In honor of Halloween yesterday, let me tell you a scary physics story:
Sarah was an ordinary college student, in an ordinary dorm room, ordinary bean bag chairs strewn around an ordinary bed with ordinary pink sheets. If she concentrated, she could imagine her ordinary parents back home in ordinary Minnesota. In her ordinary physics textbook on her ordinary desk, ordinary laws of physics were written, described as the result of centuries of experimentation.
Unbeknownst to Sarah, the universe was much more chaotic and random than she realized, and also much more vast. Arbitrary collections of matter formed and dissipated, and over the universe’s long history, any imaginable combination might come to be.
Combinations like Sarah.
You see, Sarah too was a random combination, a chance arrangement of particles formed only a bare few moments ago. In truth, she had no ordinary parents, nor was she surrounded by an ordinary college, and the laws of physics that her textbook asserted were discovered through centuries of experimentation were just a moment’s distribution of ink on a page.
And as she got up to open the door into the vast dark of the outside, her world dissipated, and she ceased to exist.
That’s the life of a Boltzmann Brain. If a universe is random and old enough, it is inevitable that such minds exist. They might have memories of an extended, orderly world, but these would just be illusions, chance arrangements of their momentary neurons. What’s more, they may think they know the laws of physics through careful experiment and reasoning, but such knowledge would be illusory as well. And most frightening of all, if the universe is truly ancient and unimaginably vast, there would be many orders of magnitude more Boltzmann Brains than real humans…so many, that it would almost certainly be the case that you are in fact a Boltzmann Brain right now!
This is legitimately worrying to some physicists. The situation gets a bit more interesting when you remember that, as a Boltzmann Brain, anything you know about physics may well be a lie, since the history of research you think exists might not have. The problem is, if you manage to prove that you are probably a Boltzmann Brain, you had to use physics to do it. But your physics is probably wrong!
This, as Sean Carroll argues is why the concept of a Boltzmann Brain is self-defeating. It is, in a way, a logical impossibility. And if a universe of Boltzmann Brains is logically impossible, then any physics that makes Boltzmann Brains more likely than normal humans must similarly be wrong. That’s Carroll’s argument, one that he uses to argue for specific physical conclusions about the real world, namely a proposal about the properties of the Higgs boson.
It might seem philosophically illegitimate to use such a paradox to argue about the real world. However, philosophers have a similar argument when it comes to such “reality is a lie” scenarios. In general, modern philosophers point out that any argument that proves that all of our knowledge is false or meaningless by necessity also proves itself false or meaningless. This is what allows analytical philosophy to carry forward and make progress, even if it can’t reject the idea that reality is an illusion by more objective means.
With that said, there seems to be a difference between simply rejecting arguments that “show” that the world is an illusion or that we are all Boltzmann Brains, and using those arguments to draw conclusions about other parts of the world. I would be curious if there are similar arguments to Carroll’s in philosophy, arguments that draw conclusions more specific than “we exist and can know things”. Any philosopher readers should feel welcome to chime in in the comments!
And for the rest of you, you probably aren’t a Boltzmann Brain. But if the outside world looks a little too dark tonight…
I call codswollip. The problem starts here: “If a universe is random and old enough, it is inevitable that such minds exist.” That is an unsupported statement that borders on nonsense. You can prove that with enough time any desired sequence of coin tosses is possible, but that example assumes that the known laws of physics and probability that we use to calculate odds will extend indefinitely – a reasonable assumption. It is a different matter to extend this to imagined realities and conclude that all are possible, however improbable. It is simple to imagine mutually exclusive realities, but then, are these possible together if we only wait long enough? No. If this were true, we would see around us strange things that we could not explain with known science, and while there are still mysteries around us, they do not rise to this level. We don’t have to be so specific as the Boltzmann Brain example. If the universe is large enough, there ought to be a planet with land features resembling my face, right? And another with yours. And they should have masses proportional to our own, if the universe is large enough. But then there should be another version of these with inhabitants that look like Mickey Mouse, and another with a race of Soupy Sales. And one where continental drift of the “faces” resembles reverse aging and the race of Mice are actually imagined only by the Donald Ducks, and that’s just for starters! Just because something COULD happen does in no way imply that it will or that it must. Seems to me that the opposite is true, that it is impossible (not inevitable) for all possible things to occur.
