This time the Boltzmann Brains issue hits the New York Times. It makes me cringe to see such faulty reasoning being paraded under the label of ‘science’. We can start with Hartle and Srednicki’s argument, which I’d previously blogged about, that the assumption that humans are typical conscious observers is not warranted. Sean Carroll purports to have an alternative formulation of the Boltzmann Brains argument that does not rely on this assumption:
Here’s how it goes. Forget that we are “typical” or any such thing. Take for granted that we are exactly who we are — in other words, that the macrostate of the universe is exactly what it appears to be, with all the stars and galaxies etc. By the “macrostate of the universe,” we mean everything we can observe about it, but not the precise position and momentum of every atom and photon. Now, you might be tempted to think that you reliably know something about the past history of our local universe — your first kiss, the French Revolution, the formation of the cosmic microwave background, etc. But you don’t really know those things — you reconstruct them from your records and memories right here and now, using some basic rules of thumb and your belief in certain laws of physics.
The point is that, within this hypothetical thermal equilibrium universe from which we are purportedly a fluctuation, there are many fluctuations that reach exactly this macrostate — one with a hundred billion galaxies, a Solar System just like ours, and a person just like you with exactly the memories you have. And in the hugely overwhelming majority of them, all of your memories and reconstructions of the past are false. In almost every fluctuation that creates universes like the ones we see, both the past and the future have a higher entropy than the present — downward fluctuations in entropy are unlikely, and the larger the fluctuation the more unlikely it is, so the vast majority of fluctuations to any particular low-entropy configuration never go lower than that.
Therefore, this hypothesis — that our universe, complete with all of our records and memories, is a thermal fluctuation around a thermal equilibrium state — makes a very strong prediction: that our past is nothing like what we reconstruct it to be, but rather that all of our memories and records are simply statistical flukes created by an unlikely conspiracy of random motions. In this view, the photograph you see before you used to be yellow and wrinkled, and before that was just a dispersed collection of dust, before miraculously forming itself out of the chaos.
Note that this scenario makes no assumptions about our typicality — it assumes, to the contrary, that we are exactly who we (presently) perceive ourselves to be, no more and no less. But in this scenario, we have absolutely no right to trust any of our memories or reconstructions of the past; they are all just a mirage.
Can you spot where he uses the typicality assumption? In his scenario, the overwhelming majority of states of consciousness containing the exact same observations, feelings, memories and so on are really momentary fluctuations with no real past history other than chaos. From this, he feels entitled to make the prediction that “our past is nothing like what we reconstruct it to be, but rather that all of our memories and records are simply statistical flukes created by an unlikely conspiracy of random motions”. But how does one get from the fact that most states of consciousness that are phenomenologically identical to mine (or his, or any given human’s) are momentary fluctuations to the conclusion that the state of consciousness I (or he, or any given human) happens to be experiencing is a momentary fluctuation? Only if he discounts the possibility that the state of consciouness he is experiencing now is in fact one of those very rare states of consciousness that is not a momentary fluctuation. And if you do discount that, then you are just making the same typicality assumption that Hartle and Srednicki criticised (and which Carroll admits is dodgy).