What Does Causal Really Mean in CDT (Causal Dynamical Triangulation) Quantum Gravity?

  1. 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:

    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:

    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)?
     
  2. jcsd
  3. Re: What Does Causal Really Mean in CDT (Causal Dynamical Triangulation) Quantum Grav

    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 spacial 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 :)
     
    Last edited: Sep 16, 2010
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