Exploring Causal Dynamical Triangulation

[inflector]

I've read the references in Wikipedia and most of the Loll et al. papers.

At wikipedia:

http://en.wikipedia.org/wiki/Causal_dynamical_triangulation

I read:

Where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many dimensions, or minimal universes with too few, CDT avoids this problem by allowing only those configurations where cause precedes any event.

This sounds logical, but the mechanism doesn't make sense to me. For example, in the July 2008 Scientific American article:

http://www.scientificamerican.com/article.cfm?id=the-self-organizing-quantum-universe&page=3

Renate Loll says:

Euclidean quantum gravity does not build in a notion of causality. The term "Euclidean" indicates that space and time are treated equally. The universes that enter the Euclidean superposition have four spatial directions instead of the usual one of time and three of space. Because Euclidean universes have no distinct notion of time, they have no structure to put events into a specific order; people living in these universes would not have the words "cause" or "effect" in their vocabulary. Hawking and others taking this approach have said that "time is imaginary," in both a mathematical sense and a colloquial one. Their hope was that causality would emerge as a large-scale property from microscopic quantum fluctuations that individually carry no imprint of a causal structure. But the computer simulations dashed that hope.

Instead of disregarding causality when assembling individual universes and hoping for it to reappear through the collective wisdom of the superposition, we decided to incorporate the causal structure at a much earlier stage. The technical term for our method is causal dynamical triangulations. In it, we first assign each simplex an arrow of time pointing from the past to the future. Then we enforce causal gluing rules: two simplices must be glued together to keep their arrows pointing in the same direction. The simplices must share a notion of time, which unfolds steadily in the direction of these arrows and never stands still or runs backward. Space keeps its overall form as time advances; it cannot break up into disconnected pieces or create wormholes.

What I don't understand is how one can have a single-direction spacetime.

If the arrows point in the same direction or there is a one-way direction of causality, this implies to my naive brain that time would only flow in one direction in this spacetime. So I feel like I must be missing something important.

What exactly is involved in the gluing of the 4-simplices together and how do these arrows work?

Is it that the 4-simplices are supposed to represent all of space and all of time (i.e. past, present, and future)?

 

[ordered_chaos]

Causal means that that time is included in the Dynamical Triangulation.

I think the arrows of time are encoded into each simplex by a discrete time variable, t. As the simulation runs (space evolves) the simplices are glued together to create space.

Only simplices that are casually connected, i.e. a simplex with t + 0 can be glued to a simplex with t + 1.

This prevents simulation from joining pieces of space that are not in the same time slice, i.e. aren't connected casuality. So you don't have some space from the far past connected to space from the future ( a worm hole ). e.g. A simplex with t + 0 shouldn't be glued to a simplex with t - 10. You now have a worm hole or some weird spatial artifact.

How these simplexes get encoded with time is through something called "discrete time slicing". As a video game programmer, I know a lot about that, but am curious if they used the same method in their universe simulation.

Generally we just keep a global time variable and use that for figuring out casual time slices. Smolin says it's ok to do this for this type of simulation, but It feels like cheating to me cause you're not having time emerge with space. But, they are ones with the results :)