That sounds encouraging, but we already knew that space-time should be 4D. Does CDT make any predictions?

It does! We predicted that if you zoom in far enough, space-time loses its 4D nature. To see it, you have to study another sort of dimension, the dimension revealed by diffusion. For example, an ink drop spreads differently on a 2D page than it does in a 3D water glass, so by looking at diffusion you can get a sense of what sort of space you’re in.

Here, we found a remarkable result. When we simulated the release of an ink drop in our 4D universe, it spread out as if it were stuck in a roughly 2D space — although only for a few instants. Once it has time to spread out further, it spreads in a normal fashion.

But it’s not like it’s literally spreading through a flat sheet. It’s more as if the quantum structure of space-time over very short distances is fractal-like. That is, the space is fully filled in, but it’s wired up in such a way that certain parts of it aren’t initially as accessible as other parts. Here we have a microstructure that has a quantum imprint, but if you zoom out, everything looks fine and 4D. Hooray!

It’s funny, actually. I initially had to convince my collaborators this could be a potentially important result, and now it’s our most cited paper.

Is that a prediction you could hope to test in reality?

It’s a genuine quantum signature, but we don’t yet know where, if anywhere, we could observe it.

There is a colossal gap between the tiny distances of the Planck scale, where the quantum nature of space-time is expected to become obvious, and the scale we can access in experiments. What’s our best bet of finding places where tiny effects get blown up large enough for giants like us to detect? It’s probably astrophysics, and we’re working out what the consequences of CDT there might be too.

If CDT has had some success in calculating features that seem to match our universe, why do you think the quantum gravity community hasn’t embraced the method?

One aspect that has always been difficult to sell is the idea that you need to employ numerical methods to understand quantum gravity. Classical general relativity is a beautiful theory. The equations you write down have a complicated but compact form. People are spoiled by the mathematical beauty and being able to do some simple things analytically.

But realistically, if you want to describe situations where gravity is strong, you can’t do it with simple equations. Numerical methods, like our triangulations, serve as a sanity check for quantum gravity models.