For some time, I have been wondering whether the Boltzmann brain paradox is a genuine one. Here’s how Wikipedia describes the paradox (emphases are mine):
In physics thought experiments, a Boltzmann brain is a self-aware entity that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium. For example, in a homogeneous Newtonian soup, theoretically by sheer chance all the atoms could bounce off and stick to one another in such a way as to assemble a functioning human brain (though this would, on average, take vastly longer than the current lifetime of the universe).
The idea is indirectly named after the Austrian physicist Ludwig Boltzmann (1844–1906), who in 1896 published a theory that the Universe is observed to be in a highly improbable non-equilibrium state because only when such states randomly occur can brains exist to be aware of the Universe. One criticism of Boltzmann’s “Boltzmann universe” hypothesis is that the most common thermal fluctuations are as close to equilibrium overall as possible; thus, by any reasonable criterion, human brains in a Boltzmann universe with myriad neighboring stars would be vastly outnumbered by “Boltzmann brains” existing alone in an empty universe.
Boltzmann brains gained new relevance around 2002, when some cosmologists started to become concerned that, in many existing theories about the Universe, human brains in the current Universe appear to be vastly outnumbered by Boltzmann brains in the future Universe who, by chance, have exactly the same perceptions that we do; this leads to the absurd conclusion that statistically we ourselves are likely to be Boltzmann brains. Such a reductio ad absurdum argument is sometimes used to argue against certain theories of the Universe.
The two assumptions I’d like to question in this post are: (i) the assumption that a Boltzmann brain could self-assemble in the first place, given enough time; and (ii) the assumption that the spontaneous self-assembly of such a brain is more likely than the spontaneous formation of human observers.
Concerning (i), I would like to point out that the brain is a multi-layered organ containing 86 billion neurons, each of which is supported by glial cells and astrocytes. Within each neuron is a nucleus, surrounded by a cell body which receives signals via dendrites and sends signals along an axon, which in turn is insulated with a myelin sheath. The idea that individual atoms could arrange themselves into a brain containing tens of billions of these multi-layered structures is simply absurd, because such a “brain” would fall apart long before it formed. Without stable intermediate stages, a brain cannot spontaneously self-assemble out of atoms, even when given an infinite amount of time.
As for (ii): it seems to me that the main argument in its favor is that thermodynamically speaking, it’s easier for an infinite box of gas in equilibrium to assemble into X than it is for the gas to assemble into X + Y. Hence the spontaneous formation of a brain alone is far more likely than the self-assembly of a brain attached to a human body, which in turn is more likely to form spontaneously than an entire planet full of organisms (including humans), which is more likely to form spontaneously than a universe full of stars and planets (including our Earth). But this kind of reasoning ignores the possibility of “springboards,” or transitional stages which generate multiple paths, some of which lead to the desired target.
Thus the likelihood of a brain forming from a box of gas is far greater if the gas is first allowed to assemble into a primordial cell, as such a cell is capable of evolving into various kinds of organisms (including humans with brains). But evolution can only proceed in a physical environment; hence we need a planet for the cell and its descendants to live on. But a planet needs a source of energy to power the chemical reactions leading to life, which in turn requires energy to power its own internal processes; hence we need a star as well. And the formation of stars is rendered more likely by the postulation of an initial Big Bang, starting from a hot, dense state. In short: while the spontaneous formation of a universe, holus bolus, is many orders of magnitude less likely than the spontaneous formation of a brain, the formation of a human being possessing a brain within the framework of a Big Bang universe which is capable of generating stars and planets, some of which are capable of generating life, which subsequently evolves into the dazzling array of creatures we see on Earth, is far more likely than the spontaneous self-assembly of a Boltzmann brain – an event whose probability I have already argued is zero.
I’d like to finish with a closing thought. Is there something wrong with the way we define entropy? Currently, physicists define it in terms of the number of possible micro-states of a system which are consistent with its macro-description (e.g. “a human brain”). This, in essence, is what Boltzmann’s entropy formula expresses. However, such a definition ignores a system’s history, and makes no attempt to calculate the number of pathways by which the atoms in the system can reach their macro-level target. Boltzmann’s definition of entropy also leads many well-meaning but misinformed laypeople to mount fallacious arguments against biological evolution. Isn’t it about time we came up with a better definition, which doesn’t generate silly paradoxes? What do readers think?
