What "simple" means to a physicist, and to everyone else

Every now and again, I like to share an email that is really interesting, but not quite right for the column. I got a question the other day which brought to mind my next book on Symmetry. A reader named Pierre asked:

When reading about collapsing the function of a wave regarding photons passing through slips, from what i got, the wave becomes a particle. It seems our models in physics have a lot of quirks and counter-intuitive notion once we get into quantum mechanics.

Is that world really that weird, or perhaps are they artifacts of a very elaborate model,with great predictive value, but which doesn’t represent the reality?
My best analogy would be, are we advancing in the “Ptolemaic system” of physics with epicycles and all other weird things?

Yes, the world really seems to be that weird. There’s a lot of talk about various interpretations of quantum mechanics but in the end, whether you believe in a Copenhagen or Bohmian or Many Worlds interpretation, to a physicist, the actual mechanics behind quantum mechanics is simple enough — elegant enough, even — and accurate enough that we’re relatively convinced that it’s a good description of the physical world. It’s kind of interesting how physicists (or mathematicians) view the concept of “simple” compared to normal people.

Take quantum mechanics, for example. Quantum mechanics predicts all sorts of very strange things. Light, for example, behaves like both a particle (the photon) and a wave (interference patterns) depending on the circumstances. We can do all sorts of weird tricks to make photons or electrons switch from wave-like or particle-like behavior. From a philosophical perspective, this is incredibly complicated.

Honestly, the math is a little hairy, too. We regularly teach classical mechanics to college freshpeople and even high school students, including parabolic motions and circular orbits, but we almost never teach quantum mechanics. But really, the laws of quantum mechanics (the Schroedinger wave equation) is almost laughably simple to write down, even if the math required to solve anything is very tough.

The Ptolemaic system, on the other hand, is just about an inelegant (and ultimately wrong) as you can get. For those of you who are unfamiliar, Ptolemy’s idea was that the earth is at the center of the solar system, and every planet and the sun orbit the earth in a circular pattern, with an additional circular orbit — an “epicycle” — added to it. The little figure up at the top should help you out. The orbit and epicycle were unique for each planet, and there was nothing which told you in advance how any given one was supposed to behave. If a new planet were to be discovered, for example, Ptolemy wouldn’t be able to tell you the orbital properties. This is the sort of model that I (and Occam) find objectionable. There are just way too many knobs and levers.

On the other hand, if you give me a new particle and tell me the mass, I can tell you just about everything about how it behaves quantum mechanically. And what’s more, observationally and experimentally, quantum mechanics has passed countless tests on countless systems to something like 10 significant digits. It has literally never failed.

Ptolemy’s system only could be measured against the solar system, and ultimately it failed even here. It wasn’t prepared to deal with Tycho Brahe’s much more precise measurements (used by Kepler) that ultimately showed that planets moved on an ellipse around the sun, and not circles (as previous believers in heliocentric models had supposed).

The cool thing is that even though elliptical orbits seem more complex, in the light of Newton’s law of gravity, it’s actually much, much simpler. Starting from the assumption that gravity obeys an inverse square law, and that the force of gravity is toward the sun, everything else falls into place. You just have to know a crap-ton of math (most of which Newton had to invent himself) in order to make it happen.

Cooler still, is the fact that even the inverse square law doesn’t have to be put in by hand. It’s actually a consequence of simple laws of symmetry (namely that gravity is the same in all directions), and the fact that we live in a 3-dimensional universe.

I think there is a perception that “complicated” means difficult, but that’s not what it means at all. It’s not simple to predict how planets will orbit, but once you understand the symmetry principle, the result is inevitable.
It’s amazing how many of the seemingly complicated phenomena in the universe are due to simple symmetries. In fact, as near as we can tell, all of them are. That’s kind of why I’m writing a book on it.


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