# Are you a Boltzmann brain?

Have you ever wondered: what if everything I see around me is just an illusion, a dream? This might sound like a silly possibility that only a child or a philosopher would seriously entertain, but I want to show you it's far more serious than that. In fact, in some sense modern physics almost guarantees that this ridiculous possibility is actually true! Yes, you heard me right, and it's not just me who is saying that. This is called the  Boltzmann brain problem in cosmology.

What is a Boltzmann brain?

Let's start simple: you have a brain, and it's made of subatomic particles. The atoms in the air in your room are made up of the same ingredients (electrons, protons, etc.). So are atoms on Jupiter or anywhere else in the universe. If you wait long enough, and I mean REALLY long, the air particles in your room will, through random motion, end up in some highly unlikely configuration, like for example all ending up in one corner of the room. Another unlikely configuration they could form is a replica of your brain as it is right now. Just as your brain thinks it's reading this sentence, the replica brain would think the same thing (but unlike you would be wrong of course). This kind of brain, that would form as an extremely unlikely result of random motion of particles, is called a Boltzmann brain.

In fact, if the universe is sufficiently big or infinite, as it quite possibly is, you can be sure that somewhere, far far away, there are Boltzmann brains that just formed, maybe in the middle of some star, or maybe somewhere between galaxies. They won't live too long but for a split second they will be conscious.

Are you a Boltzmann brain?

Yes, you, at this very moment. That's a natural question to ask because, as we said before, a Boltzmann brain could be a replica of yours and therefore could feel exactly how you feel at some specific moment, and have the illusion of being wherever you are and seeing whatever you are seeing.

The natural answer might be something like this: maybe Boltzmann brains exist somewhere, if the universe is really big, but they are incredibly rare. So the "regular" brains, those of people as well as aliens throughout the universe, must vastly outnumber the Boltzmann brains. So if I had to bet which one I am at this very moment, then even though I couldn't tell the difference, on the basis of just pure numbers I could easily put all my money on being one of the regular ones. Right?

Not so fast!

That's a natural and reasonable hypothesis, but the point of this article is to show you that in some sense physics says that it's completely the opposite: you should put all your money on being a Boltzmann brain. Before I prove this to you I should tell you that neither I nor theoretical physicists believe that we are Boltzmann brains. Rather, they are looking for cosmological models that would successfully avoid that unpalatable conclusion. But it's not easy because of how naturally that conclusion arises, as we are about to see.

Quick proof.

Just so you know where we are going, let me give you all the steps of the argument. If you are a seasoned physics pro you might not even need to read any further. Otherwise, don't worry if the steps are not quite clear - I'll explain them in more detail, I just want you to have some idea of what to expect.

1. If you are a regular person your brain is surrounded by an ordered environment, so there are vastly more configurations of the universe where you are a Boltzmann brain than configurations where you are a regular person.

2. By conservation of information, there are vastly more initial states of the universe that lead to you being a Boltzmann brain than initial states that lead to you being a regular person.

3. If you have no reason to expect any initial state of the universe to be more likely than any other state then you have no reason to expect that the current configuration of the universe is ordered, and therefore you should expect to be a Boltzmann brain.

Step 1.

By a brain like yours I will mean the exact current configuration of your brain. As we discussed, that brain can be regular or Boltzmann. If it's regular that means it's in a regular person, who is on a regular planet in a regular galaxy, and we'll call that whole situation a regular state of the universe. Otherwise, if it's Boltzmann then none of that is true, it's just a brain that randomly fluctuated into existence that could be surrounded by any random configuration of particles. I will call this a disordered state of the universe.

Clearly there are vastly more possible disordered states than regular ones. The numbers are beyond astronomical, but for the purposes of illustration let's say that there are one billion disordered states and only one thousand regular states (so the ratio is 1000000; the actual ratio has been estimated by Roger Penrose to be one followed by 10123 zeroes). You want to know which of these two types of states the universe is in. If it's disordered then you are a Boltzmann brain, if it's regular then you are a regular person.

Of course if all states were equally likely then the actual state would almost certainly be disordered, but are they equally likely? Maybe when the universe began most of its possible initial states were ones that could only evolve, over time, into regular states.

Step 2.

Conservation of information cuts against that idea. Conservation of information is a fundamental principle of quantum mechanics. The term may sound fancy, but the idea is simple: given the current configuration of all the particles, one can (in principle!) use the laws of physics to uniquely determine their configuration at any point in the future or the past.

For example, take one of the (thousand) possible regular configurations the universe could be in now, call it $R_1$. Conservation of information tells us that the laws of physics uniquely determine what initial state it came from, call it $R_1^i$. Take another regular state $R_2$, it has its own unique "ancestor" $R_2^i$. And so on, one thousand possible regular states have one thousand ancestors at $t=0$.

