Causal sets as discrete spacetime and their spectral dimension

Vejleder: Astrid Eichhorn

Projektbeskrivelse

This bachelor thesis builds on the knowledge of flat spacetime, e.g. from the course on Electrodynamics FY549 and Classical Mechanics FY546, where Special Relativity was introduced.
At the same time, it links to an active research area in theoretical physics, which is causal set theory.

1. The first goal is to understand how a causal set can be obtained from Minkowski spacetime by the so-called sprinkling process, where spacetime points are distributed at random and so-called links between them are inferred from the causal relations. Causal sets related to Minkowski spacetime (which are called sprinklings) will be constructed explicitly using Mathematica.
2.  The diffusion equation will be reviewed and how it allows to measure the dimension of the underlying structure that the diffusion process is happening on. The solution of the diffusion equation in the continuum will be reviewed. Then, a diffusion process on a regular lattice will be set up and it will be reviewed how the regular lattice shows a decrease in dimensionality compared to the continuum.
3. A diffusion process on a causal set will be set up, and it will be reviewed how the discreteness of a causal set leads to an increase of the dimensionality compared to the continuum.