I Boltzmann brains and other low probability events

[durant35]

I am interested in your opinion with regards to expectation values of low likelihood events in QM. For example, Boltzmann brains are suggested as a problem in cosmology despite their probability being extremely miniscule.

Is it realistic to expect Boltzmann brains and other low probability events to ever occur? What's your opinion on BBs in general?

 

[PeterDonis]

Is it realistic to expect Boltzmann brains and other low probability events to ever occur?

As it stands now, that would depend on one's interpretation of QM. The theory itself just predicts probabilities; it doesn't tell us what probabilities are "realistic". At some point we might come up with a more comprehensive theory that gives us a way to resolve this issue, but right now we don't have one.

What's your opinion on BBs in general?

We already have several threads where BBs have been brought up; try the PF search feature.

 

[durant35]

We already have several threads where BBs have been brought up; try the PF search feature.

I already searched almost all threads where they have been brought up and I see no convention about their possible existence and other implications of it.

What's your take on the topic?

 

[PeterDonis]

I already searched almost all threads where they have been brought up and I see no convention about their possible existence and other implications of it.

That's odd since you have posted in at least one of them:

https://www.physicsforums.com/threads/boltzmann-brains.894790/

What's your take on the topic?

What I already said in post #2.

 

[bhobba]

What's your take on the topic?

A load of rubbish - not because its impossible - it isn't - its just IMHO philosophical mumbo jumbo along the same lines as solipsism. Also consider according to inflation the universe inflated very quickly - that is NOT random behavior - its very orderly. Order emerges from chaos due to known physical laws eg slightly more dense regions collapse due to gravity - these laws work against random behavior even though the second law of thermodynamics says randomness is coming - true - but what happens in the mean time?

There are much much more important things in physics we do know eg how U(1) local symmetry leads to Maxwell's equations and QED. Now that's simply plainly weird - how the hell can symmetry lead to electrodynamics. The thing is it does. Why is IMHO a very very deep mystery and much more important than Boltzmann's brains.

Thanks
Bill

 

[Demystifier]

its just IMHO philosophical mumbo jumbo along the same lines as solipsism.

Maybe so, but I have published a paper about solipsism in a physics journal:
https://arxiv.org/abs/1112.2034

 

[durant35]

That's odd since you have posted in at least one of them:

https://www.physicsforums.com/threads/boltzmann-brains.894790/

I was referring to other threads where I was not particapating, and even in those where I posted there seems to be little consensus about the paradox. And there are many questions which are related.

1) Are BBs a certainty to happen in a spatially infinite universe?
2) Are BBs even physically possibly, despite being statistically possible? Maybe we don't know enough about entropy and the early universe, like Bill mentioned in one of his previous posts, to give a definite answer if something complex and macroscopic can pop into existence - either from a soup of particles in the late universe or from "virtual particles" in vacuum?
3) Cosmological problem - if the universe is eternal, BBs will become infinite in number. This is quite possibly the most controversial part, some posters have said that given infinite time BBs will outnumber humans and some have said that despite infinite time there is no guarantee that a single BB must happen.

So there are many divided opinions, and given that I lack understanding in statistics, I wonder what stance is logical to take on the subject?

Thanks in advance.

 

[bhobba]

Maybe so, but I have published a paper about solipsism in a physics journal:
https://arxiv.org/abs/1112.2034

But I am sure you get my drift.

Thanks
Bill

 

[Demystifier]

But I am sure you get my drift.

Of course.

 

[secur]

Infinity is not physical. Any theory that depends on or assumes the physical reality of infinity is twaddle. Concepts of infinite time, or infinite spatial extent of universe, or infinitely fine granularity of space and time, or infinite density, or infinite many-worlds, etc, are not allowable - even in philosophy, much less physics. To the extent that Boltzmann Brains and some other "low-probability events" do depend on infinity, they are meaningless. However you can speculate about BB's without invoking infinity. In that case the concept is not necessarily unphysical and some might think it meaningful.

The word infinity is used in math and physics, but only as a placeholder or special symbol indicating some specific finite algorithm. For instance we talk about "the limit as x goes to infinity". That does NOT really mean "infinity". Instead it means "given any (small) delta > 0, it can be shown that the sequence or function approaches that close to a number we call the 'limit', for an identifiable corresponding (large) finite number N". Or, some other similar finite algorithm.

Solipsism OTOH is a perfectly legitimate stance and may be used in a physical theory.

Unfortunately some physicists, such as David Deutsch, have written that infinity is physical. They're wrong.

