The Quantum Theory of Zurich Train Station

Anyone writing about quantum theory will probably use the word ‘weird’ at least once. It’s a struggle to explain quantum effects without making them seem strange and magical.

This is not a good way to help the public understand what we scientists are doing. Even worse, it makes it seem like we don’t understand ourselves. But we do. Honest!

The problem that there isn’t a lot of everyday parallels to quantum phenomena. If walking into walls occasionally resulted in you teleporting to the other side, the effect of quantum tunnelling would be pretty intuitive. But it doesn’t, and it isn’t.

This article won’t try and explain any quantum stuff. Instead I’ll try to give you an idea how we scientists can claim to understand it, despite the fact that it is so undeniably odd.

In many ways, quantum physics is like ShopVille, the shopping center underneath Zurich train station. In theory, it can be described completely by this map.

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It’s not too complex a map. There’s basically only one level, and it’s just a few rectangles stuck together. Everyone knows rectangles.

In practice, things aren’t so easy. Walk around in this monstrosity and you’ll find that it is a maze beyond understanding. It is a puzzle with no hope of solution. Shops seem to scurry about when you aren’t looking. No path will ever lead the same way twice. You may think that you have a good sense of direction. But your hard worn intuition won’t help you here. Space and time lose their meaning once you descend beneath the train tracks.

How can it be so complex? How can this map accurately capture such a labyrinthine nightmare? Is it lying to us, trying to tempt us into the realm of the Minotaur while we wait for our train?

It turns out it isn’t lying. Some experimentation will confirm that it’s actually true. Shops always seem to be where the map says they are. A route planned using the map will always get you where you want to go. It seems impossible that such a simple abstract description can explain such a seemingly complex thing. But somehow it does.

That’s what it’s like for quantum mechanics. The theory is just a few equations. They aren’t even that complex. Maths teachers taunt their students with far worse. But combinations of these equations allow us to describe pretty much everything: light and matter, electrons and cats. Solving them allows us to know what will happen in any situation. And experiments always prove them right.

Even so, try to explain what happens without using the equations and you’ll soon run into trouble. English is a language developed for complaining about the French. It struggles to cope with the non-local and non-contextual correlations that quantum particles love to play with. It makes them seem like magic, but they aren’t like that at all.

Magic may come from some inscrutable source, but it effects that are always easy to explain. Spells in Harry Potter just move objects, make things and hurt people. They don’t violate Bell inequalities or simulate impossible universes. Magic does normal things in extraordinary ways. Quantum mechanics is quite the opposite.

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