work MSC #240, Caltech
Pasadena, CA 91126-0240
United States

Interests and Objectives

My strongest interests lay in the foundational and frontier areas of physics—and especially the issues connecting them. This summer I am delving into quantum gravity, including the mathematical and physical theories required to understand it; this area is full of fascinating theories with a lot of enjoyable complexity. In the past I have also spent time in quantum foundations. Tangentially, I enjoy working in mathematical logic, although my career will probably not take me in this direction.

Currently Pondering

  • Naive attempts at embedding quantum field theory in a general-relativitistic framework
  • Formulations of quantum theory in geometric language
  • Renormalization, and analogous techniques in other areas that help me make sense of it

Currently Reading Up On

  • Quantum field theory, in several mathematical formulations
  • Topology (point–set, algebraic, geometric)
  • Differential geometry
  • Noncommutative geometry
  • Spinors and twistors
  • Representation theory, Lie groups, and spin networks

Currently On-Hold

  • Comparative axiomatizations of quantum mechanics
  • The role of quantum information and quantum computing in our understanding of quantum theory
  • Quantum paradoxes, especially those framed in terms of weak measurements and retrocausality
  • Formally axiomatizing physics in general (and possibly the necessary metaphysics), and the consequent role of Gödelization
  • The ultimate role of de Broglie–Bohm theories, in light of their integration with quantum field theory

Concrete Goals

At this time, I hope to pursue these interests by…

  • Continuing my coursework in order to get a solid understanding of basic undergraduate concepts.
  • Leaving myself enough free time so that I can pursue interests far beyond the undergraduate curriculum, albeit with a more conceptual and less problem-based focus.
  • Spending my upcoming summers doing research in both my areas of interest (per the above), and related areas that I might not understand the attraction of until I try them.
  • By June 2010, obtaining a B.Sc. in mathematics and possibly a Masters in physics at Caltech, setting myself up for a career as a mathematical physicist.
  • In the long term, earning an appointment at a theory-focused research institute aligned with my interests.

Education

Formal

Informal

  • Extensive and ongoing reading of textbooks and arXiv papers in mathematics, physics, and cosmology. I am currently alternating between several books on topology and several others on quantum field theory, while attempting to keep up with gr-qc, hep-th, and quant-ph on the arXiv.org preprint archive. For fun, I read and ponder Aharonov and Rohrlich’s Quantum Paradoxes.
  • Already, independent textbook reading has given me a detailed view of advanced quantum mechanics, (some) quantum field theory, elementary particle physics, Bohm–de Broglie hidden variable theories, the role of abstract algebra in physics, and general relativity (with the associated mathematical methods).
  • I have a qualitative grasp of the subjects of category theory, quantum information and computability theory, classical Hamiltonian/Lagrangian mechanics, canonical quantum gravity, some of the geometrical foundations of loop quantum gravity, and the causal sets program. I feel that I can at least follow talks and other somewhat-quantitative arguments in these areas.

Skills

  • Languages: written extensively in C, C++, C#, LaTeX; some experience with IDL
  • Software Experience: Mathematica, Reduce, Linux, Windows, Visual Studio
  • General Programming: in industry, in research, and for fun, I have spent a lot of time programming complex applications of many different types; I feel confident in being able to take on any programming assignment.
  • Simulation and Modeling: for both fun projects and for research or exploration purposes, I have written several numerical simulations of physical systems, usually with Mathematica but sometimes with C-based languages.
  • Teaching and Presentation: I have spent a lot of time tutoring and also more formally teaching other students, and have given several talks on various subjects in physics and mathematics.

Research Experience

Summer 2007 Perimeter Institute Research

The following is an edited version of a report I submitted to the Perimeter Institute administrators on the work I did under the supervision of Samuel Colin and Ward Struyve in the area of de Broglie–Bohm hidden variable theory.

We started out by looking into Ward and Samuel's Dirac sea pilot-wave model for quantum field theory, with the intention of attempting to introduce basic interactions into a course-grained version that would help show that it reproduced quantum predictions. After that began to look intractable, we became interested in Bohmian trajectories for the Dirac-sea particles. I worked through the results algebraically, and wrote up a Mathematica simulation using this knowledge. The simulation provided some very interesting results, the most intriguing of which was that the particles in the Dirac sea appear to have zero velocity. This was verified analytically for small numbers of particles, and we are currently attempting to prove it for the general case.

In addition, Ward gave me an interesting project to work on while we were stuck on the aforementioned proof. He showed me a pilot-wave quantum field theory model by Holland that used a trio of angles at each point [parameterizing SU(2)] to create a fermionic pilot-wave quantum field theory. Holland's model was formulated in momentum space, which provides no usable ontology; associating a trio of angles to each possible momenta is not something one can readily make sense out of in terms of the actual world. My task was to reformulate it in position space. I did so, producing a continuity equation for the position-space model. Once that was finished we determined that we needed to see if the position-space model reproduced quantum predictions. Although there were some interesting results, such as indicating that this trio of angles had one orientation for particle-filled lattice sites and another for vacuum lattice sites, in the end the fact that particle states were so sparse in a typical macroscopic system made it clear that two macroscopic states would not be distinguishable unless they were each much larger than the visible universe, which is quite unrealistic. Thus, we gave up on the position-space translation of Holland's model.

With regards to publications, we are hoping to publish one on the analysis of trajectories in the Dirac sea pilot-wave model of Ward and Samuel. This is still work in progress. The result so far obtained on Holland's model should also appear in a paper. However, because of the nature of the result, it is as yet unclear whether it should be included in Ward's paper, or whether it should be published separately. This will in part depend on the results that related avenues lead to.

To model the Bohmian trajectories of the Dirac sea particles, I implemented a portion of the formalism of quantum field theory in Mathematica. With the relativistic Bohmian guidance equation (as per Ward and Samuel’s paper), Mathematica’s native numerical differential equation solving capabilities allowed us to plot the trajectories of any finite set of particles, specifying arbitrary initial positions, momenta, and spins.

Work Experience

The details on my work experience can be found in my programming résumé. One thing to note, however, is that while in industry I worked extensively with and on multiple teams across departments, both on projects that required collaboration and projects that required synthesizing the requirements of multiple groups. In general, I enjoy working in a team, whether for a programming project or for one in research.