Expanding universe and the Boltzmann brain problem

[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

 

[mfb]

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.

 

[analyst5]

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.

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.

 

[mfb]

I don't have the book.

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

 

[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.

 

[analyst5]

I don't have the book.

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

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.

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

Could you explain with more details?

Regards.

 

[mfb]

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

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).

 

[cosmik debris]

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).

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

 

[mfb]

It is the reason for the accelerated expansion, yes.

 

[analyst5]

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.

It is the reason for the accelerated expansion, yes.

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 Earth's. 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

 

[PeroK]

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 Earth's. 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

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.

 

[mfb]

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 Earth's. If a theory predicts this kind of stuff, it must be false because statistics would put us in a unexplainable position.

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.

 

[Chalnoth]

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?

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.

 

[mfb]

An infinite universe right now would be sufficient to get an infinite number of normal brains.

but new universes are also produced

This is one of the predictions of eternal inflation.

 

[Chalnoth]

An infinite universe right now would be sufficient to get an infinite number of normal brains.

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.

 

[analyst5]

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.

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.

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

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?

 

[analyst5]

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.

Thanks for the great response Chalnoth.

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

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

 

[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

 

[Chalnoth]

Thanks for the great response Chalnoth.

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

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

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.

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

Thanks,

Analyst

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

 

[analyst5]

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.

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

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

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?

 

[mfb]

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

There is also zero experimental evidence that, if you flip coins long enough, eventually you'll get 100 heads in a row. There is also zero evidence that you'll get a million heads in a row. But do you really doubt that?

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?

In every finite volume: yes.

 

[analyst5]

There is also zero experimental evidence that, if you flip coins long enough, eventually you'll get 100 heads in a row. There is also zero evidence that you'll get a million heads in a row. But do you really doubt that?

Yes, I do.

But, as I mentioned before, I also doubt that structures emerging from high entropy states are in the same class as coin flipping, lottery etc. It is based on a number of controversial and unevidenced assumptions, like particle and energy conservation, binding energy for structures to form etc.

It is pretty naive to expect something to form just because it is made of same stuff as the stuff that we have evidence of.

In every finite volume: yes.

So we can extrapolate "every finite volume" to infinity to avoid the measure problem?

 

[PeroK]

There is also zero experimental evidence that, if you flip coins long enough, eventually you'll get 100 heads in a row. There is also zero evidence that you'll get a million heads in a row. But do you really doubt that?In every finite volume: yes.

It isn't so clear what is physically, rather than mathematically, meant by this. The maths is clear. But, the expected time is so long that the physical conditions to continue the experiment may not be physically able to prevail for long enough.

There are some mathematical things that are not realisable, as I know you know. This is not in that category, as it could happen at the first attempt. But, it perhaps falls into a category of things that are physically insignificant. The old QM prediction that we might walk through a solid wall, for example. That has no physical significance.

The fact that you could throw 100 heads in a row is possibly of no physical significance.

To take another example of the wretched monkey typing the complete works of Shakespeare. The maths is clear, but it is wrongly applied in that case. It assumes that monkeys behave in a way (eternally typing random characters) which they do not. So, the statement that eventually a monkey will produce the complete works of Shakespeare (which I know some mathematicians would defend) is, in my view, a mathematical model wrongly applied to a physical situation. In fact, one could argue that it makes a mockery of mathematics, but that's another matter.

If we turn to a computer program generating random characters, we are on more solid ground. We can estimate how long we expect to wait until we get any word, phrase, sentence, act, play etc.

But, if these timescales are longer than we can expect the computer, human civilisation and possibly the universe to endure, then what do we mean by "eventually it must happen". A more accurate statement might be:

If this process continued at 1 character per Planck time for n trillion years (expected lifetime of the universe where the experiment could continue), then the probability of getting the "to be or not to be" soliloquy is, say, $10^{-100}$.

Now, mathematically this means nothing, because we are sure mathematically of what infinity means.

But, physically, this is significant, because we are not sure what "infinite" time really means. Infinite time cannot be physically conjured by an axiom, the way it can mathematically.

That, to me, is at least an analysis of why you can't necessarily apply the conclusions of mathematics to the physical universe in these cases.

 

[mfb]

There is also zero experimental evidence that, if you flip coins long enough, eventually you'll get 100 heads in a row. There is also zero evidence that you'll get a million heads in a row. But do you really doubt that?

Yes, I do.

