The July issue of Scientific American has an interesting article on how our four-dimensional space-time could arise from basic building blocks that self-organize in a quantum superposition. Their approach, called causal dynamical triangulations, is an extension of Euclidean quantum gravity. But instead of just seeing what a superposition of self-organized building blocks that assemble arbitrarily looks like, which turns out to be a bunched up and very messy space-time with plain Euclidean quantum gravity, they imposed causality on each building block so that they can only assemble in specific ways. Their computer simulations show that the result would be a space-time that looks much like our own on large scales.

They show that at large-scales space-time should be a smooth four-dimensional space-time, but at microscopic scales the dimension of space-time shrinks down to two, which is a concept I have difficulty wrapping my head around. The concept of dimension they used is the spectral dimension, which is determined by how fast something spreads over time. For integer values of the spectral dimension I think I can understand how it relates to the more conventional notion of dimension (the number of values necessary to locate something uniquely), but fractional values of the spectral dimension is rather hard to understand.

And if the theory is correct, then the built-in causality would imply that wormholes and time travel would not be possible. While it’s cool that ordinary space-time could be built from first principles, it would be a bummer in that faster-than-light travel or direct observation of historical events would not be possible.

Causal dynamical triangulations is an interesting approach, independent from string theory, which shows promise given their simulation results. It’s also nice to see that string theory has not completely monopolized theoretical physics, despite the lack of any experimental predictions or confirmation. While I don’t think that string theory is a dead end, I do like to see a more balanced allocation of resources to alternatives, considering that all of the current theories of quantum gravity are somewhat lacking in experimental support. I also have to admit that I find background-independent theories, where space-time itself arises from the laws of physics instead of being a pre-defined background, more aesthetically pleasing in a philosophical sense.

Some of the questions I have about causal dynamical triangulations are:

With space-time being built out of basic building blocks, do these constitute a sort of “aether” which defines an absolute space-time? What happens to Lorentz invariance?

Do the simulations only show an empty vacuum universe, or does it reduce to the theory of general relativity in the classical limit?

Would the incorporation of causality in the building blocks imply a built-in arrow of time in the laws of physics?

And some questions that they still need to figure out:

Is there a fundamental building block to space-time, or is space-time infinitely divisible?

Would it have implications for the origin of the universe?

Are there any feasible experimental predictions that would differentiate causal dynamical triangulations from other theories?