Recent Posts
- The Eddington Luminosity in Spherical Accretion and Beyond
- How a Molecular Cloud Collapses Into a Star
- Why $R_{\mu\nu}=0$ does not imply $R_{\mu\nu\rho\sigma}=0$
- Derivation of the Cosmic-Ray Diffusion Coefficient from Pitch-Angle Scattering
- The rubber sheet gets the geometry right and the mechanism wrong!
Category Archives: Expository
The Eddington Luminosity in Spherical Accretion and Beyond
The Eddington luminosity is the point at which the radiation coming out of an object pushes on the surrounding gas as hard as the object’s gravity pulls it in. Above that luminosity, material near the source is pushed away instead … Continue reading
How a Molecular Cloud Collapses Into a Star
Making a star means compressing gas by something like twenty-four orders of magnitude. The warm neutral interstellar medium, the ordinary atomic gas between the stars, holds roughly a third of a hydrogen atom per cubic centimetre at a temperature of … Continue reading
Why $R_{\mu\nu}=0$ does not imply $R_{\mu\nu\rho\sigma}=0$
Almost everyone makes this mistake once, and it’s a good one to make. You learn the Einstein field equations. You learn that in vacuum, with no matter and no energy and no cosmological constant, they collapse down to something very … Continue reading
Derivation of the Cosmic-Ray Diffusion Coefficient from Pitch-Angle Scattering
Cosmic rays arrive at Earth from every direction almost perfectly evenly, to about one part in a thousand. That’s a disaster if you wanted to know where they came from, because they’re charged and the Galaxy is magnetised, so whatever … Continue reading
Posted in Expository, Projects, Research
Tagged astronomy, Astrophysics, Mathematical Physics, physics, science, theoretical physics
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The rubber sheet gets the geometry right and the mechanism wrong!
You have seen this demonstration. Somebody stretches a rubber sheet over a frame, drops a bowling ball in the middle, and the sheet sags. Then they roll a marble across it and the marble curves toward the bowling ball, maybe … Continue reading
Posted in Diary, Expository, Notes, Scratch essays
Tagged Astrophysics, debunking, equivalence principle, general relativity, Geodesics, gravitational waves, gravity, manifolds, Mathematical Physics, philosophy of science, physics, Schwarzschild metric, science, science writing, spacetime, spacetime curvature, theoretical physics
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What are Quarternions?
I used to think complex numbers were the end of the line. You start with counting, patch in zero and the negatives, then the fractions, then the irrationals to fill the gaps between them, and finally you throw in $i$ … Continue reading
So, what is a vector?
In my first year of undergraduate physics, one of my professors walked into the lecture hall, placed his notes on the desk, looked around the room, and asked a question that, at first, seemed almost too easy. “What is a … Continue reading
Posted in Expository
Tagged classical mechanics, Math, Mathematical Physics, motion, What Is...
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Deriving the Euler–Lagrange Equation for Particles, Fields, and Curved Spacetime
A good way to understand the laws of motion is not to memorize a separate equation for each situation, but to notice there is really only one trick, and every equation of motion is what falls out when you apply … Continue reading
So what are tensors, really?
I want to start with a confession. When I first heard the word “tensor,” I assumed it was one of those words that exists to make physicists sound clever. Something you learn in graduate school, surrounded by people who already … Continue reading
Posted in Expository
Tagged classical mechanics, general relativity, Mathematical Physics, Tensors, What Is...
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The mathematics behind a “wormhole”
Let me tell you something that will sound ridiculous at first. Take a piece of paper. Draw a dot on the left and a dot on the right. The shortest path between them, if you are a little ant walking … Continue reading