Exploring the Possibility of Boltzmann Brains in the Far Future

[Alltimegreat1]

A coworker of mine keeps mentioning Boltzmann Brains. I was never really interested until yesterday when reading Timeline of the Far Future on Wikipedia, which states the ultimate fate of the universe could be a Boltzmann Brain. Is this a theory scientists believe could really materialize?

 

[Chalnoth]

A coworker of mine keeps mentioning Boltzmann Brains. I was never really interested until yesterday when reading Timeline of the Far Future on Wikipedia, which states the ultimate fate of the universe could be a Boltzmann Brain. Is this a theory scientists believe could really materialize?

The Boltzmann Brain is used to exclude models: if Boltzmann Brains are more common than real brains in a particular model of the universe, then that model is not likely to be correct.

 

[Alltimegreat1]

More common than real brains or more probable do you mean?

 

[Chalnoth]

More common than real brains or more probable do you mean?

As in the number of Boltzmann Brains > the number of real brains. If a model predicts that, then it can't be right.

This argument originally came up with the simple model of the universe as a thermal fluctuation out of equilibrium. The idea there is that when a system is at equilibrium, there are random deviations from that equilibrium. Here you might imagine the universe as a giant box. Within this box, most every time you look, there will be nothing but empty space. But every once in a while, a random drop in entropy will produce something.

The problem with this is that small drops in entropy are exponentially more common than large drops in entropy. So if you only look at the box those times that there is, say, a galaxy in the box, nearly every time there will be only a single galaxy. Two galaxies will be absurdly rare compared to just one galaxy.

Similarly, a single star system will be far, far more common than having two star systems, let alone three or an entire galaxy of stars.

A single planet, one that is temporarily at a high enough temperature to support life, will be far more common still. A single person that imagines observing an external universe will be even more common than a whole planet. Just a disembodied brain that thinks it exists will be the most common thing that thinks it exists.

You might say, "But brains and galaxies don't just pop out of nothing: they form from matter that was around earlier." But that just pushes the problem back: the entropy was always lower in the past. It's harder to form the early universe from a thermal fluctuation than it is to form the present universe!

This line of reasoning shows that there had to be something special about the early, low-entropy state of our universe. There's a fair amount of theorists who are working on possible solutions to this problem. Currently there are a lot of models that avoid this problem, but we don't yet know which (if any) of them are correct.

 

[Chronos]

Boltamann brains can be avoided in any number of ways - one being the many worlds approach in quantum mechanics. This is, IMO, a rather messy solution. All those branching alternate realities would appear to make the bulk pretty crowded in short order. It's sort of like worrying about the universe going poof by decaying out of a false vacuum state. If you take the Boltzmann brain paradox seriously, you also risk falling prey to false vacuum psychosis. I find solace in the idea some events are so wildly improbable they simply never occur in a finite amount of time - of course, that opens you up to the prospect the universe is not past eternal. Either way, I have yet to encounter an altogether convincing and elegant solution to the Boltzmann brain dilemma.

 

[mfb]

As in the number of Boltzmann Brains > the number of real brains. If a model predicts that, then it can't be right.

Why not?
I have a model predicts that the majority of brains does not use "Chalnoth" as user name. Does the model have to be wrong because you are not in this majority?
Even worse, where is your proof that you are not a Boltzmann brain? It seems unlikely as your memories make sense (which seems to be unlikely for a Boltzmann brain), but you cannot exclude it.

From a philosophical point of view, a model that doesn't have a majority of Boltzmann brains sounds nicer, but that is not a scientific argument.

 

[Chalnoth]

Why not?
I have a model predicts that the majority of brains does not use "Chalnoth" as user name. Does the model have to be wrong because you are not in this majority?

Except observation confirms that I'm not in the majority. I really don't know what you're trying to argue here.

Even worse, where is your proof that you are not a Boltzmann brain? It seems unlikely as your memories make sense (which seems to be unlikely for a Boltzmann brain), but you cannot exclude it.

Nearly all Boltzmann brains will have disordered observations. Most will see nothing but random noise. Almost none of them will see an ordered world that follows natural laws.

One way to see this is to note that there are ways to tell pretty conclusively whether or not you are dreaming. If you are dreaming, then physics generally doesn't work, and there are very simple ways to test this. For example, you can hold your nose and try to breathe. In a dream, you'll still be able to breathe because your brain doesn't do a very good job of simulating the physics of holding your nose. Another method is to look at writing: in a dream, writing tends to change if you look away then look back.

