Classic Edition: Shut Up and Calculate, Already

I'm going to be away from the computer for the long weekend, but I don't want to have the site go completely dark, even over a weekend, so I'm going to schedule a few posts from the archives to show up while I'm away. Everyone else seems to be doing it (and pushing my posts off the front page, the bastards), so I might as well.

This goes back to the early days of the blog, back in August of 2002, and is at least vaguely relevant to the recent discussion of interpretations.

It's been a while now since I talked about science stuff, mostly because there hasn't been any news that I felt strongly enough about to put in the effort to write long posts about. There's been a very recent up-tick in the number of interesting science stories out there, most notably this Australian report (and what's gotten into the Aussies, anyway?) that the speed of light may be changing on cosmological time scales, which I'll get around to once I find a less garbled description of it than the Yahoo story, and get some time to think about it. (Irritatingly, the paper in question was published in Nature, whose obnoxious subscription policy makes it impossible for me to get an on-line copy of the actual paper, and forces me to-- shock! horror! walk to the library to find a physical copy of the article...)

There is a good jumping-off point for some science stuff that doesn't require me to drag my fat ass out of my office, though, as Derek Lowe's been reading Feynman and asks a number of questions about the nature of scientific knowledge, specifically quantum mechanics. Sadly, the easiest of these ("Why does a p-orbital take six electrons?") has already been answered, though I would've phrased the answer a bit differently (it's basically an issue of nomenclature-- what chemists call a "p-orbital" is really three atomic states with essentially the same energy (you're not too far wrong if you think of them as orbitals aligned along the x, y, and z-axes), each of which gets two electrons. Likewise, a "d-orbital" is five states, an "f-orbital" seven, and so on... The distinction between these states doesn't matter all that much for chemistry, but it's the stuff careers in atomic physics are made of.), leaving the difficult philosophical questions behind ("Why is angular momentum quantized in the first place?").

I haven't actually read the Feynman book in question (The Character of Physical Law), though it's on the vague list of "books I really ought to read one of these days." These philosophical and meta-physical questions also aren't the sort of thing I spend a lot of time thinking about (I subscribe to the "Shut Up and Calculate" interpretation of quantum mechanics), for the simple reason that you very quickly start banging your head against the wall. The questions are always there, though, and as Derek notes, at bottom, they all come down to "the peculiar effectiveness of mathematics." We live in a Universe that behaves (or at least appears to behave) according to very simple and elegant mathematical rules, and it's not clear why that should be.

At the level of physics where I work, there are a handful of rock-solid mathematical principles that everything else comes out of:

• Conservation of Energy: Energy is neither created nor destroyed, but only changed from one form into another. Thanks to Einstein, we can lump mass in here as well, mass and energy being interchangeable. At the end of the day, when you total up all the mass and energy you've got in whatever system you're working on, you have the same total energy you did when you started the experiment.
• Conservation of Momentum: In the absence of an external force, the total momentum of a system remains constant, though it can be redistributed among the bodies in the system. Newton's famous Laws of Motion are, in a certain sense, just a statement of the law of conservation of momentum.
• Conservation of Angular Momentum: Angular momentum, like linear momentum, remains constant unless something from outside the system acts to change it. Conservation of angular momentum is the oddest of the lot, in many ways-- it's what gives rise to the odd properties of gyroscopes, and the question about orbitals above.

Depending on how interested you are in the enumeration of rules, you can add several other rules to this list (the Second Law of Thermodynamics probably belongs, and high-energy physicists probably consider a few other conservation laws), or you can re-cast them in more formal terms (conservation of momentum is a consequence of the translational invariance of space (the structure of space-time doesn't change if you move in a straight line), conservation of angular momentum is a consequence of the rotational invariance of space), and you can even find violations of those rules on very short time scales for very small objects. You can also hand-wave your way from microscopic to microscopic versions of the rules (the angular momentum of macroscopic things is conserved, and that property has to arise from some properties of the original atoms) or vice versa (angular momentum is conserved in atoms, and thus is still conserved when you stick a whole bunch of atoms together). In the end, though, all of that just amounts to pushing the pieces of a puzzle around on the table-- you can shuffle them around all you like, but eventually, you still need to make them fit together. You're still stuck with a Universe that runs off a handful of simple mathematical rules, and you're no closer to understanding the ultimate origin of those rules.

The trivial and unhelpful answer is to invoke the Anthropic Principle in one of its many forms, which basically amounts to saying "If the Universe didn't work the way it does, we wouldn't be here to ask that question, so it doesn't matter" It's a useful way of pushing the question off, and getting it out of the way to allow yourself the room to get some work done. I suspect that, consciously or not, most scientists have a point at which they invoke the Anthropic Principle or something like it-- without it we'd get stuck on these questions forever, and all end up gibbering quietly in corners, with caring family members making sure we don't get hold of sharp objects or graph paper.

Unfortunately, I haven't heard any better answer to the fundamental question of why the Universe behaves the way it does. There's no obvious reason why the Universe has to behave in a mathematically regular way-- scientists find it very satisfying that it does (to the point that some categories of string theorists use mathematical elegance as a standard of proof), but there are other groups of people who would be happier to think that it's all Divine Providence, or invisible pink unicorns pushing objects around with their horns. There's no obvious reason why mathematical rules should work to describe the behavior of the Universe, but they do work, and they work astonishingly well. It provides a real sense of awe and wonder if you think about it a bit (though you'll go crazy if you think about it too much).

I mention this stuff to my intro classes, in passing, when I run down the conservation laws at the heart of mechanics. Mostly, I get glassy stares in response, probably the same reaction I'm getting out there in blogland. And, on some level, this really isn't material for science classes, being more the province of philosophers, or late-night dorm-room bull sessions. But it is stuff that scientists have to think about, on one level or another, and impulse to ask these questions springs from the same source that drives most of us into science in the first place.

This having been kicked off by Feynman, I should wrap it up with Feynman, in this case a famous footnote from the Feynman Lectures (by way of James Gleick's Genius):

Poets say science takes away from the beauty of the stars- mere globs of gas atoms. I, too, can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination- stuck on this carousel my little eye can catch one-million- year-old light. A vast pattern, of which I am a part.... What is the pattern, or the meaning, or the why? It does not hurt the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it.

He's talking about astrophysics there, but the same basic sentiment applies to Quantum Mechanics, and even down to the most basic level of "why does the Universe follow mathematical rules?" We're not really close to the ultimate TRVTH, if such a thing even exists, but the truth we do know is marvelous indeed.