Hi everyone, because I’m at a graduate school open house this weekend and next, I’m having trouble keeping up with everything I need to do. For this reason, I’m going to be posting very short things for the rest of the month. I’m also going to be delayed this week. The main post will probably be up sometime Sunday. Sorry about that. In the meantime, here’s a video of a cat barking. …and here’s a video of a very upset cat. I know, little guy. I’m sorry about the delay.
jonah
Jonah is the author of The Physics Mill.
Physics / Quantum Mechanics / Science And Math
Like Chords of Music: Quantum Tunneling
The world is a dynamic mess Of jiggling things It’s hard to believe ~Richard Feynman The essential nature of matter Lies not in objects, but in interconnections Like chords of music, it’s beautiful ~Sophia Hoffman +Dripto Biswas recently asked me through google plus to explain why a superfluid climbs up the walls of its container. I don’t know very much about superfluids themselves. However, I can explain the basic quantum mechanics behind their behavior. (Spoiler alert: I’m going to mention quantum tunneling!) It might be helpful to reveiw some of my previous posts on quantum mechanics. The most relevant
Geometry / Mathematics / Science And Math
TexTAG Conference Report
Hi everyone. Sorry, but I’ve been at the Texas Undergraduate Geometry and Topology conference all weekend and I haven’t had time to write my blog post yet. I will post actual content as soon as I can, probably late tomorrow afternoon. In the meantime, I gave a talk on differential geometry at the conference! It’s not much of a consolation prize, but here are my slides from the talk. To better see the families of commensurate curves on various surfaces, we can animate our numerical integral as a function of the initial conditions. Here are some of the animations:
Physics / Science And Math
Refraction: (How We See) Through the Looking Glass
We do not see the lens through which we look. ~Ruth Benedict I was recently asked to explain refraction using quantum mechanics. To really understand this on the quantum level requires understanding a field called “quantum electrodynamics,” which was invented independently by Richard Feynman, Sin-Itiro Tomonaga, and Julian Schwinger (and for which they all shared a Nobel prize). Unfortunately, I don’t know very much about quantum electrodynamics, so I can’t explain this the way a particle physicist or condensed matter physicist might. I can however, give a “pseudoclassical” model that was invented around the turn of the twentieth century…right
Geometry / Mathematics / Physics / etc.
A Space-Time Cocktail: Minkowski Space and Special Relativity
Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. ~Hermann Minkowski Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore. ~Albert Einstein In my previous discussions of how we know the speed of light is constant and how this results in special relativity, I used Albert Einstein’s thought experiments to derive the time-dilating, length-contracting results. There’s another way to describe special relativity, though, invented by the Polish mathematician Hermann Minkowski. It
Condensed Matter / Physics / Science And Math
Superconductors and the Valence Band
In the comments for my last post, Hamilton asked the following question: What does the band structure for a superconductor look like? I’m not an expert on this topic, but I thought I’d share what I know. Take it with a grain of salt. I also wanted to warn you all that my site will be going down for maintenance this Sunday. I apologize for the inconvenience. I don’t know if this will affect my regular Sunday post. The current most popular theory of superconductors is BCS theory, which is incomplete. BCS theory says that at extremely low temperatures,
Condensed Matter / Physics / Quantum Mechanics / etc.
I’m With the (Valence) Band: Band Structure and the Science of Conduction
It was not so very long ago that people thought that semiconductors were part-time orchestra leaders and microchips were very, very small snack foods. ~Geraldine A. Ferraro More is different. ~Philip Warren Anderson Metals conduct electricity. Nonmetals don’t. That’s the conventional wisdom, anyway. In truth, there is a third class of material, called semiconductors. A semiconductor sometimes conducts electricity and sometimes doesn’t. This week, we’ll learn precisely what a semiconductor is and how the forces of quantum mechanics determine whether a material is a conductor, an insulator, or a semiconductor. More is Different Nobel laureate Philip Warren Anderson said
Physics / Quantum Mechanics / Science And Math
Binary Unity: The Pauli Exclusion Principle
Sameness leaves us in peace but it is contradiction that makes us productive. ~Johann Wolfgang Von Goethe In previous entries, I’ve discussed the wave nature of particles and some consequences of that wave nature, how electrons occupy specific energy states in atoms, and how particles obey the laws of probability. This is all pretty weird stuff. However, there’s another strange phenomenon in quantum mechanics that I haven’t discussed. That phenomenon is the Pauli exclusion principle. The Mystery of Stability An atom is made of protons, neutrons, and electrons. A good (but not quite right) model of the atom is
Geometry / Mathematics / Physics / etc.
You Can’t Get There From Here: Dimension, Fractional Dimension, and the Quantum Universe
You can’t get there from here. ~Maine saying My father once quoted a saying from Maine, where he spent some of his youth: “You can’t get there from here.” It refers to Maine’s winding road system, which often prevents a traveller from taking a direct route between two places. In physics and math terms, we might say that Maine’s road system is of fractional dimension: Less than two-dimensional, but more than one-dimensional. Integer Dimensionality Traditionally, we define the dimensionality of a space as the number of directions one can move in. For instance, a ski lift lives in a
Mathematics / Physics / Quantum Mechanics / etc.
Resolution, Fourier Analysis, and The Heisenberg Uncertainty Principle
All the effects of nature are only mathematical results of a small number of immutable laws. ~Pierre-Simon Laplace In my discussion last time (corrections here), I discussed how there is a physical limit to how good a recording can sound, whether vinyl or digital. There is a more fundamental limit, however, that I glossed over—a limit that depends not on atoms or compression techniques, but on pure mathematics. This limit was partially discovered by Jean Baptiste Joseph Fourier, and the method we will discuss bears his name. The Superposition Principle Before we discuss Fourier’s discovery, let’s take a brief