Two physicists are sitting in wooden chairs at a table in a cafe, drinking coffee from plain white porcelain cups. One says to the other, “Do you believe in electrons?”
The physicist is not asking “Do you believe electrons exist?” He believes that they exist. He believes that she believes they exist as well, although that existence is contingent. The modern idea of the electron wasn’t formulated until the 19th century, and it is possible that some future theory of physics will banish the concept. Still at the moment the physicist finds the case for electrons convincing. The mathematical formalism that describes them makes sense. (It hangs together.) He has personally manipulated laboratory equipment whose behavior becomes explicable if you hypothesize that it is measuring electrons. He has heard good-faith reports from many other scientists and engineers about how the notion of electrons has helped them structure their conception of the natural world and build useful devices. If that’s not the scientific definition of existing, he doesn’t know what is.
Still, when he tries to imagine what an electron is, he finds himself stuck. What comes to mind? Maybe a set of equations in a book. Or facts about an electron: its mass and charge. But surely these are just descriptions of electrons and not the electrons themselves. He might imagine relevant readings off laboratory equipment—deflected voltmeter needles, blurs on photographic plates. But these aren’t the electrons themselves either. It is merely evidence of their existence: convincing but still indirect. The physicist decides he’s overthinking it and tries free association: he says the word “electron” to himself and makes note of the first image that comes to mind. It is a drawing of a cluster of little spheres stuck together representing protons and neutrons. Other spheres representing electrons orbit this nucleus. You can tell that they are orbiting because there are elliptical lines tracing out the orbital paths.
This is an illustration of the “solar system” model of the atom proposed by the Danish physicist Niels Bohr. The Bohr model is wrong. In the course of orbiting the electrons would radiate away energy, causing the atoms to collapse. Bohr himself was aware of this, nevertheless his model served as a stopgap that physicists made do with in the 1920s and 30s until quantum theory came up with a more convincing account of atomic structure. Even as a representation of the Bohr model of the atom, the picture is wrong: the size of the electron orbits is completely out of proportion to the size of the individual particles. And yet the physicist doesn’t feel foolish for having this image in his head. There are reasons to recommend it. It does, for instance, capture the idea that protons, neutrons and electrons combine to form atoms, with protons and neutrons bound tightly to one other while the electrons surround them in some way. A picture more in line with contemporary quantum physics would replace the image of a solar system with a series of blobby, dumbbell-shaped electron orbitals, but even those are just handy visualizations of equations that describe electrons. They are no less cartoons.
Still these are cartoons of whole atoms. What about the electrons themselves? Physics admits the idea of a free electron. What image does the physicist the free-associate for that? Probably, he reluctantly admits, just a sphere. Were he in charge of producing the artwork for a science textbook, he’d represent a lone electron as a little ball. It would be textureless, featureless, and a solid color. Its diameter would likely be no more than what could contain a short printed word. (He would not have a sphere representing an electron take up half a page, though in an astronomy textbook he might do so for a sphere representing a planet. Why? Because electrons are small and planets are big, though both are so out of proportion to the size of a book the distinction doesn’t make much sense.) Finally, in order to convey a three-dimensional sense, he’d probably put a dot of light on one part of the sphere, as if the electron were being illuminated by a desk lamp just off to the right.
This is all tremendously unsatisfying. The illustration of the Bohr model, inaccurate as it was, still had structure corresponding to features of actual atoms. Here there is no such correspondence. It is meaningless to talk about an electron’s texture, color, or shape. That dot of light makes absolutely no sense: the phenomenon of illumination is the result of collisions between vast numbers of individual photons and individual electrons. An electron can no more be illuminated than a single person can band together to form a mob. You can make a case for representing electrons as spheres rather than, say, cubes because some of their properties (mass and charge, for instance) do exhibit spherical symmetry, but that’s where the verisimilitude ends. The cartoon of a single electron says more about the nature of cartooning than the entity it is supposed to depict.
In asking “Do you believe in electrons?” what the physicist really means is “Isn’t it strange that you and I are both convinced of the existence of things that we are incapable of imagining?” His use of the phrase “believe in” is a little joke, intentionally evoking the question “Do you believe in God?” He’s not asking if the other physicist believes electrons exist by virtue of a leap of faith. (The goal of science is to obviate, or at least drastically minimize, such leaps.) But a religious person asked to free-associate an image with the word God might come up with something (a giant man with a long white beard and booming voice, perhaps) they would similarly dismiss as cartoonish and inadequate. In both cases people are willing to attribute existence to things their brains are literally not equipped to handle.
The other physicist considers the question for a moment then replies, “I believe in electrons as much as I believe in these chairs or this coffee cup.” This is her way of affirming that, yes, indeed she does believe that electrons exist. But she is making a little joke as well, because no one talks like that, at least not typically. To say that you believe in something is to affirm its existence appearances to the contrary. To admit that there is an extra burden on you, the believer, to establish its reality, whether by scientific theory, faith, or some other means. No such burden exists when discussing the chair you are sitting in, or a coffee cup you are holding. There the presumption is that these things exist. This existence is contingent as well. It may be the case that one of the physicists is actually dreaming, or that they are both just figments of a computer simulation. Maybe the physical reality of the coffee cup is so far removed from our subjective perception of it that the correspondence between them is unclear. There are many ways of casting doubt—of compelling us to say about an object in front of us that we believe in it rather than it simply is. But those ways all take a fair amount of mental gymnastics, about as much as it takes to believe in an electron that we cannot visualize. So the other physicists’ joke is this: “You have now ceased to talk about physics and begun to talk about philosophy.”
Once you are willing to perform the mental gymnastics of philosophy, you find yourself casting all manner of fundamental beliefs and sensations into doubt. This can create a sense of vertigo that leads to you want to restore certainty—to get back to the point where simple things simply are. It would be nice if physics could help with this. It does after all tell us things about the fundamental nature of coffee cups and chairs. For instance it tells us that they are made in large part out of electrons, and this has tremendous explanatory power. It illuminates much of how the world hangs together, but is ultimately no antidote for philosophical vertigo, because the scientific entities that explain the daily phenomena can never appear more real to us than the daily phenomena themselves. You start with the coffee cup and you go from there.