Honors Theses and Capstones

Date of Award

Spring 2015

Project Type

Senior Honors Thesis

College or School




Program or Major


Degree Name

Bachelor of Science

First Advisor

David Mattingly


Attempts to formulate a quantum theory of gravity have generated many sophisticated models. Though fundamentally different, they necessarily exhibit behaviors resembling experimental observations and standard theoretical expectations. Often, their similarities go no further. However many models unexpectedly predict a change in the spectral dimension of spacetime at very small scales (See [1] and references therein for examples). In particular, some of the models predict the spectral dimension changes from 4 to 2. This paper investigates the phenomenological consequences of a toy model that use Planck-scale 2D hypersurfaces, specifically triangles, embedded in 4D Minkowski spacetime. We randomly generated sequences of triangles that a particle might traverse if the distribution of triangles were Lorentz invariant, and we find that triangles further in the sequence tend to differ from those earlier, causing the spectral dimension to grow past 4 for sequences of many triangles. In so doing, we have shown that any method which uniformly fills 4D space with connected 2D triangles with Gaussian distributed proper lengths and causal paths cannot be Lorentz invariant.

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