Quantum Gravity Student Projects

Student Projects:

I have divided the projects into two categories, related to quantum gravity and not related. Some are appropriate for summer research work and others others I would like to confine to the academic year. I have added a parenthetical note indicating which is which. (Of course, the summer projects might very well extend beyond the summer as Senior Projects or independent research projects.)

Many of you have asked about required background. Generally, the more the better although only a few of the projects listed below specifically require upper-level math or physics skills. If they do, I list the necessary skills at the end. All of these projects are accessible to undergraduates.

In Quantum Gravity

Analyzing Methods of Quantization: In lQG a variety of novel techniques are used to quantize general relativity in the new variables, e.g. the choice of configuration space and "Thiemann's trick". This projects examines these techniques in simple, and well-known, quantum systems including the harmonic oscillator, a particle in a constant gravitational field, and the hydrogen atom. A good project for someone who has had 290 and is comfortable with ordinary and partial differential equations. (summer)
Toy Dynamics on Graphs: One of the concerns about the current form of the dynamics on lQG is that it appears to be ultra-local; there do not appear to be long range forces like gravity. One framework to study these is a simple 2D network and simple dynamical evolution rules. The project requires implementing these rules numerically and testing the results to look for long range effects, perhaps through self-organized criticality. Sean McGovern has made a great deal of progress. Check out his abstract on the students page. References: Borissov and Gupta Phys. Rev. D 60 (1999) 024002, Ansari and Smolin hep-th/0412307, (summer/computational fluency)
Modified Dispersion Relations: In special relativity energy and momenta are related via a "dispersion relation" E^2 = p^2 +m^2. Effects from a discrete spacetime geometry may affect this relation and effectively break Lorentz invariance. Jacobson, liberati, and Mattingly (JLM) have carefully investigated bounds on the extent of cubic modifications. This project reviews the current status of these constraints. References: JLM e.g. astro-ph/0505267 , Konopka and Major New J. Phys 4 (2002) 57.
Discrete Machian Model (DMM): I have a new model of discrete geometry phenomenology which combines "Machian effects" due to inhomogeneities in the distribution of matter and a model of discrete space. These projects will help determine whether the model is viable:
- Constraints from clock comparison experiments.(summer)
- The Pioneer effect and DMM.(summer)

In other areas:

Field lines Don't work!? There are claims, for instance in Am. J. Phys., that field lines do not work so that it is not possible to represent the electric or magnetic fields with field lines such as we plot in 195 and 295. This may be a bit uncomfortable for someone working in lQG in which the gravitational field (geometry) is represented as "field lines". Are there fundamental reasons why field lines do not accurately represent the continuum field configuration? Tunring this question on its head, if the continuum is an approximation, are there (observable) consequences of field line representations? (summer or academic year)
Why Vote?: The US has one of the most unstable voting systems in the world (see papers and books by Saari). Inspired by the 2000 presidental election debacle I wrote an op-ed peice suggesting that since there is always uncertainty in measurements, it makes sense to measure (i.e. vote) again. What is the proper role of uncertainty in voting systems? [academic year or Levitt Fellow summer work (applications due in mid-Feb)]
Random Numbers: Create and test a random number generator with a laser and a warm beverage. See me if you are curious. (academic year/lab skills)
Network Dimension: If someone hands you a network or graph, how do you determine its dimension? Or, in what dimension space could you put it? Places to start might be Hausdorf dimension or spectral dimension. (academic year)
Foucault Pendulum: We have a wonderful new Atrium. Let's build a working Foucault Pendulum for it! Josh has constructed the first version. Help us construct the second. We need work on the mount and the driving mechanism. This can be combined with Toy Week in 350. (academic year)
Magnetic Levitation: We also have many nice display cases. Wouldn't a magnetically suspended spinning top be intriguing? (academic year)
The Double Pendulum is a conservative system that displays chaos. It would be great to have a demo for a display case. (academic year)