Boltzmann posed the question of whether the universe could have arisen from a thermal fluctuation; his work presaged the idea that a fluctuation could also give rise to a conscious entity that sees the universe. In this regard Boltzmann brains are not necessarily actual brains, but rather are a metaphor for observers of the universe that might appear spontaneously.
Thus a Boltzmann brain is a conscious entity that instantaneously pops into existence as a spontaneous fluctuation of matter into a highly ordered form, rather than gradually coming into existence like us through the slow process of evolution gradually rearranging matter into a highly ordered form. The probability of a whole brain suddenly popping into existence in this way is extremely small, because the internal structure of the Boltzmann brain has to be exactly right so that it works as a brain, so you have to wait a very long time for there to be a significant likelihood of a Boltzmann brain coming into existence. This likelihood problem is very deftly avoided by evolution, because it breaks the overall problem of making a brain into very small steps, each of which is much more likely to occur than the whole big jump from start to finish; of course, evolution doesn't know in advance that this is what is going on.
More generally, you could imagine a whole spectrum of processes ranging from the instantaneous rearrangement of matter at one extreme (e.g. Boltzmann brain) all the way through to the gradual rearrangement of matter at the other extreme (e.g. evolution).
In a sufficiently large and long-lived universe Boltzmann brains will come into existence, because then the extremely small likelihood of one coming into existence at any given place and time is offset by the large number of alternative places and times that are available in the whole universe (i.e. space-time). Our universe looks exactly like the sort of place where these conditions are (or will be in the far future) satisfied, so Boltzmann brains will eventually come into existence here.
The eventual existence of Boltzmann brains worries cosmologists, because the laws of physics that are deduced by a Boltzmann brain (which is a conscious observer) would be different from the laws that are deduced by us. The reason for this difference is that Boltzmann brains would typically come into existence a very long time in our future when the universe is much larger, emptier and colder than now, so the typical observations made by a Boltzmann brain would be very different from the typical observations made by us, so a Boltzmann brain would deduce laws of physics that are very different from ours.
This fact worries cosmologists so much that they would very much like to find a way to "banish" Boltzmann brains from existence, for instance by finding some property of the currently known laws of physics that prevents favourable conditions for Boltmann brains from ever arising.
I am not as worried as cosmologists are about the potential existence of Boltzmann brains who would deduce different laws of physics from us. My reasoning is as follows:
- Firstly, we are not special in the grand scheme of things, because we are basically the same type of information processors as Boltzmann brains. Both Boltzmann brains and we are two extreme examples of the outcome of a spectrum of processes that have rearranged matter in the universe. Our brains have come into existence via the gradual process of evolution, which stores its intermediate results in the form of DNA, and then uses this as the starting point for the next step in the rearrangement of matter. Whereas Boltzmann brains pop into existence without going via any of these intermediate steps. There is also a whole spectrum of intermediate cases (e.g. partly DNA and partly random chance) that one could imagine; the only way that DNA can evolve is to live a little way into this intermediate regime where there is a small element of random chance. Our brains are not particularly special in this spectrum of possibilities, other than because evolution using DNA (or something analogous) is the only process that has a significant likelihood of making something as complex as our brains in a universe that is as (relatively) young as ours is. The other possible processes for making brains that lie nearer the Boltzmann brain end of this spectrum will need much longer to have a significant likelihood of happening.
- Secondly, the laws of physics that we deduce are (at least partly) environmentally determined, so it doesn't matter too much if observers living in very different universes (or at very different times in the same universe) deduce different laws of physics. We set up our experiments and make observations, then we discover a low-complexity "explanation" of all of these observations and call it the "standard model" (or whatever). The scientific method is driven by whatever experimental observations we make, and we have little choice in this other than the freedom to choose which particular experiments we conduct. We grandly give the name "laws of physics" to our explanation of all of our observations, but the way in which this explanation is constructed leaves a lot of room for doubt about its uniqueness or inevitability. It may yet turn out that the laws of physics are somehow unique/inevitable, but that is far from being obvious right now. It is much safer to keep an open mind, and to assume that the laws of physics are simply what we observe-then-guess them to be, and to be thankful that mathematical beauty and elegance has taken us as far as it has in constraining the precise form of the laws of physics. It may yet turn out that there is a lot more mileage to be had in the mathematical beauty/elegance approach, but we should not assume that this is inevitable.
So we are not special in the grand scheme of things, and the laws of physics that we deduce are (at least partly) environmentally determined. Together, these two points mean that I am not as worried as cosmologists about the potential existence of Boltzmann brains.
Wouldn't it be nice to write a computer simulation of a synthetic universe whose properties gradually changed as the simulation proceeded, in which different types of information processing entity (brains, if you wish) emerged at different times during the simulation, and which interacted with their simulated environment to deduce what they called the "laws of physics" that governed their existence? None of these information processing entities would be "special" in any way (although they might believe themselves to be special!), and the "laws of physics" that they deduced would be environmental.