Author Archives: Aronno Mirdha
A Few Words on Cornell
I usually write about physics here, but I felt I had to say something about what has recently been reported at Cornell University. Reading about the alleged sexual assault and everything that has followed has honestly been disturbing. I don’t … Continue reading
Why MHD Works in Weakly Collisional Astrophysical Plasmas
Here is a number that should bother you. In the solar wind near the Earth’s orbit the proton density is about $5$ per cubic centimetre and the temperature is around $10^{5}$ K. Work out how far a proton travels before … Continue reading
From the Equivalence Principle to Curved Geometry of Spacetime
Newtonian mechanics contains two masses with no obvious reason to be related. One appears in the law of gravitation, $$\mathbf{F}=-\frac{GMm_g}{r^{2}}\hat{\mathbf r},$$ where $m_g$ measures how strongly a body couples to a gravitational field. The other appears in the second law, … Continue reading
Posted in Expository, Notes
Tagged Classical Gravity, curvature, differential geometry, Einstein equations, equivalence principle, general relativity, geodesic deviation, Geodesics, gravity, Lorentzian Geometry, manifolds, Mathematical Physics, spacetime, Tensors, theoretical physics
Leave a comment
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
Leave a comment
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
Leave a comment
A Scientist Before “Scientist”
Mary Somerville is so difficult to put into words that it’s funny. To be honest, who was she? Although you would be correct in calling her a mathematician, you would then be required to clarify the astronomy. The word “astronomer” … Continue reading
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