What exactly do you expect then? Note that all 2^1000000 sequences of 1 million coin tosses are equal. 1 million heads in a row is not less likely than any other fixed sequence, and there will always be some sequence. What is special about "1 million heads", apart from our artificial choice of discussing this instead of any other sequence?

"A Boltzmann brain" is a small volume in the phase space. Every other small volume is unlikely as well - but yet we constantly see those unlikely things. The probability that all the atoms in your coffee cup are in exactly the state they currently are is tiny. We don't call those events unlikely because our artificial classification combines many of those tiny volumes to a single "nothing special happened" - you don't care about the state of every atom in your coffee cup. But that has no physical relevance. Extremely unlikely things happen in the universe all the time. They just don't appear unlikely to humans as we make very biased groups in the set of possible results.

So we can extrapolate "every finite volume" to infinity to avoid the measure problem?

The extrapolation is exactly the dangerous point, because it is not well-defined.

But, the expected time is so long that the physical conditions to continue the experiment may not be physically able to prevail for long enough.

Maybe, but that is a different topic, and not the scenario I considered in my post.

 

[analyst5]

What exactly do you expect then? Note that all 2^1000000 sequences of 1 million coin tosses are equal. 1 million heads in a row is not less likely than any other fixed sequence, and there will always be some sequence. What is special about "1 million heads", apart from our artificial choice of discussing this instead of any other sequence?

"A Boltzmann brain" is a small volume in the phase space. Every other small volume is unlikely as well - but yet we constantly see those unlikely things. The probability that all the atoms in your coffee cup are in exactly the state they currently are is tiny. We don't call those events unlikely because our artificial classification combines many of those tiny volumes to a single "nothing special happened" - you don't care about the state of every atom in your coffee cup. But that has no physical relevance. Extremely unlikely things happen in the universe all the time. They just don't appear unlikely to humans as we make very biased groups in the set of possible results.

See, this is what makes absolutely no sense. You are making conclusions based on an assumption that probability doesn't have a well-defined meaning of something objective that is happening out there. I believe that probability has nothing to do with humans and that it has a lot of physical relevance.

It is true that each coin toss has a 50-50 probability and that each sequence is no different than the previous or next one. But many same sequences, are in fact highly unlikely, and that is based on something which is physical.

It is exactly because of these kind of conclusions that the MWI is considered seriously, you just sweep the probability under the carpet while in fact probability is the one thing from which you should start building conclusions.

The state of every atom in my coffee cup is determined by a set of previous interactions and given approximate determinism, highly likely if we consider the past.

A car or Barack Obama's twin that emerges from vacuum is an unlikely event, not something that is just labeled as unlikely. The fact that you can even type this post isn't a label, many causal factors made the decision and the action extremely likely to happen.Are both the fact that you're typing on physics forum and the fact that you might quantum tunnel through your room both equally probable? Are they both 'equally unlikely'? I think that there's some underlying physics beneath it

 

[PeroK]

A car or Barack Obama's twin that emerges from vacuum is an unlikely event, not something that is just labeled as unlikely.

Although each configuration is equally likely, at the macroscopic level we are interested in the physical properties of the whole system. So, we are really interested in the number of possible states that are categorised by some macroscopic property (and hence the probability of that property for the system).

If we toss a coin 1 million times and between 49% and 51% heads represents property A; 48-49% heads property B; ... ; 0-1% heads property Z, then we almost always observe property A in the system. And, although property Z cannot be said to be impossible, it is negligibly unlikely.

So, is someone says that Barack Obama's twin might appear in front of you in the next hour and the probability is $10^{-1,000,000}$ or whatever, then you can safely answer "so what".

Or, if someone says you might be a Boltzmann Brain, you can say "so what".

When someone says there are a infinite number of Boltzmann Brains in the universe, it's not so easy to say "so what", but it may still be a valid answer. You could also say "I don't know what that means physically" or "that conclusion is based upon untestable assumptions".

There is also a mathematical way out that may or may not be relevant. These paradoxes are generally based on adding the same small probability an infinite number of times. But, if for some reason the probability reduced with time or according to different regions, then the mathematical basis vanishes.

For example, if the probability something happens in the next year is $\epsilon$ and it can be shown that the probability of its happening halves every year, then the total probability of its happening over infinite time is only $2 \epsilon$ and not $1$, which would represent certainty.

Again, it's often an untestable assumption that the probability of something happening in an infinite universe is constant and does not depend on time and space.

