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Boltzman brains

by 0xDEADBEEF
Tags: boltzman, brains
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0xDEADBEEF
#1
Jul28-09, 05:30 PM
P: 825
Could someone give me a quick explanation what Boltzmann brains are? Does it have something to do with the landscape?
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Chalnoth
#2
Jul29-09, 01:33 AM
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P: 4,802
The Boltmann Brain argument goes as follows:

If we consider thermodynamics, we know that while thermodynamics says that entropy usually increases, it also says that entropy occasionally decreases spontaneously. Perhaps our universe began as just such a random fluctuation to lower entropy?

However, when there are fluctuations to lower-entropy configurations, it is always the case that small entropy fluctuations are vastly more common than large ones. Our whole universe, were it to start from such a fluctuation, would have to stem from a massive, massive fluctuation. Small fluctuations are much more likely.

Now, consider that one possibility that we cannot absolutely rule out is the possibility that reality is an illusion. It is conceivable, for instance, that we could all be nothing but brains that exist with the impression of viewing the outside world. Now, this actually isn't reasonable because we observe order in the world around us: essentially all such random brains whose reality is just an illusion will see chaotic and nonsensical realities, not the ordered reality we observe.

That said, such a "Boltmann Brain", that is a disembodied brain that has the impression of seeing some reality, is a much, much smaller fluctuation in entropy than a whole universe. It is far easier to produce a Boltmann Brain out of a simple entropy fluctuation than it is to produce a whole universe with stars, galaxies, planets, plants, animals, etc. But since we know that our own experiences don't mesh with us being Boltmann Brains, it is clear that the simple notion of our universe stemming from a fluctuation out of equilibrium cannot be accurate. Reality must be more complicated than that.
Haelfix
#3
Jul30-09, 10:35 AM
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By assumption, if the universe is infinitely large and with infinite time (like in some versions of the multiverse scenario) you are guarenteed to produce exactly those types of fluctuations. Worse, the observed low entropy of the universe is vanishingly small in the set of random ensembles of possible universes relative to having a single entity spawned with fake memories.

ANyway, one of the problems with the Boltzmann brain argument isn't that we haven't observed nonsense *yet*, its that it makes a prediction for what we should see identically one unit of time in the future. Each additional second we observe the world, adds astronomical probabilities against the hypothesis. But thats the problem in the first place -- statistics and how to make sense of them in these infinite random cases.

Chalnoth
#4
Jul30-09, 05:11 PM
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Boltzman brains

Quote Quote by Haelfix View Post
By assumption, if the universe is infinitely large and with infinite time (like in some versions of the multiverse scenario) you are guarenteed to produce exactly those types of fluctuations. Worse, the observed low entropy of the universe is vanishingly small in the set of random ensembles of possible universes relative to having a single entity spawned with fake memories.

ANyway, one of the problems with the Boltzmann brain argument isn't that we haven't observed nonsense *yet*, its that it makes a prediction for what we should see identically one unit of time in the future. Each additional second we observe the world, adds astronomical probabilities against the hypothesis. But thats the problem in the first place -- statistics and how to make sense of them in these infinite random cases.
Well, I think what we're missing is something interesting about the physics that produces universes like our own that causes real brains to vastly outnumber such "boltmann brains". One proposal for how this may be so is given by this paper by Sean Carroll and Jennifer Chen:
http://arxiv.org/abs/hep-th/0410270
Haelfix
#5
Jul31-09, 01:04 AM
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I didn't like that paper, as its far fetched and going on about a nonissue imo.

Actually, I really don't understand the conceptual problem in the first place or why people are still harping about the arrow of time and what it can possibly solve. As far as I can see, this has been settled for nearly a hundred years and the answer was given by the second law - period! This is the unique arrow of time and we aren't reversible.

We observe the universe now (call it Z2) and to the time of last scattering (call it Z1), and we see that the entropy of Z2 is a little higher than Z1. Nothing unusual there, we'd obviously have a major problem if it was upside down. In the future at some time (call it Z3), we'd expect the entropy to be even higher. Good!

People wonder why Z1 is small relative to what it could be (we'll call that Zavg, where Zavg is the entropy of a random universe in some thermalized and highly likely state in the ensemble of possible universe wide configurations) and as far as I can see, the best answer is, it is the way it is by observation (somewhat begging the question granted).

Recently with the multiverse craze, people like to try to make everything a density fluctuation and wonder why we aren't a Boltzman brain instead. Well, again, we probably could have been, but observation again rules that out and falsifies the hypothesis. So we're back to square one. Z1 is simply an initial condition that breaks the symmetry.

If there is, for instance, a Hartle-Hawking wavefunction, then this makes perfectly good sense. A single initial state has entropy ~ln(1) = 0.
Chalnoth
#6
Jul31-09, 01:14 AM
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Quote Quote by Haelfix View Post
I didn't like that paper, as its far fetched and going on about a nonissue imo.

