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

Interests and Objectives

My strongest interests are in the foundational and frontier areas of physics (especially the issues connecting these two subjects), and in the role that new mathematical tools and frameworks can play in furthering developments in these areas. These days I am delving into the many and varied approaches to quantum gravity, including Machian principles and the possible contributions of noncommutative geometry. 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.

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.
  • Taking small breaks from school, or using the breaks that I am given, to do sustained research with other workers in these fields.
  • By June 2010, obtaining both a B.Sc. in mathematics and a M.Sc. 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

  • I am a third-year undergraduate student at Caltech:
    • I am taking a high-caliber course load, focused on theoretical physics, advanced mathematics, and including some forays into the areas of foundational mathematics (model theory et. al.) and theoretical computer science.
    • See my transcript for details.
    • 3.6 GPA
  • Attended the Perimeter Institute's Quantum Foundations Summer School.

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.
  • Independent textbook reading has given me a detailed view of advanced quantum mechanics, quantum field theory, introductory string- and superstring-theory, elementary particle physics, Bohm–de Broglie hidden variable theories, and general relativity (with the associated mathematical methods).
  • I have a qualitative grasp of the subjects of category theory, quantum information and computability theory, 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#, Java, LaTeX; some experience with IDL
  • Software Experience: Mathematica, Reduce, Visual Studio, Linux, Windows
  • 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. One specific example is the simulation of relativistic de Broglie–Bohm trajectories mentioned below.
  • 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.

Summer 2008 Self- and Guided-Study

During the summer of 2008, I stayed at Caltech with a stack of textbooks and arXiv preprints. I knew that I really wanted to do research in quantum gravity—and I wanted to do it sometime soon, instead of after the many years it would take to acquire proficiency in the requisite concepts via classes. So, I spent three months studying various textbooks on quantum field theory and general relativity, all the while reading arXiv papers that caught my fancy and playing with concepts and ideas as they came to me. Eventually I was able to graduate to arXiv review articles, thus gaining a broad—if necessarily shallow—view of the various quantum gravity research programs.

Near the end of the summer, in search of something more concrete, I spent a month working through Zwiebach's A First Course in String Theory with Professor Mark Wise. I gave biweekly “lectures” from notes I took covering the material from the textbook, so as to introduce us both to string theory. By the end, we had covered Zwiebach's approximate construction of the Standard Model on intersecting D6-branes (chapter 15); I have since continued my reading of the text.

Finally, at the beginning of the school year, I missed my first week of classes in favor of attending a Perimeter Institute conference titled “The Clock and the Quantum: Time in Quantum Foundations.” This was great fun; many of the talks were very interesting, and I connected with a variety of researchers in the field. It also spawned several new research ideas which I have had little time to pursue since, but do manage to play around with when my homework is sufficiently beaten back.

Winter 2008 Machian Quantum Gravity Research

As a result of my interactions at the aforementioned conference, I was invited by Julian Barbour to come work on his research project, which he titles Machian quantum gravity. In addition to Julian Barbour, I worked with Anne Franzen, Ward Struyve, and Hans Westman. Our focus was on the problems of quantizing reparameterization-invariant theories, and the role of time in such a process; some of these issues are explored in Julian's paper with Brendan Foster. We also investigated the possibilities for using the methods of Machian quantum gravity to produce a timeless de Broglie–Bohm theory.

I came away from this research with a great appreciation for Julian's work, and a deeper understanding of the role of time in quantum gravity. This has led to ongoing correspondence and spawned several future research ideas, which may be put in place this upcoming summer (see below).

Upcoming Summer 2009 Caltech Summer Undergraduate Research Fellowship

For summer 2009, I have applied for a Caltech Summer Undergraduate Research Fellowship under Professor Matilde Marcolli, whose class The Geometry and Arithmetic of Quantum Fields I took during Fall term 2008. My proposal, titled Quantum Gravity via Noncommutative Geometry, is available for perusal.

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.