Actually, your examples are much more straightforwardly true than mine. In a large enough universe, of course there would be a planet with land resembling any particular person’s face. There are land formations with rough resemblances to faces on Earth, after all. Enough Earths, enough rock formations, and you’re bound to get one that looks like you or me. Enough, and you could get a pretty detailed depiction.
It’s when you get into particular species (or, yes, Boltzmann Brains) that things get more tricky. The difficulty there is that some things might simply be physically or biologically impossible. If there is no possible process of continental drift that makes faces “reverse-age”, then there won’t be a planet where that happens. If there is no possible evolutionary process that yields Mickey Mouses, then you won’t have a planet populated with Mickey Mouses. But of course, if any of these are actually possible then a large enough, old enough universe will have to contain them! (And just for the record, “looking like you or me” doesn’t make something impossible!)
Remember, though, I had two conditions: old enough, and “random” enough. That latter requirement is shorthand for a more technical point, involving thermal equilibrium and entropy. Sean Carroll’s paper has a good short account of what this entails in its introduction, with references in case you want to dig deeper. Broadly, if the world is a sort of vast, undifferentiated chaotic soup, then such a soup will cycle through all possible configurations given a long enough time. Some of those configurations will be minds, or even entire worlds of Mickey Mouses, existing for an instant before vanishing again. That’s not to say that such worlds would come up in our current universe, because our current universe isn’t this sort of “soup”. It’s too “orderly”, or not “random” enough. But under the right conditions (again, technical meaning here) it could become one.
Well, I started out with the possible and went from there. A planet resembling someone is a bad example, because “resemble” is subjective. My point was that the combinations and permutations are endless, maybe literally. Enough time could form planets for X number of people’s faces, but in that time, there will be Y new faces…
On careful reading, I think we agree on most of this. But I don’t agree that “if any of these are actually possible then a large enough, old enough universe will have to contain them.” Why? And how many of them “must” it contain? Only one? Two?
I’m not a statistician, but I don’t think the odds of singular events are meaningful. It’s like the argument I heard at an evolution/creationist debate – the creationist was claiming that life evolving “randomly” from primordial soup was as likely as a tornado passing through a junkyard and forming a working jumbo jet. He actually had some probability worked out for that. Of course he ignored the process of evolution, reducing it to a crapshoot. But I don’t think you can calculate the odds of a random jet, and even if you do estimate a finite possibility, the math does in no way obligate the universe to build a jet, or “any particular local macroscopic configuration of
matter” to quote the Carroll.
It’s the wrong way around; math describes reality, it does not define it.
IMO, the “freak observer” idea is really not “a difficulty with known physics” as that paper says; it’s a thought experiment in the realm of epistemology. (I’m not a Copenhagen adherent, BTW.) And this leads to the observation that observing these coincident manifestations and/or BBs is not broadly possible, so the notion is untestable. We end up with a metaphysical extrapolation from the vantage point of ignorance on an esoteric problem of cosmological thermodynamics. Resorting to a hypothetical disordered universe ought to be the driving context here.
Enjoy your posts, BTW!
“On careful reading, I think we agree on most of this. But I don’t agree that “if any of these are actually possible then a large enough, old enough universe will have to contain them.” Why? And how many of them “must” it contain? Only one? Two?”
Instead of “must”, it would have been more proper to say “is arbitrarily likely to”. If you give the universe enough time and space (and randomness), you can set the probability for one (or two, or three) to be as high as you like, though still below one. Does that seem sufficiently uncontroversial?
I agree that the “plane in a junkyard” scenario might simply be incoherent, but I think that’s fundamentally a question of whether there is enough “randomness”. A cyclone probably just doesn’t move in the correct ways to assemble a plane, no matter how many times you let it run through the yard. But if there is a right way for it to move, then running long enough gives you as high of a probability as you like.
As for whether it’s an epistemological problem or a physical problem, I think the key distinction here is that there are physical conditions under which the epistemological problem becomes relevant. Now of course, there are other parallel epistemological problems that don’t need the physical backing: for example, the argument that were are more likely to be participants in an advanced simulation than actual people. Presumably, if these sorts of arguments can be rejected on general philosophical grounds then so can Boltzmann Brain scenarios, without need for physical restrictions. This is why I’m curious whether philosophers think this scenario is any different from their point of view, which would presumably impact whether Carroll’s argument is legitimate.
Right, now I’m in closer accord.
Of course a tornado probably can’t wire up the electronics and solder them, etc… But in reality, the time required for luck to assemble a plane is longer than the age of the universe (I’d guess) by which time the raw materials will have long decayed. In other words, it’s impossible.