We need to redefine the 2LoT.
vjtorley,
Not even sure about that. After all, a large amount of the planet’s heat comes from radioactive decay. Obviously, there was a sun, so it’s a bit academic, but I have the feeling that, if we were hurled into space, the oceans would freeze from the surface down but not necessarily beyond deep-ocean chemotrophic ecosystems, due to new heat coming from inside through vents etc.
OK, but (informed by my knowledge of chemistry and biology) I remain to be convinced that any known low-temperature structure – whose very function depends upon thermodynamic gradients – can be assumed to be reached in a dense high-entropy matrix by an infinite collection in an infinite time., simply by … ‘fluctuation’. I don’t see how one would suspend chemistry while shoving atoms about into the necessary configuration.
You are assuming two things
1) You assume A BB must be configured like a human brain.
There is no reason for a BB to formed in stages. It only has to be a universal Turing machine of a certain complexity. Some folks argue that the universe itself is a universal Turing machine and it formed instantly at the big bang.
2) You assume fluctuations like those in the quantum vacuum are ruled out in the thought experiment. There is no reason to confine the exercise to physics known at the time it was first proposed. I’m sure that Boltzmann would grant that his knowledge of physics was incomplete.
peace
You do realize that “how things work” in our universe has zero bearing when we are talking about the creator of our universe don’t you.
He is the one who proscribes how things work here his existence is not proscribed by those rules.
peace
I will happily defer to other people’s superior knowledge of physics; nevertheless, I think the following passage from Juarrero will clarify why I said what I did:
——————————————————————————————-
Thermodynamics may have brought time back into the scientific picture, but history still remained absent from the structures of classical, near-equilibrium thermodynamics: their progression toward equilibrium remains ahistorical in the sense that they forget where they came from. The specific location and circumstances from which a system started out, and the particular path it has traversed to date, are irrelevant: whatever its origin, the system will eventually reach equilibrium. Thermodynamic systems near equilibrium are therefore insensitive to initial conditions. Their past does not affect either their present or their future.
———————————————————
So while there’s an arrow of time in thermodynamics, there’s no history in the specific sense that prior states of the system matter to what the system can do now.
I’d understood Torley’s point to be that we only get brains in the universe as a functional part of a much more complicated system that takes advantage of energy gradients in far-from-equilibrium systems, e.g. siphoning off a tiny fraction of total solar output to power chemical reactions across trophic networks.
Neither, I think extrapolation the experience of material world to an immaterial being no matter where it inhabits would be unjustified. Simple or complex.
I would think the only thing God action’s would be contingent on is his Non-Contingent nature.
If that is the case , simple immaterial things are subject to the same dependency.
Understanding in every way way that is logically possible for a finite human mind with the caveat we may be mistaken.
peace
You realize that is my exact position for being opposed to divine simplicity?
I did not even realize you were apposed to divine simplicity. 😉
I thought you were just apposed to the Christian God in general
1) Because God is omnipotent he can reveal stuff so that I can’t be mistaken. If he chooses.
Unless that sort of thing is logically impossible and of it was you could never know it. 😉
Yep that is correct,
Unless the simple immaterial thing is a mind in which case it is only dependent on it’s self……get it
peace
What other universes, or extra-universal realms have you visited?
He hasn’t but if there was more then zero evidence for it I’m sure he would…
Why don’t you show us some? Fifth can’t wait…
None
That is why I think it’s a little presumptuous to say that “the way things are done” here should be all that relevant to how things are done there.
peace
Really?!
Why should I?
It’s Fair Witness who claims to know “how things are done” in those places.
I never made any such claim except to say that if they exist they must be logical. That should go with out saying.
peace
Is divine simplicity a Christian doctrine?
I was being sarcastic…
BTW: Are you Canadian like Byers and Bruce?
If you have to point it out you probably need to work on it a bit 😉
peace
It’s depends on how you define it I guess.
It’s certainly the majority opinion of orthodox Christian scholars historically.
here is how my favorite confession puts it.
The Lord our God is but one God, whose subsistence is in Himself; whose essence cannot be comprehended by any but himself, who only hath immortality, dwelling in the light, which no man can approach unto; who is in Himself most holy, every way infinite, in greatness, wisdom, power, love, merciful and gracious, long-suffering, and abundant in goodness and truth; who giveth being, moving, and preservation to all creatures.