 

[BenAS]

While my education is limited, I must say I have trouble accepting the statement that in an infinite universe every possible outcome occurs somewhere. Pardon my ignorance but I don't see any mathematical support for this statement.

I tried to write out a very simple example of what I'm thinking:

Imagine a universe made of legos (where x is the total number of pieces) and each Lego could fit into any other Lego in a number (n) of ways.

So if y is the total number of possibilities then
y = x*n

If a = the count of available (unsatisfied) possibilities then
a = x*n-s
Where s in the number of possibilities already used.

For each new lego counted, or considered to exist:
a = (x+1)n - (s+1)

If n>1 then a always increases.

So then the total number of unsatisfied possibilities continually increases the larger the universe becomes. Again, pardon my ignorance, but I don't see how we can expect to satisfy every possibility even if x is an infinite number.

 

[mfb]

But many same sequences, are in fact highly unlikely

You misunderstand the point.
Every result is unlikely. Barack Obama appearing in front of you is unlikely. But the precise arrangement of gas molecules in the air in front of you is also unlikely. They have a similar probability! You are not surprised by the atoms in front of you because many other equally unlikely results look similar: "just a bunch of atoms".

The universe doesn't know that you would consider an arrangement that resembles Obama as more interesting than an arrangement that resembles some specific arrangement of atmospheric molecules.

Everything that happens is extremely unlikely. Suggesting that extremely unlikely events cannot happen doesn't make sense.

The state of every atom in my coffee cup is determined by a set of previous interactions and given approximate determinism, highly likely if we consider the past.

It is not highly likely. It is highly likely to have one of the 10^whatever arrangements that look like a coffee cup. But "looks like a coffee cup" is an arbitrary group we invented.

@BenAS: There are more than x*n ways to combine x Lego pieces. n^x is a better approach (but not exact).

What are "available (unsatisfied) possibilities"?
Infinite Lego constructions are unphysical, and the discussions about "every possible event" are always about finite things.

 

[PeroK]

You misunderstand the point.
Every result is unlikely. Barack Obama appearing in front of you is unlikely. But the precise arrangement of gas molecules in the air in front of you is also unlikely. They have a similar probability! You are not surprised by the atoms in front of you because many other equally unlikely results look similar: "just a bunch of atoms".

The universe doesn't know that you would consider an arrangement that resembles Obama as more interesting than an arrangement that resembles some specific arrangement of atmospheric molecules.

Everything that happens is extremely unlikely. Suggesting that extremely unlikely events cannot happen doesn't make sense.It is not highly likely. It is highly likely to have one of the 10^whatever arrangements that look like a coffee cup. But "looks like a coffee cup" is an arbitrary group we invented.

It isn't arbitrary. For example, the molecules in gas have a tendency to maintain a constant gas pressure. First, this is a result of "raw" randomness. But, also, if too many molecules get into one region, the probabilistic tendency is for them to be pushed out.

Suppose there was a species out there that looked for cube-shaped planets. They would be disappointed. It's not arbitrary that all planets are (approx) spherical. They cannot be cubes.

Also, it's not arbitrary to look for the things that are invariant. We didn't decide that momentum conservation was something arbitrary to look for. Nature more or less forced it on us. It's not just good luck that momentum is conserved.

If there is a species out there that looks for conservation of velocity, then they too will be disappointed.

 

[analyst5]

You misunderstand the point.
Every result is unlikely. Barack Obama appearing in front of you is unlikely. But the precise arrangement of gas molecules in the air in front of you is also unlikely. They have a similar probability! You are not surprised by the atoms in front of you because many other equally unlikely results look similar: "just a bunch of atoms".

The universe doesn't know that you would consider an arrangement that resembles Obama as more interesting than an arrangement that resembles some specific arrangement of atmospheric molecules.

Everything that happens is extremely unlikely. Suggesting that extremely unlikely events cannot happen doesn't make sense.It is not highly likely. It is highly likely to have one of the 10^whatever arrangements that look like a coffee cup. But "looks like a coffee cup" is an arbitrary group we invented.

I understood your argument and I still disagree with you because you're clearly defending a somewhat subjective view of probability which doesn't have almost none resemblance in reality.

Every result is unlikely if we are completely ignorant. I may say that the particular length of my hair is extremely unlikely because there are enourmos possible configurations of atoms which have different lengths and physically correspond to the hair. That would be a sort of a priori probability which doesn't make absolutely no sense, if we consider every possibility in the sample space and the fact is that we only got one in front of us.