If you had a trillion-sided die, you’d have to roll it for a long time to get the number you want – probably. It is quite possible to roll it the first time. But you won’t get lucky and get a plane on the first try; assembly is a series of dependent events, each of which has an exceedingly low probability.
To digress, if the universe has only been created once, then one might calculate that to be impossible too – but unless it is eternal (possible?), it was created at least once.
Can’t help with the philosophic details, but I’m also curious to know.
To summarize, when you rely on cosmological timescales for certain results to manifest, you can’t neglect the cosmological timescales for convenience elsewhere.
“if a universe of Boltzmann Brains is logically impossible, then any physics that makes Boltzmann Brains more likely than normal humans must similarly be wrong.” See, I think this sentence is self-contradictory. If we already know BB is impossible, than we shouldn’t care how likely they are. Conversely, if I win the lottary, I don’t care how unlikely that was. Odd don’t determine anything, they just quantify the theoretical rarity.
“To summarize, when you rely on cosmological timescales for certain results to manifest, you can’t neglect the cosmological timescales for convenience elsewhere.”
““if a universe of Boltzmann Brains is logically impossible, then any physics that makes Boltzmann Brains more likely than normal humans must similarly be wrong.” See, I think this sentence is self-contradictory. If we already know BB is impossible, than we shouldn’t care how likely they are. Conversely, if I win the lottary, I don’t care how unlikely that was. Odd don’t determine anything, they just quantify the theoretical rarity.”
It’s not that we know Boltzmann Brains are logically impossible, it’s that we know that a proof that we are Boltzmann Brains, or that they fill the universe, is logically impossible. Key distinction.
Is a universe that operates according to physical laws actually “random”? That seems a big component of the comment discussion above. Coin flips and die throws, all other things being equal, can be said to deliver random results in which all possible outcomes are, well, possible. With coins and die, equally possible. [Yet the reality is that there is nothing at all “random” about a coin toss or die throw.]
The idea that some corner of the universe just “randomly” created Sarah along with her environment and memories does not seem a possible outcome of matter as we understand it. Surely it’s a highly unusual outcome, to say the least! I think it’s possible to get trapped by the phrase, “Anything is possible.”
A question I’ve been trying to find a definitive answer to is: Given that the digits of pi are random and infinite, does this mean that (for some encoding scheme) we can find, as a contiguous string, the entire works of Shakespeare? One view seems to be that, given an infinite string of “random” digits, it should appear. But does the structure of his portfolio perhaps mitigate against the idea? (I suppose one could compress the Works to derive a bit stream that looked a lot more random.)
Philosophically, you’re touching on solipsism — the idea that the only fact you know for sure is that you exist (because you experience and think — cogito ergo sum). You have to, at some level, take reality on faith. Pragmatically, you have to. If you don’t, about all you can do is contemplate your navel. Once you do accept that reality is, you can begin to explore it and try to make sense of it. The fact that it does make sense seems to argue in favor of its reality.
But in the end, it’s actually almost impossible to prove beyond a doubt that you aren’t a brain in a jar, ala The Matrix. For one thing, your brain is locked inside your skull and only experiences reality via its senses. There is no real difference if your brain is fed those senses by some mad scientist.
This is why you need the right sort of randomness and the right sort of universe. You’re correct that it’s not inevitable that everything is possible, you need to do your homework and determine if it’s actually something that could physically arise in the universe in question. That said, I’m pretty confident that the folks who figured out Boltzmann Brains did their homework.
It may feel quite unlikely that the works of Shakespeare exist in the digits of pi, but it’s actually pretty likely. The important thing to keep in mind is that there’s also a whole lot of nonsense in there too. Check out Borges’s Library of Babel (http://en.wikipedia.org/wiki/The_Library_of_Babel) for a good exploration of the concept.
I agree that, philosophically, it’s a bit dubious to actually draw conclusions from the possibility of Boltzmann brains. There are so many ways to get to solipsistic conclusions already, and philosophers these days have been good about avoiding them, I don’t think there’s anything special about this case in that respect.
One difference seems to be that Borges’ Library explicitly contains every combination. (I like the idea of how this includes valid books with misspellings and other errors. I also love the idea that an apparent gibberish sequence can be “decoded” via a second sequence. Sequences could even be viewed as input to some decoding algorithm.)
I suppose that’s really my question with regard to the digits of pi… can one find every possible sequence of digits and any given length therein?