In this divine and infinite Being there is the Father, the Word, and the Holy Spirit; each having the whole divine Essence, yet the Essence undivided; all infinite without any beginning, therefore but one God; who is not to be divided in nature, and being, but distinguished by several peculiar relative properties.
peace
As you probably know, I’m not a bible scholar or an expert in this field, but if God has not parts, how come Moses could look at God and stay alive?
One problem I have with the Boltzmann brain problem is it’s essentially solipsistic.
There is no conceivable observation you could make which you could not rationalize as being the chance occurrence of elementary particles in your brain that makes you exist in any given moment with the memories of a past life, including the idea of Boltzmann brains, and the observations of physical laws, the calculations you think you have done, etc. etc.
I can’t prove that I’m not a Boltzmann brain, but I also can’t prove that I am. So that just leaves me with my experiences, and I either act on them, or I become… what? Inanimate? I stop breathing? Walk into traffic because my experiences are just halluscinations and that truck over there doesn’t really exist?
Rumraket,
BTW: I enjoyed your take on directed mutations at PS! 🙂
I know I exist. I think I know you exist. How do you prove to me that your perception of existence is the same as mine?
My impression is they’re not.
At least you could link to a YT video with some comedic comment to supplement your own.. Maybe hire a ghost post writer?
I just read more Sean Carroll and less Sellars!
All of what you say is exactly right and I agree with it.
I see I missed something important which explains why we are talking at cross purposes.
BBs are far as physicists go do not happen now. All the things you mention are correct for our low entropy universe, where we can still have dissipative systems and a 2LT.
BBs happen in the far future, when the universe has reached thermal equilibrium, all the black holes dissipated (just for Allan), and there is no more 2LT. So no more chemistry or condensed matter physics. Only random fluctuation. And lots and lots of time.
Now maybe BBs are a problem for IDer’s because they think physics imagines they can happen in our low-entropy universe. No physicist thinks that. That’s just the plane from the tornado scenario. Only such planes are many…many orders of magnitude more likely than BBs.
It is also why no one calls “edges” when coins are flipped.
You are correct and your post shows why philosophy, not physics, is needed to argue you or I are not currently BBs. That’s what the first Sean C paper I linked is arguing.
Key point: the issue is not whether BBs are possible under far future physics, it is whether you are one now.
BruceS,
So there is no mass-energy in this universe? I don’t understand how SM applies, in that case. Quantum foam, maybe.
See my post to KN for what I suspect is just a case again us talking at cross-purposes.
I think physicists still believe in conservation of energy (ignoring the complications of GR in an expanding universe).
I suspect SM is inapplicable, since the BB scenarios do not occur when we are trying to explain macrostate behavior in terms of microstate dynamics.
I did throw that black hole stuff as a S/O to you; it is not something I have seem as part of the scenarios in Sean C. But BH dissipation will happen and none of his stuff says it matters.
I am definitely at my limits of even faking the physics, so I am back to putting my faith in the experts.
Just as I do with you, Joe, DNA-Jock etc when it comes to biology (and not with several others whose prose looks like biology to me until you guys reply).
Perhaps I can articulate my reservations differently. In ‘simple’ SM, gravity can be essentially ignored. The gravitational force between molecules in a gas contributes negligibly to the motions of those molecules, or the ‘microstates’ into which one can subdivide the box they are imagined to reside in.
Now, scale this up. You have a universe of atoms, and an infinity of time for them to unroll, and somehow, somewhere in that universe, small collections gather in unexpected ways – a small vacuum here, a house-brick there, a brain elsewhere. But, you can’t keep ignoring gravity. If you have matter, you have gravity. If you have a lot of matter, you have a lot of gravity. As I suggested, this will clump into black holes – entropy is high, because objects have ‘fallen’ into each other, releasing energy. Under those conditions, matter must behave like matter-under-those-conditions. Not a randomly jostling collection of atoms, but a squeezed matrix, which has somewhat different properties. Atoms are much, much closer together, and can’t just wibble about. Any wibbling that does happen has a much higher chance of interfering interaction than at our planetary surface (and even assembly there would have to proceed in a certain order: inside to out).
