Surfing and the double-slit experiment
Thinking about quantum mechanics can involve a lot of cognitive dissonance. That’s because, to a large degree, no one knows what quantum mechanics means. It is formulated in terms of a series of fairly arbitrary mathematical statements, and it is left up to each person to decide what those statements mean. This can be a particularly difficult task when the statements of quantum mechanics predict something that makes seemingly no sense, like wave-particle duality. There is very often no accepted “right” way to think about a quantum-mechanical phenomenon; everyone develops their own picture of what is happening. Of course, there are plenty of wrong ways to think about quantum mechanics (people claiming that quantum mechanics guarantees limitless energy sources or mystical healing abilities, for example).
The goal of this post is to present a way of thinking about the most (in)famous quantum mechanical experiment of all: the double-slit experiment. It’s an explanation that I very much liked when I first heard it, but don’t take it too literally. I’m not claiming that this is the correct explanation of the double-slit experiment, just that it presents a satisfying way to think about it. I should also give credit to the source I learned it from: a funny little book I read as an undergraduate called The Einstein Paradox: And Other Mysteries Solved By Sherlock Holmes. Unfortunately, I can’t recommend it as a very entertaining piece of fiction, but it did have a few clever explanations.
For those who have never learned about the double-slit experiment before, I’ll summarize the main results. I’ll focus on electrons, although it can be formulated in terms of any (quantum) object: light (photons), neutrons, even entire atoms.
In the double-slit experiment, single electrons are fired toward a screen with two narrow slits cut into it. A sensitive photographic film is placed downstream of the slits, so that every time an electron hits the film a bright dot shows up. After many electrons have been fired, the experimenter looks at the film and examines the pattern of bright dots. This gives him/her information about where the electrons were most likely to hit the film.
What would you expect to happen? The most reasonable expectation would be that the electrons would fall on two narrow bands directly behind the slits. Electrons that hit the screen would be blocked from reaching the film, while those that happened to pass through the slits would continue on a straight line until they reached the film, forming a “shadow” of the screen.
(Un)fortunately, the real world can be much more surprising than our reasonable expectations. Here are actual photographic films from such a double-slit experiment. The later pictures correspond to later times. At first, when only a few electrons have hit the film, their positions seem random. But after a long time a pattern starts to develop.
The crazy, wavy pattern you see at the end is the dramatic result of the double-slit experiment. What’s more, if you block off one of the slits, the wavy pattern is destroyed, and you get a single bright strip behind the unblocked slit.
There are striking parallels here to what you would get if you did the experiment with a single-frequency light source. Light, however, is an electromagnetic wave — its electric and magnetic field can add in certain places and cancel in others, allowing for a simple explanation based on interfererence between light passing through opposite slits. An electron, however, is not an electromagnetic wave; it’s an actual physical object. Besides, there is only one electron passing through the slits at a given time. So what’s going on?
The explanations I got in my introductory quantum mechanics classes were generally very weird and unsatisfying. They were mostly along the lines of “the electron passes through both slits simultaneously and interferes with itself.” Huh? How can an electron pass through both slits simultaneously? What does it mean to “interfere with yourself”?
So here’s another way of thinking about it:
Imagine that a stationary electron is like a buoyant object floating on the surface of a body of water. The action of firing the electron creates waves on the water that propagate in the same direction as the electron itself. When the electron and its accompanying waves reach the two slits, the electron gets pushed through one of the slits as the waves pass through both slits and diffract outward. I imagine it something like this:
You can see that the waves interfere with each other as they pass through the slits, creating funny patterns. Meanwhile, the electron is riding the waves as they push it through the slits and toward the film. In other words, the electron isn’t “passing through both slits simultaneously”, it is merely “surfing” on a set of waves that forms complicated patterns as the waves pass through both slits. As a result, the electron tends to get carried to certain places more often than others, forming the wavy pattern of dots that we saw on the photographic film. If you block off one of the slits, then the waves passing through the slit form a much less complicated pattern that results in a single bright band directly behind the slit.
I thought this explanation was really cool when I first heard it. It immediately begs the question, though: what is the “lake” that the electron is floating on? There are two ways of answering that question. The first is dismissive. I would remind you that the purpose of this post was to give you an interesting way to think about the double-slit experiment, and that you shouldn’t take it too literally.
The second way to address the question is much more interesting, and unfortunately requires a very long answer that will have to wait for a later post. It involves adopting the viewpoint that the universe is somehow constructed from a “fabric” which I will call “the quantum field”. In this viewpoint, a particle is a physical defect in the field, and all forms of energy can be thought of as disruptions or “ripples” in the field that propagate through it and disturb things along the way. What we call “empty space” or “vacuum” is not an absence of the fabric (which must fill all space), but an absence of any disturbances.
It’s a strange and poetic vision, and I should remind you that it is absolutely not guaranteed to be true. But it is a view that certainly does exist among physicists, and in this particular case gives a nice way of thinking about the double-slit experiment: electrons surfing on the quantum field.