Monday, December 26, 2011

From Eternity to Here

I wish I could write something insightful about Sean Carroll's book From Eternity to Here, but instead I wrote today's post. This is not to say anything bad about Carroll's book—it's a great book. Rather, it's to say there's nothing like learning a few facts to realize just how little I know, and that's what I got from reading Carroll's book: a few facts a big dose of humility. Cosmology isn't my strength.

Carroll's main point has to do with explaining time and why we experience it as moving forward. The short answer is that time appears to move in the direction of increasing entropy. But this raises another question: why is entropy steadily increasing? The majority of the book explores this question from a multitude of angles, and along the way I learned some interesting facts, which I've summarized in bullet-list form.

  • The laws of physics, even at their most fundamental level, may be reversible, which is to say time's arrow mayn't be caused because of low-level interactions. Particle physics appears reversible along the three reflections of nature: time, parity (i.e., right and left, like what a mirror changes), and charge (i.e., positive and negative). When all three reflections are inverted, a particle or a system of particles will run backwards. So, for example, imagine you start with a box, mostly empty save for gas particles crammed into one corner. That's a low-entropy state. Then let the particles bounce around until they fill the box uniformly, which is a high-entropy state. If, at some time after the particles settle into a uniform distribution, you invert each particle along all three reflections, then the particles will move in reverse, with the effect that entropy will decrease from high to low in the box.

  • Entropy isn't one-to-one with disorder. Counterexample: oil and vinegar, when mixed and allowed to increase in entropy, will separate into a higher-order state. Thus, sometimes an increase in entropy denotes a decrease in disorder. So it's a good idea to be precise with the terminology and say entropy when that's what you mean, not disorder.

  • There is something called a Boltzmann brain, which is a hypothetical brain, or mind, that floats in outer space unattached to any body. But the brain is alive, thinking and feeling just like any human brain does. As extraordinarily unlikely it is that a Boltzmann brain actually exists (for the odds of a brain forming in a near vacuum are extremely tiny), it's more likely for a Boltzmann brain to exist than Boltzmann himself. This is because Boltzmann (the physicist) comprises a brain and a body, which is even lower entropy than just a brain.

  • Indeed, Boltzmann brains are maybe the biggest reason why it's important for guys like Carroll to figure out what time is. Boltzmann brains tell us—not the actual brains, mind you, just their possible existence—that we ourselves are more likely to be Boltzmann brains than real people on a planet, just as it's more likely for the universe to spontaneously generate a loaf of bread than it is to generate a loaf of bread and a baker. But we're not Boltzmann brains, so cosmology ought to account for why the universe has much less entropy than it could otherwise have for there to exist someone who, like us, observes what's going on. If Boltzmann brains were impossible, you could merely posit a low-entropy beginning condition—i.e., the big bang—and say the universe had an infinite amount of time before that time in which to fluctuate into the big bang's hot, dense low-entropy state. But, once allowing for the possibility of Boltzmann brains and how we'd much more likely be Boltzmann brains than real people on a planet, we need to explain why the universe's past low-entropy condition was lower than it needed to be—i.e., low enough to produce us.

Carroll explains such a possible model in his book. But that's all you'll read about it here.

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