A Boltzmann Brain, or "freak observer" is a hypothetical self-aware entity that arises from a low-likelihood fluctuation in a disorganized system. Suddenly, from a chaos of gasses, say, 10^27 atoms just happen to converge in exactly the right way to form a human brain thinking to itself, "I wonder if I'm a Boltzmann Brain". Extremely unlikely. But, on many physical theories, not entirely impossible. Given infinite time, perhaps inevitable! Some cosmological theories seem to imply that Boltzmann Brains vastly outnumber ordinary observers.
This invites the question, might I be a Boltzmann brain?
The idea started getting attention in the physics community in the late 2000s. One early response, which seems to me superficially appealing but not to withstand scrutiny, is what I'll call the Still Here response. Here's how J. Richard Gott III put it in 2008:
How do I know that I am an ordinary observer, rather than just a BB [Boltzmann Brain] with the same experiences up to now? Here is how: I will wait 10 seconds and see if I am still here. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... Yes I am still here. If I were a random BB with all the perceptions I had had up to the point where I said "I will wait 10 seconds and see if I am still here," which the Copernican Principle would require -- as I should not be special among those BB's -- then I would not be answering that next question or lasting those 10 extra seconds.
There's also a version of the Still Here response in Max Tegmark's influential 2014 book:
Before you get too worried about the ontological status of your body, here's a simple test you can do to determine whether you're a Boltzmann brain. Pause. Introspect. Examine your memories. In the Boltzmann-brain scenario, it's indeed more likely that any particular memories that you have are false rather than real. However, for every set of false memories that could pass as having been real, very similar sets of memories with a few random crazy bits tossed in (say, you remembering Beethoven's Fifth Symphony sounding like pure static) are vastly more likely, because there are vastly more disembodied brains with such memories. This is because there are vastly more ways of getting things almost right than of getting them exactly right. Which means that if you really are a Boltzmann brain who at first thinks you're not, then when you start jogging your memory, you should discover more and more utter absurdities. And after that you'll feel your reality dissolving, as your constituent particles drift back into the cold and almost empty space from which they came.
In other words, if you're still reading this, you're not a Boltzmann brain (p. 307-308)
I see two problems with the Still Here response.
First, we can reset the clock. While after ten seconds I could ask the question "am I a Boltzmann Brain who has already lasted ten seconds?", that question is not the sharpest form of the skeptical worry. A sharper question would be this, "Am I a Boltzmann Brain who came into existence just now with a false memory of having counted out ten seconds?" In other words, there seems to be nothing that prevents the Boltzmann Brain skeptic from restarting the clock at will. Similarly, a Boltzmann Brain might come into existence thinking that it had just finished introspecting its memories Tegmark-style, having found them coherent. That's the possibility that the Boltzmann Brain skeptic will be worried about, after having completed (or seeming to have completed) Tegmark's test. The Still Here response begs the question, or argues in a circle, by assuming that we can have veridical memories of implementing such tests over the course of tens of seconds; but it is exactly the veridicality of such memories, even over short durations, that the Boltzmann Brain hypothesis calls into doubt.
Second, this response ignores the base rate of Boltzmann Brains. It's widely assumed that if there are Boltzmann Brains, they might be vastly more numerous than normally embodied observers. For example, a universe might produce a finite number of normal observers and then settle into an infinitely enduring high entropy state that gives rise, at extremely long intervals, to an infinite number of Boltzmann Brains. Since infinitude is hard to deal with, let's hypothesize a cosmos with a googolplex (10^(10^100)) of Boltzmann Brains for every normal observer. Given some sort of indifference principle, the Boltzmann Brain argument goes, I should initially assign a 1-in-a-googolplex chance to being a normal observer instead of a Boltzmann Brain. Not good. But now, what are the odds that a Boltzmann Brain can hold it together for ten seconds without lapsing into incoherence? Tiny! Let's assume one in a googol (10^100). The exact number doesn't matter. Setting aside worries about resetting the clock, let's assume that I now find that I have indeed endured coherently for ten seconds. What should be my new odds that I am a Boltzmann brain? Much lower than 1-in-a-googolplex. Yay! Only about a googolth of a googolplex! Let's see, how much is that? Instead of a ten followed by a googol of zeroes, it's only ten followed by a googol-minus-100 zeros. So... still virtual certainty that I am a Boltzmann Brain.
So how should we respond to the Boltzmann Brain hypothesis, then? Sean Carroll has a two-pronged answer that I think makes a lot of sense.
First, one can consider whether physical theories can be independently justified which imply a low ratio of Boltzmann Brains to normal observers. Boddy, Carroll, and Pollack 2015 offer such a theory. If it turns out that the best physical theories imply that there are zero or very few Boltzmann Brains, then we lose some of our grounds for worry.
Second, one can point to the cognitive instability of the Boltzmann Brain hypothesis (Carroll 2010, p. 223, drawing on earlier work by David Albert). Here's how I'd put it: To the extent I think it likely that I am a Boltzmann Brain, I think it likely that evidence I have in favor of that hypothesis is delusional -- which should undercut my credence in that evidence and thus my credence in the hypothesis itself. If I think it 99% likely that I'm a Boltzmann Brain, for example, then I should think it 99% likely that my evidence in favor of the Boltzmann Brain hypothesis is in fact bogus evidence -- false memories, not reflecting real evidence from the world outside -- and that should in turn reduce my credence in the Boltzmann Brain hypothesis.
An interesting feature of Carroll's responses, which distinguishes them from the Still Here response, is this: Carroll's responses appear to be compatible with still assigning a small but non-trivial subjective probability to being a Boltzmann Brain. Maybe the best cosmological theory turns out not to allow for (many) Boltzmann Brains. But we shouldn't have 100% confidence in any such theory -- certainly not at this point in the history of cosmological science -- and if there are still some contender cosmologies that allow for many Boltzmann Brains, we (you? I?) might want to assign a small probability to being a Boltzmann Brain, in view the acknowledged possibility that the cosmos might, though unlikely, have a non-trivial ratio of Boltzmann Brains to normal observers. And although a greater than 50% credence in the Boltzmann Brain hypothesis seems cognitively unstable in Carroll's sense, it's not clear that, say, an approximately 0.1% credence in the Boltzmann Brain hypothesis would be similarly unstable, since in that case one still might have quite a high degree of confidence in the physical theories that lead one to speculate about the small-but-not-minuscule possibility of being a Boltzmann Brain.