But even dreams are a hell of a lot more ordered than anything you'd get in most any Boltzmann Brain scenario, as such brains are not at all constrained by the limits that our brains operate under.

It's true that there's no absolute proof that we are not Boltzmann Brains. But that's a philosophical argument, not a scientific one. Science doesn't deal with absolute proof.

 

[mfb]

Except observation confirms that I'm not in the majority. I really don't know what you're trying to argue here.

So where would be the problem of being in a minority of non-Boltzmann brains?

Nearly all Boltzmann brains will have disordered observations. Most will see nothing but random noise. Almost none of them will see an ordered world that follows natural laws.

That's why I said "it seems unlikely" - but there will be a few Boltzmann brains where memories make sense, at least for the short period of their existence. And those Boltzmann brains will rule out that they are Boltzmann brains - incorrectly.

 

[Chronos]

If a Boltzmann Brain were not in an ordered state, it would not be much of a brain, would it? We may be digressing here in quibbling over the nature of a Boltzmann Brain. This excerpt from http://arxiv.org/abs/hep-th/0405270 sums it up nicely, IMO:

"A century ago Boltzmann considered a “cosmology” where the observed universe should be regarded as a rare fluctuation out of some equilibrium state. The prediction of this point of view, quite generically, is that we live in a universe which maximizes the total entropy of the system consistent with existing observations. Other universes simply occur as much more rare fluctuations. This means as much as possible of the system should be found in equilibrium as often as possible.

From this point of view, it is very surprising that we find the universe around us in such a low entropy state. In fact, the logical conclusion of this line of reasoning is utterly solipsistic. The most likely fluctuation consistent with everything you know is simply your brain (complete with “memories” of the Hubble Deep fields, WMAP data, etc) fluctuating briefly out of chaos and then immediately equilibrating back into chaos again. This is sometimes called the “Boltzmann’s Brain” paradox."

I find Chalnoth's comments compatible with this logic

 

[Chalnoth]

If a Boltzmann Brain were not in an ordered state, it would not be much of a brain, would it?

The brain itself may be in a very ordered state, but it still isn't likely to "observe" order (observe in quotes because it's not actually observing anything).

This is why I made the comparison to dreaming: you can reliably determine whether or not you're dreaming by testing how physics behaves. The only real obstacle to this is that it rarely occurs to us to actually test whether or not we're dreaming (if you really want to do this, one way is to get into the habit of testing yourself for dreaming regularly while you're awake).

I find Chalnoth's comments compatible with this logic

I certainly hope so! Andy Albrecht was one of my professors. I always admired his clarity of thinking when it came to theoretical physics.

 

[Chronos]

I was merely acknowledging I appeciate where you were coming from.

 

[rootone]

I asked my girlfriend about this, how do you know whether or not an observation is real or imaginary?
She said 'You know'?

 

[durant35]

So where would be the problem of being in a minority of non-Boltzmann brains?

Sorry for hijacking an old thread, but I feel I need to respond so the members who search the forum about this topic find some better insight.

This is why: https://arxiv.org/abs/1702.00850 [Sean Carroll - Why Boltzmann brains are bad]

I waited for your response and eventual opinion in the other thread because I respect it and if you haven't got any, that's ok. Just making sure that it is mentioned what is wrong with this line of thinking.

 

[windy miller]

Theres an assumption in the BB argument that a brain is more likely to thermally fluctuate into existence than a entire universe. but how sure can we can be of this statement? What if you don't need an entire universe to fluctuate but instead just a universe seed? perhaps that seed is less complicated than a brain and could thermally fluctuate into existence then it would seem Boltzman would be right all along. What's wrong with the reasoning here?

 

[PeterDonis]

perhaps that seed is less complicated than a brain and could thermally fluctuate into existence

And then what? The seed itself is not a universe or a brain. If the answer is that in 14 billion years or so it's going to develop into a universe that contains brains, then your hypothesis is not the Boltzmann Brain hypothesis, and in fact is an argument against it.

 

[Chalnoth]

Theres an assumption in the BB argument that a brain is more likely to thermally fluctuate into existence than a entire universe. but how sure can we can be of this statement? What if you don't need an entire universe to fluctuate but instead just a universe seed? perhaps that seed is less complicated than a brain and could thermally fluctuate into existence then it would seem Boltzman would be right all along. What's wrong with the reasoning here?

