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Thursday, March 20, 2008

Epicycles & Electrons Part I

A long time ago, the scientist Ptolemy was trying to understand why the planets move the way they do. He knew that things in the sky orbited around the Earth, basically. And he knew that things in the sky moved in circles. However, his observation of the planets did not match with the idea of an Earth in the center with orbiting bodies above. So, he figured out that the planets must be riding on disks that rotate, with the center of the disks rotating on the main disk holding the earth. These were epicycles that allowed Ptolemy to have his observations and at the same time keep his immutable principles. More here.

Not quite so long ago, the scientist Bohr was trying to understand the nature of matter. He hypothesized that atoms were made up of descrete subatomic particles. One of these were electrons, which orbited a nucleus. The Bohr model of the atom is the model that the non-scientists in the room know. More here & here.

The trick is both guys were wrong. Sure, in both cases the hypothesis had some support from observation. But an electron is not a ball bearing spinning around a center. Here's a bit from Wikipedia that matches my limited knowledge of physics:
According to quantum mechanics, electrons can be represented by wavefunctions, from which a calculated probabilistic electron density can be determined. The orbital of each electron in an atom can be described by a wavefunction. Based on the Heisenberg uncertainty principle, the exact momentum and position of the actual electron cannot be simultaneously determined. This is a limitation which, in this instance, simply states that the more accurately we know a particle's position, the less accurately we can know its momentum, and vice versa.
The curious thing is that Bohr's model is/was very helpful. It furthered human understanding of the natural world, while Ptolemy's was not helpful. It hindered movement toward the more accurate description of the natural world. Was there a fundamental difference in their methods?

4 comments:

Josh Gentry said...

No model is perfect. No representation of a thing is the thing. All of physics is modeling the cosmos. The models vary in accuracy, but are all ultimately inaccurate. Still, they are useful.

Is a model's worth based on its usefulness? Is usefulness directly related to accuracy?

JimII said...

In this case, I'm suggesting that a useful model furthers our understanding of the natural universe. That is not the only thing models are good for. Ptolemy's epicylces and Kepler's magic triangles are both very good an predicting the position of planets in the night sky. And in that sense, they are useful models.

But, coming from the perspective of understanding the universe, it seems to me epicycles were a road block while electrons were a step up. I guess I should have asked first if folks agree with that.

Matt Dick said...

Jim,

I think the major difference in the Ptolemy and Bohr models is the principle of parsimony.

Ptolemy had this idea that preserved his notion of the Universe, but which relied on an explanation that did not conform to the best available evidence. Epicycles were a way to get around a simple interpretation of observation.

Bohr hypothesized a model that, while wrong, fit the best available evidence. He could still have given us an understanding that might have set us back, but if you have to place your best on those hypotheses that are wrong, choosing the parsimonious explanation has been proven to get you where you need to be more often than a more complicated one.

So partly it is luck, but as luck favors the prepared mind, so does she favor the judicious use of Occam's Razor.

Josh, I think a model's worth is exactly its usefulness. At least in science. An inaccurate model can teach us things, so it can be valuable. Usefulness is not directly related to accuracy, but an accurate model is almost always more useful than an inaccurate one when you need to further science. If you want to give the public an adequate working knowledge of the physical world, that's another matter. Accuracy will sometimes get in the way, if by accuracy you mean a perfect description of the natural world.

As an example, Newton's model was not as much inaccurate as it was incomplete. Its accuracy confined itself to a range of values of forces, sizes and speeds. As such it was and is enormously useful. Probably, in allowing most of the things that contribute to today's quality of life for most people, it is the most useful model of the physical world we have. Einstein's general relativity was both more accurate and less useful to quality of life for humans. Einstein's model was both more accurate and more useful to furthering humanity's understanding of the natural world. Newton's was probably also a necessary step, which means its usefulness is 100%.

Those are my musings.

JimII said...

Only because I sensed your use was very precise I looked this up:

parsimony n. Adoption of the simplest assumption in the formulation of a theory or in the interpretation of data, especially in accordance with the rule of Ockham's razor.

I'll have to chew on this a bit. You are suggesting that Bohr's model had at its heart to be simpliest explanation of the data, while Ptolemy's model, had at its heart to be the explanation of the data that conformed with his set of requirements.

Okay. Interesting. Good.