Sometimes a new scientific idea can be like the punch line of a very long joke: You need to keep the whole setup in mind to appreciate the humor, but it's worth the effort.
There's a fledgling idea I'm working on with physicist Lee Smolin that requires quite a setup, but it's worth it. The idea is that the flow of time comes from the way that mathematics is never complete and always gets weirder the more you understand it. That sentence should not make sense yet, but it will by the end of this column.
The first part of the setup is to recap some recent physics history. Only two theories from the 20th century have matched the results of experiments so well that they seem perfect, at least thus far. These are quantum field theory and general relativity. The annoying catch is that the two great theories conflict with each other at the margins, so they can't both be completely correct.
The obvious next step would be to craft a new theory that combines the successes of quantum field theory and general relativity but avoids the conflicts between them. Einstein and many others have searched for a theory like this. Currently, the most popular candidate is M-theory, a set of concepts derived from string theory. The second most popular is loop quantum gravity. The two theories differ in many ways, but a fundamental one is philosophical: Loop quantum gravity is more "relational" than M-theory.
A theory is relational if it's defined by the relationships among its elements rather than by how the elements fit over a background of some kind. Relativity falls into this category. An extreme object like a black hole affects not just other objects but also time and space. If you can't count on time and space to stay put, you can't describe anything according to a master framework. Relativistic objects can be described only in terms of their relationships to each other.
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Quantum field theory, on the other hand, is defined on top of a master framework, which you can imagine as graph paper, and it is superb at describing many things. For instance, in order to understand particles interacting with each other in a quantum computer, you can pretend that they are located on graph paper and safely ignore gravity and other grand-scale relativistic phenomena.
M-theory starts out from quantum field theory and tries to take in general relativity. In order to do that, it doesn't quite get rid of the graph paper, but it does have to propose fabulously complicated kinds of graph paper with curled-up hidden dimensions.
Loop quantum gravity moves in the opposite direction. It starts from general relativity and attempts to incorporate quantum field theory within a relational approach. That's a more radical idea than it sounds. In this scheme, the very essence of time and space must emerge from the relationships among multitudes of elements.
Here's a metaphor to illustrate that idea. Imagine you find yourself on a raft in the middle of an ocean on an alien planet. This planet is covered in clouds, has no magnetic field, and has a lot of suns, so it's always daytime. In short, there aren't any navigational tools.
At some point, you encounter other people floating on rafts. You tie your rafts loosely together or perhaps set up planks between them. Gradually you come upon more people drifting on rafts, and they also become attached to the group.
In the beginning, there are very few rafts, and if you want to give someone directions to get to a particular raft, you might tell them to travel over a specific sequence of intermediate rafts that have names. That would be like specifying a path to a Web page; the rafts could be understood as a network.
If the collection of rafts becomes very large, though—perhaps in the millions—the network model would no longer make sense. Instead, directions would start to sound like this: "Travel 20,000 raft-lengths toward that big mast that we use for a landmark and then turn right for 10,000 raft-lengths." Having all those rafts crammed together forces them into a persistent structure. Not only can you count on landmarks, but you can start to use geometry to describe where you are and where you want to go.
In this example, imaginary graph paper emerges out of a network of elements. Is there some analogous starting element that could act like the rafts in order to create space and time?
