Rube Goldberg Reality

Quantum mechanics is famously unintuitive, but the most intuitive way to think about it is probably the path integral. In the path integral formulation, to find the chance a particle goes from point A to point B, you look at every path you can draw from one place to another. For each path you calculate a complex number, a “weight” for that path. Most of these weights cancel out, leaving the path the particle would travel under classical physics with the biggest contribution. They don’t perfectly cancel out, though, so the other paths still matter. In the end, the way the particle behaves depends on all of these possible paths.

If you’ve heard this story, it might make you feel like you have some intuition for how quantum physics works. With each path getting less likely as it strays from the classical, you might have a picture of a nice orderly set of options, with physicists able to pick out the chance of any given thing happening based on the path.

In a world with just one particle swimming along, this might not be too hard. But our world doesn’t run on the quantum mechanics of individual particles. It runs on quantum field theory. And there, things stop being so intuitive.

First, the paths aren’t “paths”. For particles, you can imagine something in one place, traveling along. But particles are just ripples in quantum fields, which can grow, shrink, or change. For quantum fields instead of quantum particles, the path integral isn’t a sum over paths of a single particle, but a sum over paths traveled by fields. The fields start out in some configuration (which may look like a particle at point A) and then end up in a different configuration (which may look like a particle at point B). You have to add up weights, not for every path a single particle could travel, but every different set of ways the fields could have been in between configuration A and configuration B.

More importantly, though, there is more than one field! Maybe you’ve heard about electric and magnetic fields shifting back and forth in a wave of light, one generating the other. Other fields interact like this, including the fields behind things you might think of as particles like electrons. For any two fields that can affect each other, a disturbance in one can lead to a disturbance in the other. An electromagnetic field can disturb the electron field, which can disturb the Higgs field, and so on.

The path integral formulation tells you that all of these paths matter. Not just the path of one particle or one field chugging along by itself, but the path where the electromagnetic field kicks off a Higgs field disturbance down the line, only to become a disturbance in the electromagnetic field again. Reality is all of these paths at once, a Rube Goldberg machine of a universe.

In such a universe, intuition is a fool’s errand. Mathematics fares a bit better, but is still difficult. While physicists sometimes have shortcuts, most of the time these calculations have to be done piece by piece, breaking the paths down into simpler stories that approximate the true answer.

In the path integral formulation of quantum physics, everything happens at once. And “everything” may be quite a bit larger than you expect.

Leave a comment! If it's your first time, it will go into moderation.