string theory and other pleasant diversions
Symmetry factors are often confusing, and existing calculation techniques seem to involve excessive drawings and computations. My personal technique is simple: For example, this diagram has , since we can interchange and at the same time, and get the same diagram (assuming the endpoints are fixed). This one has , coming from With a bit Continue reading "Symmetry factor of Feynman diagrams"
You re an astronaut at a space station orbiting a black hole. You are assigned to fly a shuttle near the black hole and take some measurements. You are very careful to keep track of your position and not cross the invisible event horizon that marks the edge of the black hole, as you know that Continue reading "How to escape a black hole: adventures in causal structure"
Like every adult male entering his thirties, I had recently developed an interest in military history, so what better way to spend a Saturday than at the local Midway Museum, the dubiously self-proclaimed #1 attraction in San Diego. Besides the endless labyrinth of tiny hallways and crew quarters, perhaps the most interesting exhibit was the Continue reading "Magnetic-core memory, Faraday s Law…
Inspired by the classic: A Brief, Incomplete, and Mostly Wrong History of Programming Languages. BASIC: 10 PRINT "HELLO WORLD"; 20 GOTO 10 is the only BASIC program ever written. C: Invented by Alan Turing as a precursor to the Turing Machine. C++: Invented to give employment to C++ Standard Committee members. CSS: The CSS standard Continue reading "Programming languages summarized in one line"
This post explains quantum mechanics (QM) without any advanced math. Unlike most introductions, I will focus on the interpretation of QM: what the objects in the theory mean and how they fit into a broader philosophy of doing physics. Specifically, I explain why the Von Neumann-Wigner interpretation, a variant of the standard Copenhagen interpretation, is Continue reading "Quantum mechanics for…
A recent HN post reminded me of Newcomb s paradox, which goes as follows (from Wiki): There is a reliable predictor, another player, and two boxes designated A and B. The player is given a choice between taking only box B, or taking both boxes A and B. The player knows the following: Box A is Continue reading "Solving Newcomb s paradox for classical and quantum predictors"
Despite its simplicity, classical mechanics is not taught well in the typical physics curriculum. This is unfortunate because the general philosophy of constructing Lagrangians based on symmetries underlies all of modern physics. In this article, I explain basic Lagrangian mechanics in a systematic way starting from fundamental physical principles. It basically follows Landau and Lifshitz Continue…
Here are some physics textbooks that I ve read over the years. Each textbook is rated from 1-5 Diracs () on quality for self-study. Most topics are divided into (basic) and (advanced). Tips for self-study: Shorter is better when it comes to textbooks. The problem with self-study is missing the forest for the trees. Most textbooks Continue reading "Physics textbooks for self-study"
Gravity has often been called a gauge theory of the Poincaré or Lorentz group. Here, I develop general relativity in direct analogy to Yang-Mills theory, avoiding geometry entirely1. None of this is original, but I have tried to simplify the presentation compared to the literature, where the similarities and differences between the two theories are Continue reading "Notes on gravity as a gauge…
After being a strong believer in the many-worlds interpretation of quantum mechanics for years, I have now completely changed my mind. Many-worlds is seriously flawed, and the good old Copenhagen interpretation is not so bad. Specifically, the correct interpretation of quantum mechanics is the Von Neumann-Wigner interpretation, a flavor of Copenhagen that puts the Heisenberg Continue reading…