Similarly, one billion possible disordered states the universe could be in now have exactly one billion ancestors $D_1^i$, $D_2^i$, ... at $t=0$. And so the initial state of the universe was either one of the thousand regular ancestors or one of the billion disordered ancestors.

Step 3.

If you have no reason to expect any initial state of the universe to be more likely than any other state then you have no reason to expect that the initial state was one of the few regular ancestors, as opposed to one of the many disordered ones. Which means you have no reason to expect that the current state is one of the few regular ones, and therefore you should expect to be a Boltzmann brain.

You might wonder: but maybe we do have some reason to expect the regular initial states to be somehow privileged over the disordered ones? That's what cosmologists are working on, they are trying to find plausible mechanisms for that, because, as I said at the beginning, they don't actually believe they are Boltzmann brains!

But it's tough, and here's one reason why. The laws of physics tell us, given some initial configuration at time $t_i$, how it will evolve over time. But they don't tell us which of the possible initial configurations "reality" had to start from. This is where physics ends and metaphysics begins.

Questions, doubts, objections.

You might have thought of some possible objections to this analysis, or have some clarifying questions. Please post them in the comments, and I will add my answers to some of them here.

Q. Much of the matter in the universe is in the state of plasma and since it is a different state of matter than a brain, I don't think a brain could be produced in one. (I'm not a physicist).

A. The basic subatomic ingredients are still the same, electrons, quarks, etc.

Q. Quantum mechanics involves probabilities, so one initial state can end up in many possible final states. Likewise, several different initial states can end up in the same final state. But you claimed that conservation of information means the initial and final states are in one-to-one correspondence.

A. This is not very easy to explain on a popular level. First, the quantum state evolves according to the Schrodinger equation, which is completely deterministic, no probabilities involved. What about wavefunction collapse? That only happens in some interpretations of QM, but even then the crucial result remains true: an n-dimensional space of states evolves to an n-dimensional space even if collapses happen along the way. So the counting of states we did is still correct.  There is definitely much more to say about the subtleties of conservation of information in quantum mechanics, which I plan to do in a separate article, but for now the bottom line is that information is still definitely conserved in QM and it's still true that a thousand (billion) states have a thousand (billion) ancestors.

Q. It seems like we have nothing more than "common sense" (aka human bias) to rule against the Boltzmann brain hypothesis. If this is true then we have no rational reason to privilege a cosmological model on account of it "solving" the Boltzmann brain problem.

A. A model that says we are Boltzmann brains is "cognitively unstable", in the words of Sean Carroll, because then our memories are illusory. We would then have no reason to trust any reasoning and evidence we think we have that led us to that model in the first place. So basically if we accept such a model then we have to reject it.

### 12 Comments - Go to bottom

1. There are two difficulties with the argument I see - one might be a problem, the other I consider rather deadly.
Physics- this might be a problem- much of the matter in the universe is in the state of plasma and since it is a different state of matter than a brain, I don't think a brain could be produced in one. (I'm not a physicist).

Probability and logic - the process in making a Boltzmann brain involves events that occur at random.
Since the events occur at random, there is no guarantee that even one Boltzmann brain would ever be produced given an infinite universe and endless time.

The random process is not a sufficient cause to produce even one Boltzmann brain.
We have some pretty good idea how the brains we have did get here- an evolutionary process that has pretty good evidence in support that it did happen.

I'm thinking to get to the conclusion " therefore you should expect to be a Boltzmann brain."
is going to involve some misstep or two.

Let's see- it could be interesting- I could be wrong.

2. Thanks for the interesting objections. About the physics one: the basic subatomic ingredients are still the same, electrons, quarks, etc.

About the probability one: It's not required by the analysis that the probability of producing at least one Boltzmann brain be literally exactly 100%. The more relevant quantity would be the total expected number of Boltzmann brains, which, if the universe is sufficiently big, can be arbitrarily high (and btw the probability that there would be at least one Bolzmann brain would then be arbitrarily close to 100%).

1. I'm not sure if the physical realities are as you say, but let's assume they are.

Wouldn't the same argument apply to 'non Boltzmann brains' assuming that's what I have?
It seems non-Boltzmann brains are even more probable than Boltzmann brains.
So it makes more sense to assume I'm a "non".

How's that?

3. I would also like to point out our being a Boltzmann is very much contingent on the mechanism of consciousness. In the absence of our understanding this mechanism we really can't say too much here. For example, if functionalism is true, then non-functional systems lack consciousness and random assortments of matter in the middle of Jupiter are not conscious.

