Are you a Boltzmann brain?


In the nineteenth century, Ludwig Boltzmann found a thermodynamic explanation for the existence of the Universe.  Essentially, in an infinite Universe anything can happen:

   “We assume that the whole universe is, and rests for ever, in thermal equilibrium.  The probability that one (only one) part of the universe is in a certain state, is the smaller the further this state is from thermal equilibrium; but this probability is greater, the greater is the universe itself.  If we assume the universe great enough, we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please.  We can also make the probability great that, though the whole universe is in thermal equilibrium, our world is in its present state.  It may be said that the world is so far from thermal equilibrium that we cannot imagine the improbability of such a state.  But can we imagine, on the other side, how small a part of the whole universe this world is?  Assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.

   If this assumption were correct, our world would return more and more to thermal equilibrium; but because the whole universe is so great, it might be probable that at some future time some other world might deviate as far from thermal equilibrium as our world does at present.”

   This is an astonishing passage to find in a paper published in 1895, and is directly relevant to modern ideas about the Multiverse, if we replace Boltzmann’s term “universe” with our “Multiverse,” and his “world” with our “Universe.”  It even includes implicit, if unconscious, anthropic reasoning – observers like us can only exist in fluctuations like these, so it is no surprise that we find ourselves living in such a fluctuation.

     Boltzmann defended the idea vigorously.  In 1897, he wrote:

“This viewpoint seems to me to be the only way in which one can understand the validity of the Second Law and the heat death of each individual world without invoking a unidirectional change of the entire universe from a definite initial state to a final state.  The objection that it is uneconomical and hence senseless to imagine such a large part of the universe as being dead in order to explain why a small part is living – this objection I consider invalid.  I remember only too well a person who absolutely refused to believe that the sun could be 20 million miles from Earth, on the grounds that it is inconceivable that there could be so much space filled only with aether and so little with life.”

     There is, though one point that Boltzmann overlooks, where he refers to other “worlds” like ours forming “at some future time.”  In the wider universe he envisages (a better term might be the meta-universe), there is no time.  In thermodynamic equilibrium, there is no way to distinguish the past from the future, any more than a series of snapshots of a box of gas in thermal equilibrium can be jumbled up and then arranged in the order they were taken simply by looking at the distribution of atoms on each snapshot.  If we are living in a fluctuation within such a meta-universe, all that can be said about the meta-universe is that it exists, and that within it other fluctuations exist.  The arrow of time (or arrows of time) only exist within those fluctuations.

     There’s another puzzle, which Boltzmann addresses but which worries a lot of people today.  Why do we live in such a large fluctuation from thermodynamic equilibrium?  Boltzmann was happy that no matter how big our “world” (Universe) is, “assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.”  There may be smaller fluctuations as well, but so what?  The puzzle, as it is usually expressed today, is that from the perspective of the meta-universe it should be much easier to make a much smaller fluctuation, starting out from thermodynamic equilibrium.

     To take an extreme example, if a fluctuation can occur that is as large and complex as the entire Universe, it ought to be much easier, and therefore much more likely, that a fluctuation could produce the room you are sitting in, all it contains, yourself, complete with all your memories, and the computer on which you are reading this blog.  It could have happened a second ago, and it could all disappear before you finish reading this sentence.

     It gets worse.  In the early years of the present century,  a team of researchers from Stanford University and MIT put the cat among the cosmological pigeons by suggesting that even within the context of inflation, the modern version of the Big Bang idea, the overwhelming majority of states which could have evolved into a world similar to ours would not start from a low entropy state.  The puzzle suggested that it is still easier to make a single individual sitting in a room, or a naked brain complete with (false) memories of learning about the Big Bang and the history of the Universe, and equally false memories of having read about Boltzmann fluctuations earlier in this book (Actually, of course, if you are simply a naked brain, the memories are real, but the events you remember never happened), rather than making the Universe itself.  This is sometimes known as the “Boltzmann’s brain” paradox, since a naked brain lasting for just long enough to “know” all the things we think we know about the Universe seems to be the simplest statistical fluctuation that would explain why you think you are sitting there reading these words.

     I’m sure you will be glad to learn (if you have indeed survived to read this far) that there is a major flaw in this argument, and it turns out, as explained in my book, that it is much easier to make a big bang out of a Boltzmann fluctuation than it is to make, say, a human brain in one step. If you want to know more without reading the book, try Googling “Causal Patch Physics”.


Adapted from my book In Search of the Multiverse.



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