Honors Theses and Capstones
Date of Award
Spring 2015
Project Type
Senior Honors Thesis
College or School
CEPS
Department
Physics
Program or Major
Physics
Degree Name
Bachelor of Science
First Advisor
David Mattingly
Abstract
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.
Recommended Citation
Greene, Patrick A., "Phenomenology of a Toy Model Inspired by the Spontaneous Reduction of the Spectral Dimension in Quantum Gravity" (2015). Honors Theses and Capstones. 317.
https://scholars.unh.edu/honors/317
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