So, OK, we get round that by saying the black holes are gone – Hawking radiation, perhaps. The matter has all been turned into energy – a universe of photons. Somehow, the universe got so big that a ‘clump-free’ universe is the highest-entropy state of all. Any attraction between fields of mass-energy is counterbalanced by increased separation between them, so they never re-collapse. There is no higher-entropy state accessible – by definition.
Yet somehow, this set of points of mass-energy, so separated that they cannot interact gravitationally, can form brains – not just a physical arrangement, but with an appropriate distribution of electronegativity to permit at least one brief thought, achieved without any chemical interference between atoms during assembly. Hmmmm, I say, and hmmm again.
I can only echo what I hear biologists say to pseudo-biologists. Write a paper and publish it for peer review by physicists.
My knowledge of physics is insufficient to give a substantive reply to your points. I miss Sophisticat at times like these…
ETA: I have a possible easy way to get physicists’ feedback on your thoughts. I support Sean C’s podcast on Patreon which means I can ask him questions at his monthly Patreon-only AMA. So I can try to post a summary of your points and see how he answers. If you want to summarize in a sentence or two, I’ll use that. Otherwise I’ll do my best to paraphrase your input briefly enough for a question.
BruceS,
A summary … (chews pencil).
To form a physical object, matter must be physically capable of getting from its current state to the configured state. For a physico-chemical system, this entails an additional constraint: the path must avoid ectopic interactions during assembly, and yet the final state must be ‘poised’ – ready to generate a thought from reactive atoms whose tendency to react must (somehow) be suspended en route. There clearly are paths to such a state; what is less clear is that alternative paths would be available in the ‘special’ physics of high-entropy arrangements.
Two possible maximum-entropy (equilibrium) states suggest themselves:
1) Maximally condensed (black holes).
2) Maximally dissipated (mass-energy is only photons).
In neither of these states is it adequately shown that simple motion of matter (or mass-energy) can physically achieve the necessary structure, by pathways other than those already taken.
I don’t think you are factoring in infinity. In an infinite universe it’s bound to happen over and over again as long as the probability is not zero.
By the way this is why probability arguments suck. Your comment reminds me of the sort of thing that IDers might say about some especially unlikely biological feature. To which critics would respond well it happened so now the probability is one.
As long as it’s not entirely impossible it could happen and in an infinite universe it will eventually happen over and over again.
peace
I’m saying the probability is zero. Or, not adequately proven to be non-zero. And I mean, how many infinite universes are there?
There are an infinity of numbers between 1 and 2 but none of them are 3.
A sensible critic would say the probability is not zero.
I would make similar objections to the notion that functional organisms can be ‘created’ whole-cloth, if that creation is accepted as constrained by the physics of the environment it happens in.
One is effectively saying that, for every functional piece of biological material, there must exist an alternative path from separated constituents to the functional whole, which is radically different from the path actually taken – cellular dynamics, in sum: biology and chemistry. That, simply by moving atoms in the correct way, you can get to the same end-point. I don’t think that’s a given.
FWIW, FMM is aligned with the predictions of some interpretations of eternal inflation. There are are unlimited number of bubble universes. There are finitely many quantum possibilities. Hence you and I are each duplicated an unlimited number of times across bubble universes.
ETA: just to avoid some confusions: infinite inflation bubble universes all have the same laws. String theory landscape universes need not.
The latter assumption of a finite number of quantum states is also important for BBs. It seems to me to be related to the second Carroll paper I linked where Carroll says the possibilities of BBs may depend on whether we assume a quantum cosmology involving finite or infinite dimensional Hilbert spaces. However, I have not read that paper closely so any corrections based on the paper are welcome.
Some fine points I am not sure of: possibly a countable infinity may do, rather than just finite. Possibly sets of measure zero would enter the uncountable case (whether they ever occur is something Neil would be better suited to comment on, although I suspect he is not comfortable at all with the physics underlying the BB stuff).
Of course, there is also Allan’s core point that the probability of some quantum fluctuations is zero, eg due to gravity. That’s what I will ask Sean C about at AMA.
I think the underlying point is that any restrictions rely, at base, on thermodynamics constraints, eg on which proteins can hold together. But TD is not a a necessity-based law, it is statistical, and so anything that can happen will happen in an unlimited time with finite number of possibilities, no matter how small the probability is. Using chemistry or other TD-based arguments doesn’t help, if that is right.
