Tim Minella '09 (Kennett Square, Pa.) studied loop quantum gravity (LQG) this summer under the advisement of Associate Professor of Physics Seth Major. According to LQG, which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity, the basic structure of space turns out to be made up of small discrete units of volume. This means that space cannot exist in any smaller quantity than these quantized volumes, which are as small compared to a proton (one of the subatomic particles that make up atoms) as a proton is to us. Physicists represent these fundamental units of space as a network of interconnected loops, hence the name of the theory.
Minella's research utilized a computer program developed by Shawn McGovern '07 that models space and the discrete units or "loops" comprising it in two dimensions. Each loop was represented by a triangle and space was represented by a finite sized grid or lattice of these triangles. The edges of the triangles were assigned a certain value (called their "color"), which determined the area of the surface of discrete space they represented. Furthermore, these edges could not converge at vertices to form the triangles unless certain rules were satisfied and they met in a certain way. (It is important to note that the edges used by the program have no physical reality. They simply were used by the program to define the dimensions of the discrete units.)
For his project, Minella would create a lattice of triangles of some size in which all the rules were satisfied. He then added to or subtracted from the edge colors. If the rules were violated due to this change, the program would automatically fix the violation by altering the color of the other edges in the triangle. Since the triangles were arranged in a lattice and each edge belonged to more than one triangle, changing the value of an edge in one triangle would inevitably cause a rules violation in neighboring triangles. Thus, an avalanche of color change propagated throughout the lattice until all the rule violations were resolved.
The program's ability to evolve on its own in response to the outside tuning of its initial parameters is called self-organized criticality, and it was this property that Minella studied over the summer. He measured and recorded the size of the avalanches caused by certain color changes and the number of times a particularly sized avalanche occurred. In general, small magnitude avalanches occurred more frequently than large magnitude ones. This data was then used to construct a logarithmic graph of the avalanche size versus frequency. Theoretically, the graph should be linear with a drop off corresponding to the inherent restrictions of a finite sized lattice. Minella said his summer was spent fining tuning the program, gathering enough data to construct a suitable graph, modifying the way in which he changes edge color, and fixing problems.
Minella is a government major and physics minor. He is vice president of the College Republicans and a member of the Ski Team. This was his first summer of research at Hamilton.
-- by Nick Berry '09
Minella's research utilized a computer program developed by Shawn McGovern '07 that models space and the discrete units or "loops" comprising it in two dimensions. Each loop was represented by a triangle and space was represented by a finite sized grid or lattice of these triangles. The edges of the triangles were assigned a certain value (called their "color"), which determined the area of the surface of discrete space they represented. Furthermore, these edges could not converge at vertices to form the triangles unless certain rules were satisfied and they met in a certain way. (It is important to note that the edges used by the program have no physical reality. They simply were used by the program to define the dimensions of the discrete units.)
For his project, Minella would create a lattice of triangles of some size in which all the rules were satisfied. He then added to or subtracted from the edge colors. If the rules were violated due to this change, the program would automatically fix the violation by altering the color of the other edges in the triangle. Since the triangles were arranged in a lattice and each edge belonged to more than one triangle, changing the value of an edge in one triangle would inevitably cause a rules violation in neighboring triangles. Thus, an avalanche of color change propagated throughout the lattice until all the rule violations were resolved.
The program's ability to evolve on its own in response to the outside tuning of its initial parameters is called self-organized criticality, and it was this property that Minella studied over the summer. He measured and recorded the size of the avalanches caused by certain color changes and the number of times a particularly sized avalanche occurred. In general, small magnitude avalanches occurred more frequently than large magnitude ones. This data was then used to construct a logarithmic graph of the avalanche size versus frequency. Theoretically, the graph should be linear with a drop off corresponding to the inherent restrictions of a finite sized lattice. Minella said his summer was spent fining tuning the program, gathering enough data to construct a suitable graph, modifying the way in which he changes edge color, and fixing problems.
Minella is a government major and physics minor. He is vice president of the College Republicans and a member of the Ski Team. This was his first summer of research at Hamilton.
-- by Nick Berry '09
