I recently posted an article on Kaluza-Klein theory. This was partly because I was working a paper on it as a final project in my second semester of general relativity. The paper is finished, and I thought I’d upload it for the more mathematically inclined of my readers. If you’re interested, you can find it here.
physics
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
Computer Related / Science And Math
Sound: Vinyl Records Vs. Digital Files
All music is beautiful ~Billy Strayhorn I apologize to everyone who looked for my article earlier today. I was delayed in writing it last night. I think I need to start working ahead and building a buffer. sunstreetreviews asks Audiophile friends tell me that vinyl records have a much richer sound than MP3 files. Is that really the case, and if so, why? In principle, there’s no reason a digital file should produce lower-quality sound than a vinyl record. In reality, tests are inconclusive. Why this is the case has to do with how sound works, and how sound
Physics / Quantum Mechanics / Science And Math
Unreal Truths: Matter Waves and the Bohr Model of the Atom
Everything we call real is made of things that cannot be regarded as real ~Niels Bohr This is the second part of a multi-part series on quantum mechanics. In part one, I described and motivated particle-wave duality for light. I demonstrated that light waves are also particles (photons). But does this duality go the other way? Are particles like electrons also waves? As I hinted last time, the answer is yes. These are called matter waves, and their story is very interesting. The Mystery of the Emission Spectrum Last time, I discussed the emission spectrum of hydrogen, and the
Physics / Quantum Mechanics / Science And Math
The Charming Doubleness: Particle-Wave Duality
But the beauty here lay in the duality, in the charming doubleness… ~ Thomas Mann (Felix Krull) I apologize to those of you who have requested a topic. The current requests are all pretty in-depth and I want some time to think about how to explain them properly. So, in a bid to buy time, I’m going to do a multi-part series on quantum mechanics. In this part, I’ll describe some of the experimental results motivating the fundamental principle of quantum mechanics: particle wave duality. As amazing as it may seem, quantum mechanics tells us that every particle is