Another interesting thing to point out, is that we really have no good reason for thinking that we're not Boltzmann brains (this seems an unfalsifiable hypothesis). Hence the "natural assumption' of cosmologists that a Boltzmann brain side effect of a cosmological model is an unwanted one, may be questionable. On what grounds are we warranted to deem a cosmological model defective in this way? It seems like our only justification is our steadfast belief that, while we could be a Boltzmann brain with a 10 second lifespan replete with false memories; it nevertheless seems "obvious" that we are in fact organisms equipped with an entire life history that we've lived through.

It seems like we have nothing more than "common sense" (aka human bias) to rule against the Boltzmann brain hypothesis. If this is true then we have no rational reason to privilege a cosmological model on account of it "solving" the Boltzmann brain problem.

Having said this, I'd also like to point out that the existence of our long lifespan shifts the probabilities somewhat (assuming that we can trust our memories). If you're an average Boltzmann brain, you should expect to die any second (milli-second). The longer life goes by without this happening, the more improbable one's being a Boltzmann brain becomes. Of course the problem here is that Boltzmann brains so vastly outnumber physical brains in some multiverse landscapes, that it might still be more likely that one is a lucky aged Boltzmann brain instead of a physical entity.

But I'm not sure of this (I haven't done the math). Because there is no actual mechanism in place that forces a Boltzmann brain to adopt a mind-like structure; the probability that it will remain a mind-like entity for a long period of time (decades) may in fact be so incredibly unlikely that it is more probable that one is physical brain after all.

I wonder what you think of this? On the one hand, it seems irrational for cosmologists to favor a particular model over another on the grounds that one "solves" the Boltzmann brain problem, on the other hand it might turn out that being an 80 year old physical brain is still more probable than being an 80 year old Boltzmann brain, even if the latter immeasurably outnumber the former.

1. Alex,

You bring up a lot of interesting points. The functionalism concern can be taken care of by noting that if for some reason you need more than a brain to be conscious then simply replace the word brain in the analysis by whatever is needed for consciousness (for example the whole body).

"It seems like we have nothing more than "common sense" (aka human bias) to rule against the Boltzmann brain hypothesis. If this is true then we have no rational reason to privilege a cosmological model on account of it "solving" the Boltzmann brain problem."

A model that says we are Boltzmann brains is "cognitively unstable", in the words of Sean Carroll, because then our memories are illusory. We would then have no reason to trust any reasoning and evidence we think we have that led us to that model in the first place. So basically if we accept such a model then we have to reject it.

"Having said this, I'd also like to point out that the existence of our long lifespan shifts the probabilities somewhat (assuming that we can trust our memories). "

That's the key, we can't trust our memories if we are Boltzmann brains, so we can't take our memories of being alive for a long time as evidence.

4. Dmitriy,

Thanks for that. I had read Carroll at some point and forgotten that argument of his. That seems to pretty conclusively settle the argument against Boltzmann brains. However I'm not so sure about your functionalism retort. Consider that if we need a body etc.. in order to be functional and therefore conscious, it then follows that we must have access to reliable senses. By definition, a system wouldn't really be functional if your senses were not at least somewhat reliable. As such, the abundance of observed astronomical evidence around us would have to be explained. And the Boltzmann hypothesis no longer does this.

1. Alex,

If the senses need to be reliable for consciousness (which I don't agree with since we can have conscious experiences while dreaming) then replace "brain" in the above with something like "brain plus body with reliable senses plus suitable local environment". By the latter I mean for example a room, maybe when you are not looking at the window. Everything within that local environment could be as your senses tell you, but everything outside of it would still be in a disordered state.

5. Hey Dmitriy,

I agree that our senses being reliable is not a necessary condition for consciousness; my point was that the system (be it a body, local environment etc...) has to be reliable. Whether you think the senses have to be reliable is going to depend on the type of functionalism you endorse (i.e. to what degree the "system" has to be external). But that wasn't my main point.

The point I was trying to make is that functionalism would necessitate that there be a consciousness-producing mechanism for every such agent. If you grant that functionalism is correct; then we need some kind of reliable consciousness producing system (like the biological brain, body, or local system that you spoke of). Once we have this system, then we are not a Boltzmann brain by definition. Our continued conscious experience is no longer a byproduct of a stochastic process, and we are not in danger of vanishing at any random moment.

The point about the senses beyond the local environment not being reliable is, I think, a separate philosophical concern. That will always be true from an epistemological perspective (see: the brain in the vat scenario). That concern still holds for us right now, with our presumably physical brains. So that's not really an argument to the favor of physical brains.

So there are two entirely different things here. Are we a Boltzmann brain with no existing consciousness-producing mechanism? And can we generally trust our senses as a matter of sound epistemology? Notice that the former, if true, entails unreliable senses and memories per Carroll. But even if one rejects the Boltzmann hypothesis, one can continue to press epistemological concerns along the lines of the latter statement.