Anyway, I better stop, because the reality is I only have a finite number of things to say and I suspect I have started to repeat myself.
If there is an arrow of time, where is it? Because it’s not in the equations.
🙂
There are many different formulations of the second law. Can we agree on that? Do you now of any other law of physics that is like that?
You should accept that you have already said the same thing an infinite number of times and just embrace it. 🙂
I should live that long!
No we cannot. There is only one formulation of the law, which is a law based in equilibrium TD. It is the one given by the TD formula in my first post (which should have mentioned the inequality, however). There are equivalent math and English wordings.
There are different ways of trying to show how microstate dynamics give rise to that law using SM (Boltzmann versus Gibbs eg) and then added to that there are different ways to add probabilities and interpretations of probabilities to the derivations of SM. But none are new formulations of the second law. And all of the SM derivations have issues (see my post to Keith for link).
So the OP is also incorrect when it says physics defines the second law via Boltzmann.
For example, the SM attempt to understand how the second law arises from microstates alone fails without the extra postulates, which Albert discusses in his books and Carroll more loosely in his populatziation on time.
Ben Naim does not represent a common view of people who specialize in these issues in philosophy of physics As best I can tell from Google scholar, he is not widely cited in that field. He did not work in that field. His views are idiosyncratic, as far as I can tell.
The word “interpretations” in his book title that you link is, I think, effectively making my point about the correct way to think about SM and the law.
I agree that the relation of the 2LT and the arrow of time is not something that follows easily.
And similarly, there are philosophical issues with laws.
But if anything is a law, the TD 2LT is one. If you happen to find a book title that suggests otherwise, don’t say I did not predict it.
Actually not even divine simplicity, rather that it is true by the definition of God not by a presumption which faces the same problem as Fair Witness’s position which you just pointed out.
Hardly, just not a fan of unquestioning belief in any version of God.
Again my position, so no matter what the revelation there is always uncertainity with a finite mind.
Unless you accept a God who can force you to believe something and that opens another can of worms.
The Boltzman Brain scenario has largely been taken over by the Computer Simulation scenario. It goes something like this . . .
Assuming human-like species have evolved elsewhere in the universe and have had longer to develop technology than humans it is possible for these species to develop computer simulations that are self aware. Such a species could make millions of such simulations, complete with digital individuals who think they are alive. If intelligent species are somewhat rare, it is possible that the number of simulations far outnumbers the number of actual intelligent species. This means we may have a better chance of being part of a simulation than a physical species.
That is your position but you can’t be certain it’s correct. In fact you can’t be certain of anything at all given your worldview.
On the other hand I can be very certain that if a thing is possible God can do it………..Get it??
I’m not sure what “unquestioning” belief is.
Beliefs don’t ask questions persons do.
Do you mean belief held by a person who does not have any questions at all? I’m not sure that could be even called belief
Or do you mean a belief that is held even though not every single one of our questions has been answered as of yet?
God is the greatest thing that can be conceived and to be not dependent is greater than to be dependent.
That much should not be controversial though I understand that you can’t be certain that it is the case given your worldview.
peace
I think you are still assuming that a BB must be similar to a human brain.
If materialism is true then our thoughts are just complex computations and BBs are just universal Turing machines.
Long ago Shannon demonstrated a universal Turing machine which could perform any computation whatsoever could be as simple as a contraption with just two internal states
https://www.researchgate.net/publication/270268060_Shannon_Claude_E_A_universal_Turing_machine_with_two_internal_states_Automata_studies_edited_by_Shannon_C_E_and_McCarthy_J_Annals_of_Mathematics_studies_no_34_lithoprinted_Princeton_University_Press_P
we are not talking a huge amount of complexity here though it might take some processing time to have the sorts of thoughts that we have.
In an infinite universe time is not a problem.
peace
Combine the two scenario’s and we could even be in a simulation imagined by a BB who inhabits yet another simulation etc etc etc…….world with out end amen
sans God the probability that our experience reflects reality is vanishingly small to the point of being far less than wishful thinking
peace
It does make one wonder if the Holographic Theory is on to something. Perhaps strange action at a distance in the quantum world is the product of a computer calculation.
Perhaps the very idea of distance itself is simply a line of code entirely imagined by a BB.
If there is no God It’s much more likely to be something like that than anything like what we experience.
peace