Electron estimators filled with uncertainty

In response to a recent column on the electric company, I have been besieged by questions from readers wanting to know how to tell if they are being resold the same electrons as last month. Well, OK, two people asked. But that’s a bigger response than usual, so I thought I would look into it.

It turns out that this is actually more difficult than it first appears, and it appeared plenty difficult to me at first. Electrons are pretty small. In fact, they are so small that there really isn’t any way to express their size in any terms that make sense. The classic definition of an electron is that it is “the size it would need to be for its mass to be completely due to its electrostatic potential energy.” Huh? I’m also told that’s not taking quantum mechanics into account. (Having trouble even taking into account my bank account quantity, I don’t think I’ll worry about quantum mechanics.)

The electron’s mass, its weight, is a little easier to be precise about. An electron has a mass that is said to be 1/1836th that of the proton. A proton is about one Femtometer or a one with “15 zeros-in-front-of-it-before-the-decimal” meters. An electron is less than one Attometer, which is 0.000000000000000001 meters (that’s eighteen zeros). There! Now things are so much clearer.

So just how small is an electron? Well, if we were to string electrons on a thread at the rate of one per second, for eight hours a day, every day, for 3,000 years, at minimum wage, the union would file a grievance. Even then the thread would only be about two-tenths of a millimeter long. Not taking quantum mechanics into account, of course.

There are even other problems for the electrical consumer to consider. These little electrons never sit still. Like people, different electrons have different speeds. Some electrons zip about the nucleus of their atom at 2 million meters/sec. But don’t be discouraged because the electrons moving through the wires in your house are considered slow electrons that only move at 0.024 cm/sec.

However, the biggest problem the homeowner who wants to examine his electrons will face is that if you know an electron’s position, you can’t know its direction and speed at the same time. This idea is called the Uncertainty Principle, because it’s uncertain whether it comes under science or philosophy. We’re also uncertain where the electron is or where it’s going. In 1927 Werner Heisenberg proposed his Heisenberg Uncertainty Principle, which states that it is impossible to determine simultaneously both the position and momentum of an electron, or any other particle, with any great degree of accuracy or certainty.

It’s even worse than that sounds. Electrons are so small that any effort we make to try and determine their location, speed or direction will exert sufficient force to change their position, speed or direction. This is called the Observer Effect. It is slightly different from the Heisenberg Uncertainty Principle.  But again don’t worry because the Observer Effect is only a problem for homeowners when they actually attempt to identify their electrons. The Uncertainty Principle and the Observer Effect make it impossible to be sure which electrons have been counted and which ones haven’t. This is where philosophy comes into the picture. It appears that any sincere attempt by humans to determine where they stand will almost always cause a change in where they are going.

OK, so it is practically impossible to prove if the electric companies are selling the same electrons over and over. Is this why they have apparently gotten away with it for so long? The electric field might not be a good career choice because the demand for new electrons is limited. They are all being recycled. So while you may not want to go into an electric field, you might want to buy stock in an electric company.

Gary McCallister is professor of biology at Mesa State College.


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