A "universe seed" by definition has lower entropy than a brain (for the reason that a whole universe has lower entropy than a single brain, and an early universe has lower entropy than a late one). As long as the probability of a fluctuation is proportional to an exponential function of entropy, the brain is going to be far more likely.

Basically the way out of this is to provide a coherent argument that the probability is not simply proportional to an exponential function of entropy.

 

[durant35]

A "universe seed" by definition has lower entropy than a brain (for the reason that a whole universe has lower entropy than a single brain, and an early universe has lower entropy than a late one). As long as the probability of a fluctuation is proportional to an exponential function of entropy, the brain is going to be far more likely.

Basically the way out of this is to provide a coherent argument that the probability is not simply proportional to an exponential function of entropy.

Which is very tough, of course, but there's something else which is controversial when discussing what can fluctuate. Sean mentions it in the article, and the term is ergodicity. All these issues are based on a pretty unproven assumption that everything obeys Boltzmann's ergodic theorem which is almost 150 years old.

 

[Chalnoth]

Which is very tough, of course, but there's something else which is controversial when discussing what can fluctuate. Sean mentions it in the article, and the term is ergodicity. All these issues are based on a pretty unproven assumption that everything obeys Boltzmann's ergodic theorem which is almost 150 years old.

I think this boils down to the question of unitarity. If the fundamental laws of physics are unitary (which many theorists feel is a requirement for causality), then the system follows Liouville's Theorem, which is closely related to ergodicity. Ergodicity and Liouville's Theorem are not exactly the same, but I think it's the latter which is more related to this subject.

 

[durant35]

I think this boils down to the question of unitarity. If the fundamental laws of physics are unitary (which many theorists feel is a requirement for causality), then the system follows Liouville's Theorem, which is closely related to ergodicity. Ergodicity and Liouville's Theorem are not exactly the same, but I think it's the latter which is more related to this subject.

Could you please explain why in your previous post you mentioned that the current universe has a lower entropy than a brain?

Isn't entropy the measure for the number of microstates and by definition a bigger object would have more, so the entropy would be higher in the mentioned example?

 

[Chalnoth]

Could you please explain why in your previous post you mentioned that the current universe has a lower entropy than a brain?

Isn't entropy the measure for the number of microstates and by definition a bigger object would have more, so the entropy would be higher in the mentioned example?

The way to do this properly is not to just look at the entropy of the brain in isolation, but rather compare its entropy to the maximal entropy of the system in question. A brain is a much smaller difference in entropy compared to empty space over the same region than our current universe is from empty space over the whole universe.

 

[durant35]

The way to do this properly is not to just look at the entropy of the brain in isolation, but rather compare its entropy to the maximal entropy of the system in question. A brain is a much smaller difference in entropy compared to empty space over the same region than our current universe is from empty space over the whole universe.

That makes much more sense, thank you.

 

[windy miller]

A "universe seed" by definition has lower entropy than a brain (for the reason that a whole universe has lower entropy than a single brain, and an early universe has lower entropy than a late one). As long as the probability of a fluctuation is proportional to an exponential function of entropy, the brain is going to be far more likely.

Basically the way out of this is to provide a coherent argument that the probability is not simply proportional to an exponential function of entropy.

Alan Guth seems to be saying something like this .perhaps I have misunderstood it. But In his book "the inflationary universe". he gives the example of two possible universes, universe A and universe B. Universe A is ten to the power 1,000,000 times more likely to start an inflationary phase than universe B. But universe B has .001% faster exponential growth rate. According to Guth after one second Universe b will have 10^3*10^31 more volume. he says "The factor of 10^ 1,000,000 is so unimportant , coopered to the exponential expansion , that the affect disappears when answer is rounded off. The effect of the exponential expansion is so dramatic that even an unbelievably large difference in initial probabilities can be compensated in less than a second."
To me that seems mohave some relevance here. It may be the case that the Brain has more probability to form but that isn't the only question , if the seed is something like an inflating nugget that leads to a huge universe. then the initial low probability for it to form is irrelevant. In terms of the phase space the universe may dominate over the brain.
There is an interview where he seems to be saying exactly this:

 

[durant35]

The way to do this properly is not to just look at the entropy of the brain in isolation, but rather compare its entropy to the maximal entropy of the system in question. A brain is a much smaller difference in entropy compared to empty space over the same region than our current universe is from empty space over the whole universe.

Mr Chalnoth, I have a question regarding Carroll's previous paper in which he claims that there are no fluctuations in de Sitter space. I'm sure you are aware of that paper, if not I can link it to you.