Actually, I really don't understand the conceptual problem in the first place or why people are still harping about the arrow of time and what it can possibly solve. As far as I can see, this has been settled for nearly a hundred years and the answer was given by the second law - period! This is the unique arrow of time and we aren't reversible.
Except that one can use the same derivation of the second law of thermodynamics that proves that entropy must increase in the future to equally prove that entropy must increase in the past. You just can't derive a time-asymmetric law from underlying laws of physics that are perfectly symmetric in time.

So no, the arrow of time isn't a non-issue at all. It is a surprise, from how the second law is derived, that entropy is lower in the past. That is something that must be reconciled.
Haelfix
#7
Jul31-09, 02:01 AM
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I don't agree at all. This is explained at length in the Feynman lectures.

It is true, that if you naively send t --> -t, you will still see an entropy increase into the past, but the point is you cannot do this operation b/c of friction and dissapative effects.

The classical picture of an egg breaking (it never comes back together again) or of a red/blue liquid mixing but not unmixing is an example of this. The local laws of course are still time symmetric (well CPT invariant), but the origin of the asymmetry is macroscopic and it is derivable.

Forget about the big bang. Right now the entropy of the world is x. Five minutes in the future, the entropy of the world will be x + epsilon. Five minutes in the future we can correctly say that it makes sense that five minutes in the past we were at a lower entropy state even if we forgot all memories of the event (say we had short term amnesia). This is the origin of all irreversability and there is no paradox.
Chalnoth
#8
Jul31-09, 02:48 AM
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Quote Quote by Haelfix View Post
I don't agree at all. This is explained at length in the Feynman lectures.

It is true, that if you naively send t --> -t, you will still see an entropy increase into the past, but the point is you cannot do this operation b/c of friction and dissapative effects.
You can't derive an arrow of time by putting it in by hand! The only reason why we derive the second law of thermodynamics going forward in time is that that is the direction that accords with observation. That assumption is still put in by hand, though, and does not stem from the underlying laws.

I think Sean Carroll has it right when he says that the answer for the time-asymmetric reality that we observe is a consequence of how our region of the universe began, not directly a consequence of the nature of fundamental law.
Haelfix
#9
Jul31-09, 03:17 AM
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The obvious problem with that idea is the following.

If there was some special property of the early universe/cosmology that allowed us to evolve from a low entropy state to a large entropy state, then there should be another universe that has the opposite behaviour, at least in principle. So they would by hypothesis go from a high entropy state to a low entropy state. Or in other words, an observer in that universe would see humpty dumpty spontaneously coming back together again. He would see large scale structures flying apart, rather than being clumped by gravity.

But thats crazy! The large scale behaviour of spacetime absolutely cannot change the local laws of physics (say solar system physics). Ergo the perpetual rise in entropy and the irreversability that it entails (even on human scales) cannot possibly be explained by cosmological initial conditions.

The only thing that cosmology can tell us, is in principle why is the initial condition so low relative to what it could be (eg not why z1 < z2 for any universe, but why z1 was not ~ z avg).
Chalnoth
#10
Jul31-09, 03:32 AM
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Quote Quote by Haelfix View Post
The obvious problem with that idea is the following.

If there was some special property of the early universe/cosmology that allowed us to evolve from a low entropy state to a large entropy state, then there should be another universe that has the opposite behaviour, at least in principle. So they would by hypothesis go from a high entropy state to a low entropy state. Or in other words, an observer in that universe would see humpty dumpty spontaneously coming back together again. He would see large scale structures flying apart, rather than being clumped by gravity.

But thats crazy!
It's not crazy at all. It just means that the arrow of time is dependent upon the initial conditions. It's counterintuitive, to be sure. But the physics work out identically for an arrow of time like the one we experience, or one in the opposite direction.

Quote Quote by Haelfix View Post
The large scale behaviour of spacetime absolutely cannot change the local laws of physics (say solar system physics). Ergo the perpetual rise in entropy and the irreversability that it entails (even on human scales) cannot possibly be explained by cosmological initial conditions.

The only thing that cosmology can tell us, is in principle why is the initial condition so low relative to what it could be (eg not why z1 < z2 for any universe, but why z1 was not ~ z avg).
That would require that the arrow of time be different in different regions of the universe, or different on different size scales. And that does appear to be disallowed.

And besides, I think you're forgetting that all of the stuff around us originally came from a very small expanding patch.
Haelfix
#11
Jul31-09, 05:18 AM
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The point is changing cosmological initial conditions or models won't change the nature of the 2nd law, nor can it define it. It simply cannot, by locality.