 

[akvadrako]

Infinity is not physical. Any theory that depends on or assumes the physical reality of infinity is twaddle.

Hi secur, could you explain why you think this? I can image a few possibilities. The universe either...

1. doesn't exist
2. is of finite size A
3. is of finite size B
4. is infinite

To me, 2 and 3 seem the most arbitrary. As long as the universe exists at all, doesn't an infinite size seem the most natural? It also seems to be suggested by the evidence, like flatness of space.

 

[PeterDonis]

Infinity is not physical.

This statement is not a statement of established mainstream science; it's a personal opinion. Please bear in mind the PF rules.

 

[PeterDonis]

there are many questions which are related.

And they're questions to which we currently don't have established answers. Different people have different opinions and there's no way to test them. That's why I responded the way I did in post #2.

 

[clarkvangilder]

The universe either...
1. doesn't exist
2. is of finite size A
3. is of finite size B
4. is infinite
To me, 2 and 3 seem the most arbitrary. As long as the universe exists at all, doesn't an infinite size seem the most natural?

If infinite in size, then infinite in time too; therefore, we have already had the heat death of the universe. I don't think BB's can emerge after the heat death.

 

[Stephen Tashi]

How restrictive is the definition of a "Boltzman brain"? For example, by one definition, if the universe randomly entered an ordered state billions of years ago then, indirectly, the evolution of our own brains from that ordered state makes them a consequence of that random event. So our own brains are "Boltzman brains".

By contrast, if we require that a "Boltzman brain" is a conscious entity that arises "immediately" from a random event, we are thinking about concepts such as a cloud of gas suddenly becoming a conscious entity.

 

[durant35]

How restrictive is the definition of a "Boltzman brain"? For example, by one definition, if the universe randomly entered an ordered state billions of years ago then, indirectly, the evolution of our own brains from that ordered state makes them a consequence of that random event. So our own brains are "Boltzman brains".

By contrast, if we require that a "Boltzman brain" is a conscious entity that arises "immediately" from a random event, we are thinking about concepts such as a cloud of gas suddenly becoming a conscious entity.

Normal brains require evolution as the intermediate step, while BBs come strictly from a fluctuation (sort of a shortcut).

The real question is - is this really possible, despite statistics giving it a non zero probability. It is true that atoms can fluctuate into a set of positions, but to me it is debatable can organization into a structured macroscopic object emerge from chaos. It doesn't have to be a brain, though it's probably even more complex, it is debatable can chairs, cars etc. organize themselves from fluctuation. I think that we should get to know more about entropy before coming to extreme conclusions.

 

[durant35]

And they're questions to which we currently don't have established answers. Different people have different opinions and there's no way to test them. That's why I responded the way I did in post #2.

That's fair. Do you have an opinion about this or you're agnostic until new evidence/theories emerge?

 

[PeterDonis]

is this really possible

This question has already been answered. The answer is "we don't know".

Do you have an opinion about this

No.

 

[secur]

Hi secur, could you explain why you think this? I can image a few possibilities. The universe either...

1. doesn't exist
2. is of finite size A
3. is of finite size B
4. is infinite

To me, 2 and 3 seem the most arbitrary. As long as the universe exists at all, doesn't an infinite size seem the most natural? It also seems to be suggested by the evidence, like flatness of space.

Of course I could explain it. It's not a personal opinion, it's a fact - of philosophy. Or, if you prefer, a fact of logic and reasoning, or of mathematical foundations. Obviously you can't prove it within the realm of physics. Unfortunately mainstream physicists are wrong on this issue, but can't be corrected, since their mistake can't be discussed. It's sort of a catch-22. Anyway, read Kant, Aristotle, Berkeley, Wittgenstein, Popper etc. They should convince you.

BTW it's important to note, you can't prove the (entire) universe is finite, either! (Of course you might prove some portion of it, such as the visible part, is finite.) You can't assume the whole thing is either finite or infinite. See Kant's antinomies for the basic idea.

Personally, I first learned it from my (mathematics) doctoral advisor, when we were reading Dirac's "Principles of Quantum Mechanics" (from a Functional Analysis point of view). There's been a lot of discussion about the problems of "infinity" in the field of mathematics foundations. Look up "constructivism", for instance. But that's philosophy also, just like foundational issues in physics, such as QM interpretations. QM interpretation is mostly philosophy, not physics.

