There’s a hole at the heart of quantum physics.
It’s a deep hole. Yet it’s not a hole that prevents the theory from working. Quantum physics is, by any measure, astonishingly successful. It’s the theory that underpins nearly all of modern technology, from the silicon chips buried in your phone to the LEDs in its screen, from the nuclear hearts of the most distant space probes to the lasers in the supermarket checkout scanner. It explains why the sun shines and how your eyes can see. Quantum physics works.
Yet the hole remains: Despite the wild success of the theory, we don’t really understand what it says about the world around us. The mathematics of the theory makes incredibly accurate predictions about the outcomes of experiments and natural phenomena. In order to do that so well, the theory must have captured some essential and profound truth about the nature of the world around us. Yet there’s a great deal of disagreement over what the theory says about reality — or even whether it says anything at all about it.
Even the simplest possible things become difficult to decipher in quantum physics. Say you want to describe the position of a single tiny object — the location of just one electron, the simplest subatomic particle we know of. There are three dimensions, so you might expect that you need three numbers to describe the electron’s location. This is certainly true in everyday life: If you want to know where I am, you need to know my latitude, my longitude, and how high above the ground I am. But in quantum physics, it turns out three numbers isn’t enough. Instead, you need an infinity of numbers, scattered across all of space, just to describe the position of a single electron.
This infinite collection of numbers is called a “wave function,” because these numbers scattered across space usually change smoothly, undulating like a wave. There’s a beautiful equation that describes how wave functions wave about through space, called the Schrödinger equation (after Erwin Schrödinger, the Austrian physicist who first discovered it in 1925). Wave functions mostly obey the Schrödinger equation the same way a falling rock obeys Newton’s laws of motion: It’s something like a law of nature. And as laws of nature go, it’s a pretty simple one, though it can look mathematically forbidding at first.
Yet despite the simplicity and beauty of the Schrödinger equation, wave functions are pretty weird. Why would you need so much information — an infinity of numbers scattered across all of space — just to describe the position of a single object? Maybe this means that the electron is smeared out somehow. But as it turns out, that’s not true. When you actually look for the electron, it shows up in only one spot. And when you do find the electron, something even stranger happens: The electron’s wave function temporarily stops obeying the Schrödinger equation. Instead, it “collapses,” with all of its infinity of numbers turning to zero except in the place where you found the electron.
So what are wave functions? And why do they only obey the Schrödinger equation sometimes? Specifically, why do they only obey the Schrödinger equation when nobody is looking? These unanswered questions circumscribe the hole at the heart of quantum physics. The last question, in particular, is notorious enough that it has been given a special name: the “measurement problem.”
The measurement problem seems like it should stop quantum physics in its tracks. What does “looking” or “measurement” mean? There’s no generally agreed-upon answer to this. And that means, in turn, that we don’t really know when the Schrödinger equation applies and when it doesn’t. And if we don’t know that — if we don’t know when to use this law and when instead to put it aside — how can we use the theory at all?
The pragmatic answer is that when we physicists do quantum physics, we tend to think of it only as the physics of the ultra-tiny. We usually assume that the Schrödinger equation doesn’t really apply to sufficiently large objects — objects like tables and chairs and humans, the things in our everyday lives. Instead, as a practical matter, we assume that those objects obey the classical physics of Isaac Newton, and that the Schrödinger equation stops applying when one of these objects interacts with something from the quantum world of the small. This works well enough to get the right answer in most cases. But almost no physicists truly believe this is how the world actually works. Experiments over the past few decades have shown that quantum physics applies to larger and larger objects, and at this point few doubt that it applies to objects of all sizes. Indeed, quantum physics is routinely and successfully used to describe the largest thing there is — the universe itself — in the well-established field of physical cosmology.