The thing that's not very understandable to me is that he says that our universe is asymptotically approaching the Bunch-Davies vacuum/de Sitter space. I'm no expert in terminology but it seems to me that 'approaching asymptotically' is not the same as reaching the state that I already mentioned, so does our universe reach at all the de Sitter phase where there is no normal matter and fluctuations, just empty space with a horizon that is radiating? Therefore, does the paper make sense since it is debatable that the universe settles into de Sitter phase (which is not the same as asymptotically aproaching but never quite reaching)?

 

[Chalnoth]

To me that seems mohave some relevance here. It may be the case that the Brain has more probability to form but that isn't the only question , if the seed is something like an inflating nugget that leads to a huge universe. then the initial low probability for it to form is irrelevant. In terms of the phase space the universe may dominate over the brain.

The problem with this argument is that the production probability is exponentially-suppressed as a function of the entropy. Appealing to exponential growth of the outcome won't necessarily be able to overcome this obstacle.

 

[Chalnoth]

The thing that's not very understandable to me is that he says that our universe is asymptotically approaching the Bunch-Davies vacuum/de Sitter space. I'm no expert in terminology but it seems to me that 'approaching asymptotically' is not the same as reaching the state that I already mentioned, so does our universe reach at all the de Sitter phase where there is no normal matter and fluctuations, just empty space with a horizon that is radiating? Therefore, does the paper make sense since it is debatable that the universe settles into de Sitter phase (which is not the same as asymptotically aproaching but never quite reaching)?

The argument for the fluctuations into the infinite future comes from the statement that the far future state is one with nothing but a cosmological constant but a finite temperature, due to the Hawking radiation produced by the horizon. What this paper is saying is that it doesn't work that way: the Hawking radiation from the horizon can't produce quantum fluctuations because it comes from a system in a stationary state.

Yes, it is true that the universe will only approach this state asymptotically, but it means that such fluctuations can only arise from matter/radiation that gets diluted by the expansion, decreasing in probability as time passes, eventually tapering off to zero (when there are one or zero particles per cosmological horizon). So instead of having an infinite amount of time to wait in an exponentially-growing space in order to allow fluctuations to happen, such fluctuations will peter out and eventually reach zero amplitude. Provided the paper in question accurately describes reality.

 

[durant35]

The argument for the fluctuations into the infinite future comes from the statement that the far future state is one with nothing but a cosmological constant but a finite temperature, due to the Hawking radiation produced by the horizon. What this paper is saying is that it doesn't work that way: the Hawking radiation from the horizon can't produce quantum fluctuations because it comes from a system in a stationary state.

Yes, it is true that the universe will only approach this state asymptotically, but it means that such fluctuations can only arise from matter/radiation that gets diluted by the expansion, decreasing in probability as time passes, eventually tapering off to zero (when there are one or zero particles per cosmological horizon). So instead of having an infinite amount of time to wait in an exponentially-growing space in order to allow fluctuations to happen, such fluctuations will peter out and eventually reach zero amplitude. Provided the paper in question accurately describes reality.

Hey Mr Chalnoth, sorry for again resurrecting an old thread but I have one question about the stuff mentioned in the paper and in your post. Everything that you said seems very reasonable.

My question is: does it apply to the global picture, when we consider multiple patches and the spacetime volume bigger than the observable universe?

I've red some papers about inflation where it is mentioned that the number of the BBs is proportional to the total spacetime volume. But the spacetime volume grows, so it seems that the total number should also grow in a line with the expansion of space (or spacetime). In this paper, and intuitively it seems that expansion of space suppresses low entropy fluctuations because everything including matter and vacuum radiation dilutes away and gets further away from each other, but this is directly opposite to the picture I mentioned before where the growth of space globally causes the increase in fluctuations? So if fluctuations are suppressed - is it because the rate of exit and diluting is greater than the rate of fluctuations multiplied with the growth of space...?

Does expansion of space add something new (like particles) to the universe because I cannot see directly why growth of space would increase fluctuations?

Thanks for the patience and your eventual reply

 

[julcab12]

Does expansion of space add something new (like particles) to the universe because I cannot see directly why growth of space would increase fluctuations?

Thanks for the patience and your eventual reply

.. Nope. The expansion of space merely means that the distances between objects are getting farther apart over time. With space-- We don't know the extent of it.

In QM. The density of field fluctuation energy in the vacuum -- elementary particles represent percentage‐ wise almost completely negligible change in the locally. Matter is no more than fluctuations in vacuum.