Posts Tagged ‘causal dynamical triangulation’

A Little Background

May 25, 2012 9 comments

In this blog, we’ve talked a lot about particles, relativity, quantum mechanics, and even the reason for the universe itself. One important topic that I haven’t yet covered is spacetime. Where does it come from and why does it take the form that it does? Any Grand Unified Theory that we’d like to propose can’t just satisfy itself with describing the matter and energy that makes up the things we see. It also has to explain how the gaps between the things come to be there. In other words, it needs to be ‘background independent‘.

This feature has also been conspicuously absent from all of the research I’ve shared so far. In each case I’ve outlined, I’ve simulated space by sprinkling dots onto a preexisting smooth surface and hooking them up to those nearby. This isn’t good enough. In fact, it’s avoiding one of the hardest problems of the lot, and the physics community know this. If you look at any of the most promising research on discrete approaches, the main focus is on the structure of spacetime itself and how it changes. From that, it’s felt, everything else can spring.

People have had mixed success in this regard. There’s loop quantum gravity, which has been a relatively successful physical theory. However, at least as I understand it, it presupposes structures that have the four dimensions of spacetime we expect.

There’s the theory of causal sets, which starts with nothing but the idea of a partial order, and which can derive something roughly spacetime-like from it. However, reconciling it with quantum mechanics has proven tricky.

Then there’s causal dynamical triangulation, which has successfully assembled spacetime-like structures out of very simple raw ingredients. However, those ingredients once again have an implicit four-dimensionality built in at the smallest scales.

Do I have a model of spacetime to share with you that’s better than any of these? No. Categorically not. As with all of my research, I’m deliberately not trying to do physics directly. Instead, my goal is simply to illustrate ways that discrete techniques might make solving thorny physics problems easier, and to add to the theoretical toolkit with tricks from computer science.

What I do have is a way of building large, irregular networks from scratch that behave like smooth spatial surfaces, while using no geometrical information whatsoever. I’m going to share it with you over a sequence of posts. You’ll have to assess for yourselves whether you think it’s a good fit for nature.

As a starting point, let’s look at a simplified version of the problem. We’ll forget about time, and concentrate on only a single dimension of space.

Imagine you have fifty friends who you’re playing a party game with. The aim is to use your cellphones to form an invisible circle. When the circle is finished, you’ll be able to call Alice. Alice will then able to call Bob. Bob can call Cindy, and so on. At the end of the chain, Zachary can call you and tell you what message he received. The message will have gone through everyone in turn.

Each person is allowed to store the numbers of up to two friends on his phone. They can swap their numbers for others by calling one of their contacts and saying ‘who do you know?’ and picking which numbers to keep or discard. They can also say to someone, ‘you’re my friend now’. They can’t say anything else, or rank the contacts they receive by name or number.

At the start of the game, the numbers in everyone’s phones are random. How do they organize themselves into a chain?

As party organizer, you have one extra perk you can use if you want to. You can add people to the party one at a time if you like. If you decide to do that, people will receive their random phone numbers when they join, and the numbers they receive will always be for people who’re already at the party.

Any ideas?