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This page is for my research and other work at Smith College. I have another website that blatantly promotes my textbook "Mathematical Methods for Engineers and Physicists" as well as my other writings, and those of my brother Kenny Felder.
Much of my research deals with the very early universe. Almost all models of the early universe are based on the theory of inflation, which describes the evolution of the universe during its first fraction of a second (roughly 10^-31 seconds in the simplest version of the theory). While the general predictions of inflation have been well-tested, many of the details of the model are still poorly understood, mostly because we don't have a good theory of fundamental physics at such high energies.
I work on a variety of problems involved in understanding how the universe got from this early state to the state we see it in today. How did all the particles and fields around today get produced? How would the evolution of the early universe be different if we're really living in more than three dimensions (as many modern theories claim)? Can theories like supersymmetry and string theory be tested in the early universe?
While this sounds highly technical, many of these problems could be (and have been) approached by an undergraduates with an interest in learning cosmology. Much of my work involves running computer simulations of the early universe to test the effects of different models.
My other research interests include numerical simulations more generally (wave propagation in the sun, phase transitions in field theory, ...) and the development of computer and written tools for teaching physics concepts.
There's room in my research program for students in physics, computer science, or anyone interested in these areas. No background in cosmology or numerical simulations is necessary. Feel free to come talk to me.
LATTICEEASY: Working together with Igor Tkachev of CERN, I developed a C++ program for doing lattice simulations of interacting scalar fields. We have used this program for a number of research projects in early-universe cosmology. In August of 2000 we made the program freely available on the Web under the name LATTICEEASY. The LATTICEEASY home page has the program and documentation. In November 2007 I released CLUSTEREASY, a parallel computing version of LATTICEEASY.
FFTEASY: In May of 2000 I wrote a series of C functions for calculating Fast Fourier Transforms of real or complex data in any number of dimensions. For more information or to download the functions see my FFTEASY page."
CurvedLand: Stephanie Erickson and I developed a mapping program to illustrate curved geometry. You can place objects and navigate around them like you would in a mapping program like MapQuest or Google Maps, but as you move the objects around you appear to move in curved paths because of the geometry of the space.
Science for the General Public
One of my hobbies is writing papers on scientific topics. These papers should be accessible to people with no math or science background, although I like to think they might also be interesting to some people in those fields. All of these papers are hosted on the Math and Physics Help Home Page maintained by my brother, who has many more papers of his own there. Alternatively, you can jump directly to any of my papers from here:
The Expanding Universe
This paper is an introduction the the big bang model of the universe, including what it means to say the universe is expanding and what we mean by "The Big Bang."
Beyond the Big Bang: Inflation and the Very Early Universe
This paper discusses some of the problems with the standard big bang model and how cosmologists have solved these problems with a theory known as "inflation." As the paper explains, inflation doesn't replace the big bang model but rather supplements it.
Quantum Mechanics: The Young Double-Slit Experiment
My brother Kenny Felder and I co-authored this paper, which introduces the basic concepts of quantum mechanics. We use for illustration the famous double-slit experiment, which shows how matter acts both like particles and like waves.
Quantum Mechanics: What Do You Do with a Wavefunction?
Another collaboration with my brother, this paper is the only one in the bunch that requires a physics background. This paper is designed for people who are taking or have taken a course in quantum mechanics and want some help pulling all the ideas and the math together to see the big picture.
Spooky Action at a Distance: An Explanation of Bell's Theorem
This paper outlines Bell's proof that the experimental results of quantum mechanics can only occur if particles can instantly affect each other at large distances. As with all these papers, no math or science background is necessary.
Things Fall Apart: An Introduction to Entropy
Everyone from physics students to readers of popular science literature has heard that entropy is a measure of disorder and that it always increases in the universe. In this paper I explain what entropy is and why it always increases. Put another way, this paper explains why some processes in nature are irreversible.
Bumps and Wiggles: An Introduction to General Relativity
As the title suggests, this paper introduces some of the basic ideas of Einstein's General Theory of Relativity: curved spacetimes, black holes and more. This one might be best read after my brother's paper on special relativity.
Curriculum Vita (PDF)