 

[MrRobotoToo]

Sean Carroll has done some interesting work on this. He argues that the Everettian interpretation implies that the final equilibrium state of a de Sitter universe is truly static, i.e. no possibility for fluctuations of any kind. He then contrasts this with decoherent histories, which implies that there exists coarse grainings of the final state that are dynamical, and which therefore allow fluctuations. So the Boltzmann brains problem can be used as a testbed for different interpretations of QM.

 

[durant35]

Sean Carroll has done some interesting work on this. He argues that the Everettian interpretation implies that the final equilibrium state of a de Sitter universe is truly static, i.e. no possibility for fluctuations of any kind. He then contrasts this with decoherent histories, which implies that there exists coarse grainings of the final state that are dynamical, and which therefore allow fluctuations. So the Boltzmann brains problem can be used as a testbed for different interpretations of QM.

I've red a lot of Carroll's work and I agree with the conclusion that fluctuations don't occur after heat death.

The problem is do they occur before and how to divide them. That's something that might be answered here. Basically, he mentions Boltzmann fluctuations as classical fluctuations from the average/equilibrium state. Now my question is: do those fluctuations include both classical thermal fluctuations (the one which Boltzmann originally had in mind) and also quantum fluctuations (where unlikely things occur because of the randomness of the particle-wavefunctions).

Often on the forum it was mentioned that even in classical mechanics all the molecules of air may come to one corner of the room and that would be a classical fluctuation. But in QM, this effect is also possible, not because of the jiggling around of the particles, but because of their random wavefunctions. So the conclusion would be that particles can show 2 types of fluctuations which lead to unlikely behavior.

Is this reasoning correct or are these fluctuations one and the same thing?

 

[MrRobotoToo]

I've red a lot of Carroll's work and I agree with the conclusion that fluctuations don't occur after heat death.

The problem is do they occur before and how to divide them. That's something that might be answered here. Basically, he mentions Boltzmann fluctuations as classical fluctuations from the average/equilibrium state. Now my question is: do those fluctuations include both classical thermal fluctuations (the one which Boltzmann originally had in mind) and also quantum fluctuations (where unlikely things occur because of the randomness of the particle-wavefunctions).

Often on the forum it was mentioned that even in classical mechanics all the molecules of air may come to one corner of the room and that would be a classical fluctuation. But in QM, this effect is also possible, not because of the jiggling around of the particles, but because of their random wavefunctions. So the conclusion would be that particles can show 2 types of fluctuations which lead to unlikely behavior.

Is this reasoning correct or are these fluctuations one and the same thing?

Classical fluctuations occur within decoherent branches of the wavefunction. Once the universe settles into equilibrium, all of the decoherent structure will dissolve and there'll be no possibility for classical fluctuations. As Carroll explains in the video, so-called 'quantum fluctuations' only occur when a system is measured, which obviously isn't possible after the heat death.

 

[PeterDonis]

it's a fact - of philosophy

This is a physics forum, not a philosphy forum. If you want to state something as a fact, you need to show the experimental evidence and/or the well-established physical theory that demonstrates it. Quoting philosophers is not sufficient. Please bear this in mind for future posts.

 

[bhobba]

If infinite in size, then infinite in time too; therefore, we have already had the heat death of the universe. I don't think BB's can emerge after the heat death.

Take the real line. Start at zero and go outwards towards increasing numbers. Its infinite with the possibility of heat death open - or rebirth for that matter.

There is so much unknown in cosmology (admittedly what we do know in the sense of models being put forward is rapidly advancing) its very important not to make assumptions beyond what the evidence supports.

I really am scratching my head about the fascination for this topic.

Thanks
Bill

 

[bhobba]

As Carroll explains in the video, so-called 'quantum fluctuations' only occur when a system is measured, which obviously isn't possible after the heat death.

Decoherence and measurement are pretty much synonymous these days. After heat death no decoherence? That strikes me as rather strange - I would like to see the reason for that claim.

Thanks
Bill

 

[MrRobotoToo]

Decoherence and measurement are pretty much synonymous these days. After heat death no decoherence? That strikes me as rather strange - I would like to see the reason for that claim.

Thanks
Bill

I’m not sure about that, either. Carroll says that after a sufficiently long time the off-diagonal elements of a decohered subsystem’s density matrix will become non-zero as the system reaches equilibrium, which makes intuitive sense if one considers what it means to be in thermal equilibrium, but I don’t know how one goes about proving it.

 

[durant35]

Decoherence and measurement are pretty much synonymous these days. After heat death no decoherence? That strikes me as rather strange - I would like to see the reason for that claim.