My argument was simply that if functionalism is true, then we have a consciousness producing mechanism. And if we have a consciousness producing mechanism, then we can no longer deduce from the Boltzmann hypothesis that our senses and memories are unreliable. That is because the Boltzmann hypothesis entailing unreliable memories and senses follows from the unreliability of the conscious experience itself.

Without a consciousness producing mechanism, there is no guarantee that a random conscious experience represents anything real. That we can nevertheless continue to state general epistemological concerns, regarding the reliability of conscious mechanisms (i.e. physical brains), does not refute the fact that functionalism would disprove the Boltzmann hypothesis.

1. In other words, if we are Boltzmann brains then there is no reason whatsoever to think that our senses/memories are about the world, except for blind/random luck. If we are functional systems; then we have a plausible reason to believe in our memories and senses being reliable (e.g. evolution selects reliable brains, our brains collect data through senses etc...). The point is that we have plausibility with a physical mechanism, but not a guarantee. Epistemological conundrums will always exist.

2. To make sure I understand your argument, why do you think this:
" If we are functional systems; then we have a plausible reason to believe in our memories and senses being reliable (e.g. evolution selects reliable brains, our brains collect data through senses etc...)."

Imagine that room with you in it I was talking about, with a disordered configuration outside of it. It's not a Boltzmann brain but a Boltzmann room if you will. You will die probably within seconds, longer than if you were just a brain but still. Also you are not a product of evolution, and you have only been conscious for probably only seconds, despite whatever memories of a seemingly long life you have.

The argument in this article shows that this situation is vastly more "probable" (in the sense of the total number of microstates) than a regular situation with a regular you in an identical room.

So even if you have a normally functioning body that doesn't immunize you at all from being a Boltzmann-type system with fake memories.

6. Okay, got it. I thought you were granting that the local system was a relatively, functional stable one (i.e. at thermal equilibrium with the outside environment). You are right that such a situation (random room evolved in the middle of deep space) is both not stable and vastly more probable. But notice your system isn't functioning; it's not doing anything like eating, drinking, thinking about a problem, solving a problem, etc... Maybe it'll have time to do one respiration pattern. Your system, at best, has the "potential to function". But for reasons I elaborate below; that's typically not considered a sufficient condition for consciousness.

If that sounds excessively picky; then realize the whole point of functionalism was to solve this problem of arbitrary computation. I could implement a human mind by picking out thermodynamic states across rocks on earth to represent it. You might say that strong connectedness across time/space is really what matters (Integrated Information Theory). But nothing stops me from picking out arbitrary microscopic states "in a single rock" as representative of a human mind either (just map each neuron state corresponding to each atomic/quark state of the rock). If I am clever enough in my mapping, the process may even be dynamic to some extent (e.g. milliseconds).

Finally, causality is typically brought up as counter. There are no cause/effect mechanisms in the rock forcing it to adopt a mind like state, but there are in the brain. But the problem with this too is that your hypothetical brain-room floating in space isn't going to be in a mind-like state for long either. The only difference (apparently) is that the brain room has the potential to function in a certain environment (i.e. earth). However, almost any system has the "potential to function". Even my rock system can hypothetically function quite well in a carefully crafted thermodynamic environment where the rock states conveniently are dynamic mind states. Not the same as chance, rather imagine an advanced technological species knew how to modify the exact thermodynamic characteristics of the local environment, to retain the arbitrary mappings of the rock-mind state for many years.

Such a rock can't be conscious, I arbitrarily selected the mapping pattern. So for all those reasons "potential to function" can't be enough. And that's why most functionalists (although there are many varieties) would probably say your hypothetical brain-room isn't conscious, unless it was in a thermodynamic equilibrium and stable environment (and more preferably in a "rich" environment where functional routines are frequently employed). In any case, it should be obvious that there are some varieties/interpretations of functionalism where the Boltzmann brain/body/room come out false.

1. To elaborate; the rock I randomly picked out wouldn't be considered conscious. On the other hand, the one in the special state crafted by advanced beings that spits out computational outputs would probably be considered conscious by most functionalists. So it's the 'potential to function' attribute which is considered the insufficient condition; hypothetical transient floating objects in space aren't actually functioning.

Granted, your Boltzmann brain instantiates some functioning (i.e. breathing, temporary blood flow), but no one considers such functions vital to consciousness (otherwise brain dead people are conscious). Obviously, functionalism has potential defeaters. For example, it might seem like a brain should still be conscious even when not functioning in the environment (i.e. no output). But I did not come here to defend functionalism.