Even if you start with a very high entropy initial condition, whatever universe (and by universe I mean the whole thing) you are in, will simply proceed to an even higher entropy (you'll get more and more blackholes) state. Thats what the 2nd law tells us. Eg, the one thing that is explicitly forbidden is to go from high to low entropy globally. It could be that we are a quasi local fluctuation in the multiverse but that same multiverse is still monotonically increasing its entropy.

Any observer, regardless of which cosmology they are in will almost never see a liquid spontaneously going from a mixed state into blue and red, whether they are in a fluctuation or not.. This perfectly local arrow of time will not change directions depending on location either, why would it.. Its identically the same everywhere we look, contrary to what a cosmological origin would indicate (where you might have various parts of the universe changing their cosmological arrows willy nilly).
Chalnoth
#12
Jul31-09, 06:30 AM
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Quote Quote by Haelfix View Post
The point is changing cosmological initial conditions or models won't change the nature of the 2nd law, nor can it define it. It simply cannot, by locality.

Even if you start with a very high entropy initial condition, whatever universe (and by universe I mean the whole thing) you are in, will simply proceed to an even higher entropy (you'll get more and more blackholes) state. Thats what the 2nd law tells us. Eg, the one thing that is explicitly forbidden is to go from high to low entropy globally. It could be that we are a quasi local fluctuation in the multiverse but that same multiverse is still monotonically increasing its entropy.

Any observer, regardless of which cosmology they are in will almost never see a liquid spontaneously going from a mixed state into blue and red, whether they are in a fluctuation or not.. This perfectly local arrow of time will not change directions depending on location either, why would it.. Its identically the same everywhere we look, contrary to what a cosmological origin would indicate (where you might have various parts of the universe changing their cosmological arrows willy nilly).
You still haven't grasped the fundamental point: from the way we have derived the second law of thermodynamics, watching a liquid go from blue and red to a mixed state is exactly as weird as watching it go from that mixed state back to blue and red.

The only reason why the second law of thermodynamics in any way conforms to the reality which we observe is because we put "that way = forward in time" in by hand. Otherwise, if we sit with a tank that is split into partitions of blue and red as an initial condition, then statistical mechanics, ignoring the overall arrow of time, says that it will appear more and more mixed both into the past and into the future.
Haelfix
#13
Jul31-09, 01:25 PM
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Thats just a statement of Loschmidt's paradox, which was succesfully resolved eons ago by Boltzman himself (and proved conclusively in the 50s).

Its wrong to argue that the 2nd law is reversable and time symmetric (you can't replace t-->-t and expect things to be the same b/c the probabilities and the volume of the phase spaces are not symmetrical). So the 2nd law, together with the initial condition of the universe, defines past and future for all observers uniquely. The past is the low entropy state, and the future is the high entropy state and it can't be any other way, even in principle! I dont see why you think this is put in by hand, as its a derivable consequence and I still fail to see what the fuss is about.

Hawking himself made this error at one point during his career, when he incorrectly argued that a big crunch in his no boundary proposal would lead to a reversal of the thermodynamic arrow. He correctly changed that position shortly thereafter.
Chalnoth
#14
Jul31-09, 02:03 PM
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Quote Quote by Haelfix View Post
Thats just a statement of Loschmidt's paradox, which was succesfully resolved eons ago by Boltzman himself (and proved conclusively in the 50s).
No, it wasn't. As far as I can tell, Boltmann's solution depends critically upon the assumption that the correlations between velocities are uninteresting. But even if we assume that, there's the problem that if you take the "initial point" and then go backward in time, statistical mechanics says you'll get an increase in entropy backward in time.

What proof in the 50's are you pointing to, anyway?

Quote Quote by Haelfix View Post
Its wrong to argue that the 2nd law is reversable and time symmetric (you can't replace t-->-t and expect things to be the same b/c the probabilities and the volume of the phase spaces are not symmetrical). So the 2nd law, together with the initial condition of the universe, defines past and future for all observers uniquely. The past is the low entropy state, and the future is the high entropy state and it can't be any other way, even in principle! I dont see why you think this is put in by hand, as its a derivable consequence and I still fail to see what the fuss is about.
Because it is a fundamental impossibility to derive time-asymmetric behavior from underlying laws which are symmetric in time. People keep trying, but nobody has succeeded. The arrow of time is always put in by hand.

The way that this is done cosmologically is to make use of a low-entropy boundary condition that starts off a region of the universe like our own. Then the arrow of time simply points away from that beginning.

Quote Quote by Haelfix View Post
Hawking himself made this error at one point during his career, when he incorrectly argued that a big crunch in his no boundary proposal would lead to a reversal of the thermodynamic arrow. He correctly changed that position shortly thereafter.
Well, that's why a "big crunch" in the most naive sense, where such a reversal is required, can be considered a fundamental impossibility. Apparently the ekpyrotic scenario claims to get around this, but I am as yet unclear how this is accomplished.


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