Thanks
Bill

https://arxiv.org/abs/1405.0298

 

[durant35]

Take the real line. Start at zero and go outwards towards increasing numbers. Its infinite with the possibility of heat death open - or rebirth for that matter.

There is so much unknown in cosmology (admittedly what we do know in the sense of models being put forward is rapidly advancing) its very important not to make assumptions beyond what the evidence supports.

I really am scratching my head about the fascination for this topic.

Thanks
Bill

But doesn't an infinite universe open up the prospect of infinite Boltzmann brains, infinite copies of ours etc.?

I know it's pretty speculative but that's what the maths and statistics would tell you.

 

[bhobba]

But doesn't an infinite universe open up the prospect of infinite Boltzmann brains, infinite copies of ours etc.?
I know it's pretty speculative but that's what the maths and statistics would tell you.

Its just another of the weird consequences of infinity - there are tons of them. They have been known for yonks eg the Grand Hotel:
https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

It's more of an issue for the set theory and logic sub-forum. I learned about it first year uni. Interesting but really only something for the pure math guys. I had those tendencies once and used to terrorize my lecturers with points of rigor, but, at least for me, eventually tired of abstract thought alone. It started when one lecturer said - look Bill I can give you books where all your questions are answered. But they are so dry and boring you wouldn't read them. He was right.

Don't believe me - try reading Russell's - Principa Mathematica:
https://plato.stanford.edu/entries/principia-mathematica/

Thanks
Bill

 

[bhobba]

https://arxiv.org/abs/1405.0298

Its conclusion:
'A better understanding of complementarity and the correct formulation of quantum mechanics will help establish what happens in the real universe.'

That supposes so many issues many physicists would disagree with and leaves me shaking my head. Complementary for example is not even a rigorously defined principle little alone a universally accepted one. Personally I think its gobbly gook - but that's just me. When I first heard about it all those years ago I tried hard. really hard to understand it. I failed and thought I simply wasn't up understanding this quantum stuff. I now think it's a total crock left over from the early days of QM that we have moved well and truly on from.

Thanks
Bill

 

[bhobba]

but because of their random wavefunctions.

Random wave-functions?

I like to think I know QM pretty well to the level of Ballentine, but I think that one needs further elaboration.

Please no links to papers - it should be explainable without that.

Thanks
Bill

 

[durant35]

Random wave-functions?

I like to think I know QM pretty well but I think that one needs further elaboration.

Please no links to papers - it should be explainable without that.

Thanks
Bill

My bad, error in writing. I didn't really mean that wavefunctions are random.

 

[bhobba]

Now my question is: do those fluctuations include both classical thermal fluctuations (the one which Boltzmann originally had in mind) and also quantum fluctuations (where unlikely things occur because of the randomness of the particle-wavefunctions).

My bad, error in writing. I didn't really mean that wavefunctions are random.

Sean is a very serious scientist - his GR textbook is VERY good.

But I must say I find some of his QM writings on the obscure side with this thread an example. A lot of stuff like randomness of the particle-wavefunctions leave me scratching my head exactly what is meant. Wavefunctions change either by Schrodinger's equation or some kind of preparatiom procedure - at least that's the modern view found in texts like Ballentine. Does he mean the result of preparation procedures is random?

Thanks
Bill

 

[zonde]

What's your opinion on BBs in general?

If you are Boltzmann brains then all your knowledge about science is fiction including unjustified extrapolations that lead to speculation about Boltzmann brains. Idea sort of defeats itself.

 

[newjerseyrunner]

My view is that it'll never happen even if it's theoretically possible. A common complaint among fundamentalists who don't understand evolution is that the odds of atoms randomly creating a mind as complex as us is ridiculously unlikely. I agree. Without an iterative, self-propelling process like Darwinian evolution, objects will remain simple. Even if a thought formed randomly, why would it not dissipate instantly? It has to be self-containing in order to have a stream of consciousness.

 

[durant35]

My view is that it'll never happen even if it's theoretically possible. A common complaint among fundamentalists who don't understand evolution is that the odds of atoms randomly creating a mind as complex as us is ridiculously unlikely. I agree. Without an iterative, self-propelling process like Darwinian evolution, objects will remain simple. Even if a thought formed randomly, why would it not dissipate instantly? It has to be self-containing in order to have a stream of consciousness.

I agree with you.

Would you agree that we need a better understanding of evolution, entropy and their relationship in order to have a legitimate discussion about something that sounds very drastic and extraordinary like a BB?