Welcome to Quantum Magazine's podcast.

Each episode we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

Over the past century, quantum field theory has proved to be the single most sweeping

and successful physical theory ever invented. It's an umbrella term that encompasses many

specific quantum field theories, the way shape covers specific examples like the square and

the circle.

Quantum field theory is incomplete, but can mathematics solve the mystery?

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The most prominent of the quantum field theories is known as the standard model.

It's this framework of physics that's been so successful.

David Tong, a physicist at the University of Cambridge, says quantum field theory can explain...

Everything. Just literally everything. I know at the fundamental level, every single experiment that we've ever done in a way that's just deeply distressing, because we really want this theory to be wrong so we can understand what lies beyond it, but that's just not happening. But more than that, you know, physics is a reductionist science. And so quantum field theory is the right description at the fundamental level, but from that we then

get the other layers, not always with all the details filled in, but from quantum field theory,

we understand classical field theory, how it emerges, Maxwell's equations, how quantum mechanics

emerges.

But quantum field theory, or QFT, is indisputably incomplete. Neither physicists nor mathematicians know exactly what makes a

quantum field theory a quantum field theory. They have glimpses of the full picture,

but they can't yet make it out. Mathematics, which requires internal consistency and attention to every last

...