Functional General Relativity in Scheme

Bryan Newbold, bnewbold@mit.edu
http://web.mit.edu/bnewbold/thesis/

Title: A Compuational Elucidation of Curved Spacetime
Advisor: Prof. Gerald Sussman, EECS
Year: 2009

The old version of this page is here, outlining what kind of projects I was interested in.

Quick Links

Schedule

My course schedule etc can be found at bnewbold.net/cal.

When What to do
Jan 16-22 Self teach some more scheme and differential geometry, documenting examples. Maybe work through 2 or 3 problems from SICM textbook or implement some classic physics problems (eg current through wire cross section, variational principle examples in Feynman lectures, derivation of magnetism at the 8.022 level).
Understand and document scmutils package and compiler interactions (at least conceptually).
If I'm going to put mit-scheme in sage, this is the time to do it, after this point I shouldn't be focusing on the software tools as much.
Jan 19-26? Work through "Functional Differential Geometry", writing out examples by hand
Jan 31 By this date have a proposed outline with length estimates so I can sanity check with somebody in the physics department.
Feb 28? Have something resembling a draft and be working out details, getting comments from professors and other students. At least one interesting application should be demonstrated.
March 23-27 Spring break week
May 8 Final due to department (non-doctoral degree)

Journal Entries

References

Summary/Abstract

from proposal:

I propose to implement a geometric formulation of curved space time in a functional computer programming language, and to explore the space of simulations and manipulations made possible by such a formulation. A primary motivation is to state the foundations of General Relativity in a non-ambiguous manner.

This work follows several attempts to formulate curved spacetime on computers for the purpose of numerical calculations and algebraic manipulation. Most of these packages are specially designed for the tasks of tensor analysis and/or efficient numerical calculation, as is appropriate for use in calculations. A crucial difference of this proposed work will be to carefully build up the geometric and analytical tools in a general purpose functional programing language (mit-scheme). As a learning and reference tool, this will allow users to explore the inner workings and structure of the system, which I believe is essential to understanding the system as a whole.

The frame field representation will be used to emphasize the geometric properties of curved space time, as opposed to the more traditional coordinate heavy tensor analysis approach.

The resulting work will include a full implementation with source code and documentation, as well as example problems and qualitative comparisons with existing packages and software systems.