The Atomic Solar System or Five Things Dirac Wants You to Know About the Electron

The troubles begin in tenth grade biology. It is announced that all life and it’s diversity in the biosphere is due to variations in a DNA molecule. So what’s a “molecule?” A simple explanation is provided involving a large helix made of different colored balls, but the details are left for next year’s chemistry class. Once in chemistry class it’s revealed that molecules are the result of various atoms binding to each other in certain specific ways. So what’s an “atom?” For that we’re told to wait until physics class next year. Finally, as a senior, you know the moment of truth is at hand if for no other reason than that there are no more classes to be had. Then after months of discussing Newton’s Laws, in the last days before graduation, the teacher casually tells you atoms are miniature solar systems with a heavy, tiny nucleus sun in the center and nearly weightless electrons orbiting like planets. Mystery explained, off to graduation and a lifetime of believing in tiny atomic solar systems! As Einstein would say: “Oy vey!”

A few of us managed to stumble into university physics classes where we started hearing about how electrons were sometimes particles, sometimes waves, depending on how you interacted with them. And in atoms they were more like clouds than planets. We may have even heard they had spin, but a spin unlike anything we knew from before! But I’m willing to bet that even those of us lucky few who graduated in physics still see an atomic solar system in our mind’s eye when we hear the word “atom.” And so, for the vast majority of people, atomic solar system it is. But can we do better?

Yes and no. When quantum mechanics began in the early years of the 20th Century there was some justification early on for a solar system model. It was the very first conceptualization made by the scientists who were trying to be develop a quantitative understanding. Niels Bohr was one of the founders of quantum mechanics who was able to mathematically analyze a solar system model to made some useful predictions. This is his sketch drawn in 1910 of a hydrogen atom clearly showing a little “x” for the electron and a circular arrow for its orbit in the hydrogen atom and below the dihydrogen molecule where now the orbit circles the line connecting the two individual atoms.

But by 1925 it had become clear that little balls of negative electricity whizzing around a heavy, inert, nearly invisible, positively charged nucleus was not a sophisticated enough model to explain the intricate physics of atoms. Yet this mental image of little balls orbiting a tiny sun remains, firmly rooted in our educational consciousness ever since, to be handed down to generations of students just because it is so easy to visualize. To do better we have to read and understand the works of the great physicists like P.A.M. Dirac who finally solved the mysteries of atomic physics making it one of the most well analyzed fields of all physics.

A few years ago in an article in SIAM News recounting the life and work of Paul Dirac (SIAM News, Volume 36, Number 2, March 2003 “Spinning into Posterity,” by Dana Mackenzie) included a list, page 2, that gave the five things Dirac wants you and all posterity to know about atomic electrons. The list:

“Why Spin Does Not Equal Rotation

“Seventy-five years after Dirac’s breakthrough, nearly every popular account of electron spin still describes electrons as if they were rotating billiard balls. And they are all equally wrong. Here are five reasons that this “mental picture,” as Dirac would call it, does not conform to reality:

“Electron spin is quantized; the angular momentum of a classical billiard ball is not. Nothing can gradually “slow down” or “speed up” an electron’s spin.

“The electron’s spin “axis” is completely reassigned by any attempt to measure it. That is, a spin ½ electron will, if measured, also have spin ½ or –½ around the x-axis, spin ½ or –½ around the y-axis, and spin ½ or –½ around the z-axis. (These measurements cannot be performed simultaneously.) By contrast, a billiard ball’s axis of rotation is independent of (and may be oblique to) any axis chosen by an experimenter.

“The electron’s magnetic moment is two times too large for a spinning ball of charge. (Or its spin is two times too small for its magnetic moment.)

“If an electron were a spinning ball, the linear velocity of its surface would exceed the speed of light.

“Quantum physicists know that an electron does not orbit a nucleus in the same way a planet orbits the Sun. So why should the electron rotate like a planet?”

I think the lesson is that just because something is easy to see it is not necessarily right; and if something is complicated there must be a lot of interesting things going on!

As a post script to this blog entry one may infer from the first paragraph that one way to enhance the educational process might be to teach physics first in ninth grade, then chemistry and finally senior biology since each subject builds upon the logical foundation provided by the previous one. And this in fact is presently being proposed and debated. Check the American Association of Physics Teachers web site for “Physics First” to read about the benefits of a logical progression, the reverse of what I described above, in learning science.