We live in (or at least, perceive, with various branches of string theory including up to 26 dimensions) a universe with three dimensions (plus time), and there are reasons to suspect why we find ourselves in a 3D world.
Scientists and mathematicians have suggested universes with more than three dimensions would be unpredictable and unstable “dead worlds” devoid of all life and observers. The three body problem is unpredictable in a 3D world, but even a two body problem – describing and predicting the orbit of two bodies – becomes too chaotic in higher dimensions, and no stable orbits are possible.
“This means that such a world cannot contain any objects that are stable over time,” one paper on the topic explains, “and thus probably cannot contain stable observers”.
“In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures,” the paper adds.
As such, we should not be surprised that we find ourselves in a 3D (plus time) universe – you can only live in universes where life is possible. There are suggestions that life could not take place in a 2D (plus time) universe, meanwhile, because of insufficient complexity. The main argument, which would make 2D universes a non-starter, is that two-dimensional universes would not allow for gravity, making the complex mix required for life impossible.
But that may not be the case, according to physicist James Scargill. In a 2020 paper, Scargill showed that scalar gravitational fields could exist in two dimensions.
“I have presented a purely scalar theory of gravity which allows stable orbits around point sources, and has a not-obviously-fatal (though unusual) cosmology; it could potentially be improved by making the whole metric dynamical,” Scargill writes in the paper. “One could also imagine a brane-world scenario in which the massless graviton is not localized to the brane, thus allowing two-dimensional life to enjoy fully four-dimensional gravity.”
Gravity and stable orbits are not the only requirements for life – or, more important when you are using anthropic reasoning to explain why we are in a 3D universe, for observers to exist. For instance, you could not have a digestive tract in an animal (at least not the kind we are used to) as it would split the organism in two.
Scargill went on to look at whether a 2D universe (again, plus time) would be sufficiently complex to allow for complex life. In the paper, he looked at biological networks and created planar graphs which “seem to exhibit many of the properties which have been conjectured to be important for complex brains.”
This, he writes, is suggestive that complex brains could exist in two dimensions, though more work would be needed to compare the planar graphs to real-world neural networks.
“In particular, they are approximately ‘small-world,’” he added, “they have a hierarchical and modular construction, and they show evidence of the stretching (in parameter space) of a critical point into a finite critical region for certain stochastic processes.”
This is, of course, highly hypothetical, and more of a thought exercise than saying life in 2D universes is real. But it puts a bit of a constraint on arguments that we experience a 3D world because it is the only type that could sustain life, because – perhaps – life in 2D could be possible as well.
The paper is published in Physical Research Review.
Dr. Thomas Hughes is a UK-based scientist and science communicator who makes complex topics accessible to readers. His articles explore breakthroughs in various scientific disciplines, from space exploration to cutting-edge research.
