation human, you would have no logical reason to think that you aren't a brain floating in space and all your memories are false.

Thank God (or whoever) that we're first-generation humans, and we can believe our senses. But then...how do you know that you're a first-generation human? And why can first-generation humans believe their senses? For us to be able to believe our senses means that the rest of the galaxy is not heat-dead, which means that in the far past, the entropy was very, very low compared to the maximum possible entropy. Why did that happen? What reason do we have for believing that it happened (as opposed to our memories being false)?

So to me, the logical puzzle, or brain-teaser, is to understand why the universe should be in a low-entropy state (compared to the highest possible entropy state). Boltzmann's brains are just one way to illustrate the puzzle. I'm not sure that there is any answer other than to shrug our shoulders and say: We're just going to assume that the universe is in the low-entropy state that it appears to be in, and stop worrying about it.

4. Nov 26, 2016

### durant35

But you could still be a BB, it really doesn't matter which generation human are you, if the BB's from the future outnumber humans through history than chances are you should be a BB. The ratio is what matters and if there are infinitely many BB's in spacetime the odds would be that you are a BB. So what is needed is a model where BB's are really an impossibility.

5. Nov 26, 2016

### stevendaryl

Staff Emeritus
It seems to me that of course they are possible, if you say that something with a nonzero probability is possible (no matter how small that probability is).

6. Nov 27, 2016

### windy miller

i dont see that you need BB to be impossible, you only need them to be less probable than normal observers. A model like eternal inflation can generate this. Alan Guth discusses this 27: 13 into this film:

7. Nov 28, 2016

### Chalnoth

I don't think that's accurate. They are a problem in a number of specific cosmological models. They are not a problem in others.

8. Nov 28, 2016

### ShayanJ

This question can only be answered through observations and any observation can be called a fake memory later. So, the way you described it, there is no way to say whether we are first or second generation humans.
But let's say the probability for a Boltzmann brain to form is p. And the probability for it to have a memory worth of one-day is q. And of course you should consider that the probability of having d days of memory is actually less than $q^d$ because the memories can give you an illusion of life only if they're consistent with each other. Also, the more complicated the memory, the less likely. Then as you get older, which means for someone who is there and has a lot of memory, you know that its very improbable for you to be a Boltzmann brain and its more likely that you are a complete human in a real world with other real humans. So I can say, almost with certainty, that I'm not a Boltzmann brain.

9. Nov 28, 2016

### durant35

What would be the chances of creating a Boltzmann brain which is identical with some human who lived in some time in human history (doesn't matter if it's the past, present or the future), so the person would say there's a 50-50 chance that he is a BB. Is that kind of event far unlikely to even consider, despite that there will be many, many humans and many, many brains in the history of universe?

10. Nov 28, 2016

### ShayanJ

The probability of a Boltzmann brain with some special type of memory to come into existence has nothing to do with the number of actual people with that type of memory hat have existed or will exist!

11. Nov 28, 2016

### stevendaryl

Staff Emeritus
But the issue is not the absolute probability of a BB forming, it's the conditional probability. We have certain observations $O$. We're trying to figure out the most likely explanation for those observations. For simplicity, let's suppose that there are only two possible explanations:
1. Evolution: The universe started at an extremely low entropy (compared to the maximum possible entropy), and the usual story is true: hydrogen formed into stars and planets, and one of those planets evolved life.
2. Boltzmann's Brain: The universe is heat-dead except for just me, and my memories are all false.
So, let $P(L)$ be the a-priori probability of an initially low-entropy universe, and let $P(H)$ be the probability of a high-entropy (heat-dead) universe. Then the conditional probability that we evolved or that we are BBs, given observations $O$ is given by:

$P(L|O) = P(L \wedge O)/P(O) = \dfrac{P(L) P(O|L)}{P(O)}$

$P(H|O) = P(H \wedge O)/P(O) = \dfrac{P(H) P(O|H)}{P(O)}$

where $P(A|B)$ means the probability of $A$ given $B$. From probability theory, we have:
$P(A|B) = \dfrac{P(A \wedge B)}{P(B)} = \dfrac{(B|A) P(A)}{P(B)}$

So the argument for Boltzmann's Brain is that, even though $P(O|H)$ is extremely low, the probability $P(H)$ is very high compared with $P(L)$. So the product $P(O|H) P(H) > P(O|L) P(L)$.

The fuzzy part of this is figuring out how to calculate $P(L)$ and $P(H)$. Boltzmann just assumed it was a matter of the volume in phase space. There are many, many more ways to have high entropy than to have low entropy, so $P(H) \gg P(L)$.

When it comes to our universe, we don't really know how to judge the probability of a low-entropy universe versus a high-entropy universe. Some people (Alan Guth, from the above-posted video) believe that eternal inflation naturally leads to lots and lots of low-entropy universes, so maybe $P(L)$ is greater than Boltzmann thought.

12. Nov 28, 2016

### stevendaryl

Staff Emeritus
Let me illustrate the problem with a simpler example:

Suppose I thoroughly shuffle an ordinary deck of 52 cards. Then I deal out the first 4 cards, face-up. They happen to turn out to be, in order,
People give two explanations for this result:
• The deck was in descending order (according to the usual ranking of card values).
• The deck was random, but there just happened to be those 4 cards on top.
(For the purposes of this discussion, I'm just going to equate "random" with "NOT being in descending order").

