Why do we live in a universe with three spatial and one time dimensions - 3 + 1, as cosmologists would say? Why exactly this combination, and not 4 + 2 or 2 + 1? Over the past decade, physicists have explored this question many times, contemplating other universes with different properties in order to understand whether complex life could exist in them or not. And they inevitably came to the conclusion that it could not exist in a universe with four spatial dimensions or two temporal ones. So humans will inevitably end up (and end up) in a 3 + 1 universe.
This is the anthropic argument: the idea that the universe must have the properties necessary for the survival of observers.
What does a two-dimensional universe look like?
But what about simpler universes like 2 + 1? Physicists theorized that the two dimensions of space may not provide enough complexity to support life. They also believe that gravity will not work in two dimensions, so objects such as the solar system cannot form. But is it really so?
James Scargill of the University of California at Davis, contrary to all expectations, showed that a 2 + 1-dimensional universe could support both gravity and complex life. His work undermines the anthropic argument for cosmologists and philosophers, who will have to look for another reason why the universe takes the form it takes.
First, a little background. One of the great scientific mysteries is why the laws of physics seem to be sharpened (or fine-tuned) for life. For example, the numerical value of the fine structure constant seems arbitrary (about 1/137), and yet various physicists have pointed out that if it were even slightly different, atoms and more complex objects could not have formed. In such a universe, life would be impossible.
The anthropic approach is that if the fine structure constant took on any other value, there would be no observers who could measure it. This is why it has the value that we measure!
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In the 1990s, Max Tegmark, now a physicist at the Massachusetts Institute of Technology, developed a similar argument for the number of dimensions of the universe. He argued that if there were more than one time dimension, the laws of physics would not have the properties that observers need to predict. This would definitely rule out the existence of physicists and possibly life itself.
Now let's move on to the properties of universes with four spatial dimensions. In such a space, Newton's laws of motion would be very sensitive to tiny perturbations. One consequence of this is that stable orbits could not form, so there would be no solar systems or other similar structures. “In a space with more than three dimensions, there can be no traditional atoms and possibly stable structures,” says Tegmark.
Thus, conditions for life seem unlikely in universes with more dimensions than ours. But the argument is that universes with fewer dimensions are less secure.
There is an opinion that the general theory of relativity does not work in two dimensions, therefore there can be no gravity.
But James Scargill thinks differently. In his paper, he shows that a much simpler, purely scalar gravitational field can be possible in two dimensions, and this would allow for stable orbits and intelligent cosmology. It remains only to show how complexity can arise in 2 + 1 dimensions. Scargill approaches this problem in terms of neural networks. He points out that the complexity of biological neural networks can be characterized by various special properties that any 2D system must reproduce.
Among them is the "small world" property, a communication model that allows you to traverse a complex network in a few small steps. Another property of brain networks is that they operate in a mode that is delicately balanced between the transition from high activity to low activity - criticality mode. This also only appears to be possible in networks with a modular hierarchy, in which small subnets are combined into larger networks.
The question Scargill asks is whether there are any 2D networks that have all of these features - small world properties, modular hierarchy, and critical behavior.
At first, this seems unlikely, because in 2D graphs, nodes are connected through edges that intersect each other. But Scargill shows that 2D meshes can indeed be built in a modular fashion and that these graphs have certain small-world properties.
He also shows that these networks can operate at a transition point between two behaviors, thus demonstrating criticality. And this is an amazing result, which suggests that 2D networks can indeed support surprisingly complex behavior. Of course, this doesn't prove that the 2 + 1 universe can actually support life. It will take more work to find out for sure.