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We can be more specific about what the universe would look like if it were an eternal system fluctuating around equilibrium. Boltzmann invoked the anthropic principle (although he didn’t call it that) to explain why we wouldn’t find ourselves in one of the very common equilibrium phases: In equilibrium, life cannot exist. Clearly, what we want to do is find the most common conditions within such a universe that are hospitable to life. Or, if we want to be a bit more careful, perhaps we should look for conditions that are not only hospitable to life, but hospitable to the particular kind of intelligent and self-aware life that we like to think we are.
Maybe this is a way out? Maybe, we might reason, in order for an advanced scientific civilization such as ours to arise, we require a “support system” in the form of an entire universe filled with stars and galaxies, originating in some sort of super-low-entropy early condition. Maybe that could explain why we find such a profligate universe around us.
No. Here is how the game should be played: You tell me the particular thing you insist must exist in the universe, for anthropic reasons. A solar system, a planet, a particular ecosystem, a type of complex life, the room you are sitting in now, whatever you like. And then we ask, “Given that requirement, what is the most likely state of the rest of the universe in the Boltzmann-Lucretius scenario, in addition to the particular thing we are asking for?”
And the answer is always the same: The most likely state of the rest of the universe is to be in equilibrium. If we ask, “What is the most likely way for an infinite box of gas in equilibrium to fluctuate into a state containing a pumpkin pie?,” the answer is “By fluctuating into a state that consists of a pumpkin pie floating by itself in an otherwise homogeneous box of gas.” Adding anything else to the picture, either in space or in time—an oven, a baker, a previously existing pumpkin patch—only makes the scenario less likely, because the entropy would have to dip lower to make that happen. By far the easiest way to get a pumpkin pie in this context is for it to gradually fluctuate all by itself out of the surrounding chaos.
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