So we can give two conditional probabilities and two a-priori probabilities:
• $P(result| ordered) = 1$
• $P(result| random) \approx 1.5 \times 10^{-7}$
• $P(ordered) \approx 6 \times 10^{-90}$
• $P(random) \approx 1$
It is very unlikely that a random arrangement of cards just happened to have Ace, King, Queen and Jack of spades as the first four cards. On the other hand, it is very likely (probability = 1) that an ordered arrangement had those cards as the first four. But the odds are tremendously against the deck being ordered. So the random explanation is by far the most likely.

(Unless you propose a mechanism that makes ordered arrangements more likely--that would completely change the calculations.)

13. Dec 12, 2016

### durant35

It is supposed in cosmology that for a theory to be valid it must yield more regular observers than Boltzmann brains. But is that enough?

For instance, we know that the overwhelming majority of Boltzmann brains will have disordered consciousness and observations, vastly different than what we experience. So the minority of BB observations will be like our.

Now suppose that the number of ordered human observers throughout the history is a extremely large number. So large that all the observations that we consider normal and possible brain/mental states that are ordered have been realized in the history of our universe, but without duplication of humans.

So the overwhelming minority of BBs that are ordered would be let's say, 1 percent of the total number of BBs - the total number of BBs is smaller but approximately identical to the number of normal observers. Then the BB minority would have a ratio of 1/100 to normal observers. If all the possible normal observers mental states have been realized there would be a real, real chance of duplication of a brain of an ordinary observer - so even the theory where BBs are in a minority would have some ludacris consequences.

So my question is - what is wrong with this reasoning, and what is really meant when it is said that normal observers should outnumber BBs - do they have to outnumber them by a very, very big number so that the eventual duplication should become extremely unlikely, or is it extremely unlikely that every human brain configuration (or every possible person for that matter) is realized before the thermal equilibrium.

Thanks for the patience.

14. Dec 12, 2016

### stoomart

It seems the answer to your original question "Are the Boltzmann brains seriously taken by the scientific community?" is no; like ShayanJ said earlier, any observation made can be called a fake memory later. I like what the Wikipedia article says on this:

15. Dec 14, 2016

### newjerseyrunner

Do a YouTube search for the biggest number ever printed in a scientific paper. I think the channel was numberphile. It dealt with something like this.

I don't see any way to show that it's impossible, only that it's extremely unlikely. When you deal with very complicated things that require randomness, the time frames involved make heat death seem like next week by comparison.

16. Dec 14, 2016

### Chalnoth

I'm sure it has nothing on calling the Ackerman Function with Graham's Number as the arguments, though (https://xkcd.com/207/).

In all seriousness, conscious brains are extraordinarily complex, and are necessarily extremely far from maximum entropy. It is certainly possible, according to the math, to produce a human brain out of thermal quantum fluctuations, but the frequency is small enough the possibility can be safely ignored in nearly all contexts.

The one context where it does come up is if you have a universe that expands eternally but maintains a finite, non-zero temperature. In such a universe, there's a finite number of real brains produced, because heat death stops the production of new brains after a sufficient amount of time has passed. But after that there's an infinite amount of time to wait, such that even events with absurdly tiny probability will happen an infinite number of times.

The Boltzmann Brain paradox shows that this cannot be right. Any number of things could solve the paradox. It could be that the method of counting probabilities is way off, so that it doesn't make sense to compare a few billion brains that exist right now to the very occasional but still infinite Boltzmann brains that may occur in the far distant future. It could be that the supposition that quantum fluctuations keep happening is wrong: perhaps the fluctuations stop once the universe reaches some final ground state. It could be that Boltzmann Brains are produced, but new pocket universes are produced in greater number, so that real brains vastly outnumber the Boltzmann Brains.

There are lots of ideas here, but the main point is that this is a bit of arcane solipsistic discussion that isn't well-grounded in reality, as it relies upon a lot of unevidenced assumptions. For any real problem that matters for our lives here on Earth, Boltzmann Brains are irrelevant.

17. Dec 15, 2016

### Demystifier

Last edited: Dec 15, 2016
18. Dec 20, 2016

### durant35

On wikipedia there is an article about the timeline of the far future:

https://en.wikipedia.org/wiki/Timeline_of_the_far_future

So it's stated that the estimated time for a Boltzmann brain to appear is 101050.

It is also stated that the estimated time for the Universe to reach its final energy state is 1010120.

Seems like a quite great difference in time. So even before the heat death/thermal equilibrium there seems to be a risk of overproducing BB-s, because the number of the estimated time for the heat death is so much larger than the time for a BB to appear.

What is your take on this, and why or why not is this a problem? Is it valid to compare these two numbers?

19. Dec 20, 2016

### newjerseyrunner

I don't think it's valid to compare the two numbers because of entropy. Things will happen at a slower rate as the universe ages.

20. Dec 20, 2016

### durant35

So the BB production rate/probability to happen would decrease in that age relative to now?