Thoughts for the week, July 16

My actual PhD work is coming along slowly but steadily. I've briefly mentioned my general area of study, which is General Relativity(GR) and, in particular, an approach to Quantum Gravity known as Causal Dynamic Triangulations (CDT). I've thought of writing something about this, but I can do no better than the explanation of the subject at The Physics Mill. There's a lot of good stuff over there and Jonah, the author, is much further along this area of study than I am (I do not know him in any world, real or virtual).

I can, however, explain a little bit of what I'm trying to do or, at least, what my professor has me working on at present. The idea is that, according to a proposed model of spacetime, we can have an elementary "cell" that divides into other spacetime cells, and those cells each divide as well, and so on. Each cell is a tiny, four-dimensional spacetime pyramid called a simplex. The way to keep track of the divisions is to keep track of the vertices, which is a lot easier, since each vertex is just a point. Simplex division in this case follows a specific set of rules: for example, the distance between any two vertices has to be greater than or equal to a minimum length, \(l\). This is the consequence of insisting that spacetime be quantized, which is the whole point of what CDT is about: we want to get tiny, indivisible chunks of spacetime that, when seen from far away, look like the smooth, continuous spacetime that GR describes.

My job, then, is to use computational methods to put a specific model of CDT to the test. The paper that outlines this model, sadly, is behind a paywall, but related papers on the physics arxiv are here and here. Anyway, here is a preliminary result:

I know, I know, it's not very impressive—but it took hours and hours of coding! An obvious remark would be that this is only a three dimensional spacetime, since that's what can be plotted in an image. This 3-D version of spacetime is a proxy for the real, 4-D thing that can't be visualized. The radius of the sphere that contains the vertices increases by a magnitude equal to the minimum length \(l\) at each step, and each step is a quantum "tick" of time. The mechanism by which the points divide is by "mating" with other points according to a specific operation and generating a new point at the new radius. All points mate with all other points, and the resulting points are located on the next sphere. This creates an enormous number of points that can't possibly fit on the surface of the sphere and maintain the condition that the distance between them is at least \(l\), so points are eliminated one by one until this condition is met (you can see the number of points in each stage at the top of the figure).

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On completely different topics, this has been a tumultuous week. There was the attack in Nice, France, and the attempted military coup in Turkey. I wish I could write about these events, but I'm still overwhelmed by the amount of information to be digested in order to write something worth reading.