But so what? The universe knows that depending on the initial and present conditions, some configurations are far more likely than others. The configuration where you stay in one place while typing is one of many, many possibilities. The configuration where all of the atoms in your body quantum tunnel through the wall iis another of many, many possibilites.

Does that mean that they are equally likely? I simply don't know where are you coming from and why do you propose such a bizarre view regarding probabilities and reality.

Near you avatar it is clearly written that you are a mentor and have many posts so I assume you have much more credibility than any of the laymen-members including me. But that doesn't mean you can't be wrong, since your assumptions regarding this are very much non-sensical.

 

[Grinkle]

Everything that happens is extremely unlikely.

There is a big difference in entropy change between:

A. The gas molecules in front of me going from one state to a different state, the two states not being distinguishable by a human
B. The gas molecules in front of me coalescing to a twin of an existing human being

The 2nd law of thermodynamics predicts that transition B is much less likely than transition A.

The universe doesn't know that you would consider an arrangement that resembles Obama as more interesting than an arrangement that resembles some specific arrangement of atmospheric molecules.

The 2nd law of thermodyanmics predicts that the universe will behave such that transition from uninteresting to human-interesting configurations are more rare than transitions from uninteresting to yet-another-uninteresting.

 

[PeterDonis]

Every result is unlikely.

If by "result" you mean "single microstate of the system", yes, this is true. But if we are talking about thermodynamics and the second law, we by definition aren't modeling the system based on its particular microstate. In the context of thermodynamics, your statement is not true. See below.

The 2nd law of thermodyanmics predicts that the universe will behave such that transition from uninteresting to human-interesting configurations are more rare than transitions from uninteresting to yet-another-uninteresting.

That isn't quite what the second law predicts. The second law predicts that, if the phase space of the system is coarse-grained by values of a particular small set of thermodynamic variables, transitions to states which are in large coarse-grained phase space volumes (the largest being the one corresponding to thermodynamic equilibrium) will be much, much more common than transitions to states which are in small coarse-grained phase space volumes (roughly speaking, the further from thermodynamic equilibrium the state variables are, the smaller the coarse-grained phase space volume that it is in will be).

So a better way of responding to mfb's claim is to say that, for example, the phase space volume in which the state "Barack Obama is in front of me" occurs is much smaller than the phase space volume in which the state "a bundle of gas in thermodynamic equilibrium at atmospheric temperature and pressure is in front of me" occurs. The justification for this is that Barack Obama, unlike the bundle of gas, is far from being in thermodynamic equilibrium. It has nothing to do with the fact that Barack Obama is interesting to humans while a bundle of gas in thermodynamic equilibrium is not.

 

[Chronos]

The specific outcome of any random sequence of event is, strictly speaking, an improbability. You can make it look truly impressive by dressing it up with enough irrelevant details [I never would have won the lottery if aunt Jane had not been drinking the day I bought my ticket]. The probability of some outcome occurring is, however, certain. Nobody finds that astonishing. But, hit the lottery, and you will be astonished by your own popularity. A Boltzmann brain is astonishing only when you anthropomorphize it. Some physicists ask why anything at all even exists - and they are only half joking. If you want to know Why?, ask a philosopher, theologian, or a nutbox, not a scientist - they suck at why and will probably whine 'not my job'.

 

[Grinkle]

It has nothing to do with the fact that Barack Obama is interesting to humans

Certainly correct - thanks for that much more proper perspective / articulation.

 

[analyst5]

Certainly correct - thanks for that much more proper perspective / articulation.

I agree, thanks for the clarification PeterDonis.

The specific outcome of any random sequence of event is, strictly speaking, an improbability. You can make it look truly impressive by dressing it up with enough irrelevant details [I never would have won the lottery if aunt Jane had not been drinking the day I bought my ticket]. The probability of some outcome occurring is, however, certain. Nobody finds that astonishing. But, hit the lottery, and you will be astonished by your own popularity. A Boltzmann brain is astonishing only when you anthropomorphize it. Some physicists ask why anything at all even exists - and they are only half joking. If you want to know Why?, ask a philosopher, theologian, or a nutbox, not a scientist - they suck at why and will probably whine 'not my job'.

I was trying to make sense of what you said but I couldn't (not that I doubt that what you said makes absolutely perfect sense). What do you mean by antropomorphizing in this context and by considering every sequence of events as improbability?

Is it in line with what I've said that if we a priori consider every outcome in relation with all the possibilites that we are basically considering a priori probability?