What I said about entropy yesterday is interesting (at least to me) but not really mind-bending. Today’s continuation has stranger things, largely based on a couple of books by noted physicists, The Fabric of the Universe by Brian Greene and From Eternity to Here by Sean Carroll (both books have long subtitles, which I have omitted because I can’t remember them and because I disapprove of the way all non-fiction books have to have long subtitles now). I first encountered these ideas in Greene’s book, but found the presentation not very convincing, and I would recommend Carroll’s more thorough discussion.
So here’s the weird thing about entropy and the second law…OK, one of the weird things. They don’t seem to fit with the basic laws of physics. The kinds of stuff you study in Intro Physics, perfect pendulums swinging in identical arcs, ideal planets in elliptical orbits, etc., are time-reversible: if you saw a movie of these things played backwards, it would still look just like a pendulum or a planet doing what it does. The same is true of the fancier laws that govern the microscopic behavior of matter, and in fact this is one of the key insights in the so-called Feynmann diagrams, that some particles move forward in time and some move backward.
Indeed, as I’ve mentioned before, physicists tend to have a Tralfamadorian view of time (remember the aliens from Slaughterhouse-Five). They see it as a whole, not as something where only one moment at a time is real and where only one direction is possible. Instead, time is like each dimension of space: you can choose a particular orientation as your reality, say, “towards Manhattan” vs. “away from Manhattan,” but that choice will seem arbitrary and provincial (unless you’re a New Yorker, in which case it’s the natural order of the universe). The world of physics, at the microscopic level, is time-reversible (with some fudging, since charge and parity also have to be reversed, but whatevs).
All this goes to hell when applied to the world at the level we can perceive. Eggs turn into omelets, but you can wait a long time and not see an omelet turn into eggs. A movie of animals doing almost anything will look totally wrong if you reverse it, and the same goes for a movie of the formation of the solar system: stars and planets don’t spontaneously turn into diffuse lumps of gas.
And yet we’re supposed to believe that these larger bodies consist of particles following all those aforementioned laws, and in theory, if we knew everything about the particles, we would be able to assemble the behavior of the larger objects. So how can we have each part behaving reversibly, but the whole behaving irreversibly?
Here’s a way to look at this paradox, which shows, among other things, how physicists are willing to adopt a truly bizarre perspective on reality. Because the laws of motion are reversible, the same argument that we used to show that things get more jumbled as we move into the future work equally well to show that they get more jumbled as we move into the past. For example, if we see a shattered egg on the kitchen floor, it is absurdly unlikely that, returning in a minute, we will find that the egg has repaired itself and is now whole. We can show this with probability, because turning into a whole egg represents an infinitesimally small percentage of the things the egg’s molecules might do. The kicker is that the same is true if we run time backwards–it is so unlikely that the egg will be (i.e., was) whole one minute ago that it is a safer proposition to suppose that there was never a whole egg and the broken egg is just the result of a random coincidence of molecules coming together.
To take it one ste further (and physicists always do), think about what we know of the past. What we know now consists of current memories and perceptions–as a frinstance, a photograph of your 10th birthday. Looking at that photo, you might see youself wearing a red shirt and naturally take that as evidence that you were wearing a red shirt on your 10th birthday. But from the point of view of statistical mechanics, it is more likely that the photograph is a freakish random fluctuation, in which quadrillions of atoms happened to coalesce into an apparetn picture of your 10th birthday, than that you really had a 10th birthday as represented. The reason is that, while making a photo from scratch would require a monstrous lowering of entropy, assembling your actual red shirt, and you, and all the other guests, and the cake and the camera, represents an even more monstrous lowering of entropy.
By the same token, it is more probably that your brain is a random coalescence of atoms, and that all your memories are fake, than that the world you remember exists. As Edgar says to Gloucester after thwarting his suicide attempt, “Thy life’s a miracle.”
That way madness lies, obviously. One way out is to say that this idea, that the whole world (including physics) is just a fantasy that chance has implanted in your brain, is plain stupid, and if that’s where the laws of physics lead then they suck. Or we could say that we need one additional assumption that will make things work out properly, and that assumption is that our universe started out in a state of amazingly, one might almost say miraculously low entropy. If we start out with such low entropy, then positing low-entropy things like whole eggs and birthday parties in the past becomes rational.
In fact, Boltzmann pointed out that this low-entropy state _defines_ the past: the part of time that we can remember or reconstruct is, by definition, a time of lower entropy (otherwise our memories would be bogus). If we got lost in time, not just unstuck like Billy Pilgrim but turned around, we would be able to re-orient ourselves by saying, the future is where entropy increases, where eggs break and fire turns wood into ashes rather than the other way round.
I have not yet seen a good explanation of why our universe experienced such an astonishing entropy minimum, not only creating enough order for us obersvers to exist, but going hog-wild in making galaxies supernovas and lizards and whatnot. Greene got off onto suerstrings, which I find dubious pending any kind of experimental support, but I haven’t finished the Carroll book yet, and maybe he will have something good to say.