The Quantum
of Charge

Michele Diego

A man with a box, two plates, and some oil can reach and touch the abyss of the infinitely small, measuring with the naked eye something that it is already difficult to imagine.

I don’t know if it happens to you too, but I often think back to the years at University remembering classes, professors, the most difficult exams, and the funniest scenes. However, sometimes something goes missing: the name of a professor, the grade of an exam, a question during an oral test. I will never forget when I helped replicate the “oil drop experiment”; in which Robert A. Millikan measured the electrical charge of an electron, in the early ‘900. At the time, I was a freshman and I wandered around the Physics department with the apprehension of who was unsure of being worthy of the path he has chosen. One day, while I was walking from one classroom to another, I was dragged into a lab by a friend who was ahead of me in the course. He remembered that my passion for physics came from small experiments (maybe I would be more honest by calling them games) with electromagnetism that I had fun doing at home using batteries, magnets, and the powder from a printer toner. Anyway, he thought of including me in the group with his colleagues, while they were busy replicating Millikan’s experiment. So, we can say, this represents the first real physics experiment in which I took part, and the memory of the day I experienced firsthand the simplicity of a genius idea.

This experiment represents a true conquest made by human intellect over Nature. With it, Millikan and, generally speaking, humanity, was able to measure the minimum and naturally fundamental charge, one of the electrons – a particle so small that it is still considered as a single dot. «He who has seen that experiment, and hundreds of investigators have observed it, has literally seen the electron» Millikan himself, after being awarded the Nobel prize, said in his speech. The beauty and the simplicity of the experiment are not the only reasons for which the experiment is so famous. There is a controversy that brings a shadow on Millikan’s scientific integrity during the measurements. Indeed, reading through the scientist’s private notes, we find out that he had conducted the experiment with the goal of obtaining exactly what he was looking for.
So, there are two sides to the experiment: its indisputable beauty and the conduct of who conceived it, that still divide scientists today.

Let’s begin with understanding in simple words how this experiment works. Imagine, in front of us, a box of the dimension of a dollhouse. Inside, instead of the rooms, there are two horizontal plates (one on top and one below) connected to a tension generator, in such a way that we can generate a vertical magnetic field. On one side of the box, there is a small hole in which we can spray some drops of nebulized oil. In order to ionize the droplets, meaning to make them have an electrical charge, we use an X-ray source. Finally, on the front wall of the box, we have a small window through which we can see with the naked eye what happens on the inside and, in particular, the movement of the oil droplets.

Now let’s begin the experiment. The electric field is off. What will an oil drop do once it has entered the hole in the box? It will fall below, like anything else on Earth. And what happens when we turn on the electric field? It will act on the droplet’s charge, pushing it upwards and contrasting its fall. It is Newton’s principle: F = ma; the sum of forces acting on the particle that determines its acceleration. And which are the forces acting on the single drop? Gravity, which pushes it downwards; the force generated by the electric field, which depends on the charge of the drop itself and pushes it upwards; lastly the force of air resistance, which will slow the fall down .
Millikan, timing how much the drops took to fall, turning the electric field on and off, was able to measure the electric charge of the single oil drops. Once he had measured many electric charges of countless drops, he realized that they were all multiples of an elementary charge. This elementary charge had to be the smallest in absolute, the charge of a single electron.

Let’s now get to the controversy on Millikan’s conduct. Opening his experimental diary, where every scientist keeps track of any progress made by their research, we find some suspicious notes. In addition to the classic notes typical of any scientist (lab temperature, pressure, electric fields, etc.), there are others such as «Beauty, publish», «Best yet, beauty, publish», «Almost perfectly exact», «Very low, something wrong: not sure of distance». But what does “almost perfectly exact” or “very low” mean when compared to a quantity that we do not know? It almost seems as if he had discarded the results that he did not like while keeping the those consistent with his idea. To be kind to a scientist who was undoubtedly a genius and winner of a Nobel prize, we can say that he was meticulously searching for possible causes of measurements he considered wrong, not equally considering the ones he considered correct. This inevitably introduced a bias in his observations.
The critiques of his conduct are still there. On one hand, there is who really thinks that there was bad faith in his work. On the other hand, we find those who consider his notes too partial for a final judgment, and it could be that they were referring to a study that was preliminary to the one which was published. Then, there are those who claim that an expert scientist is called to judge their ongoing experiment and it is normal that they discard certain measurements; and that the power of science is the following: the possibility for everyone to replicate the experiment and verify its reproducibility.

In any case, the goal of this article is certainly not to put an end to the discussion on Millikan’s experiment. For now, we can be satisfied with getting to know his story, learning its simplicity and beauty, to remember how a man with a box, two plates, and some oil can reach and touch the abyss of the infinitely small, measuring with the naked eye something that it is already difficult to imagine.


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