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
Computer Related / Science And Math
Corrections to Vinyl Records Vs Digital Files
In my previous post, it seems I’ve made some serious errors when discussing the technicalities of music recording, both digital and vinyl. This is not my area of expertise and I apparently did not do nearly enough research. Thanks to Gregor Robinson and Jonathan Griffitts for correcting me. Here are Gregor Robinson’s and Jonathan Griffitts’ corrections verbatum. Thanks to both of you. Gregor Robinson said: There is actually a big difference between lossy formats and lossless digital audio formats (which may be in fact compressed; see FLAC). It’s not just that the sample rate is lower. Lossy compression makes
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
The Dice Are Loaded: Probability Waves
God does not play dice ~Albert Einstein Einstein, stop telling God what to do! ~Niels Bohr This is part three of a multi-part series on quantum mechanics. In part one, I discussed how we discovered that light is both a wave and a particle. The dual nature of light suggests that massive particles like electrons might be waves too. In part two, I gave a theoretical underpinning to the dual nature of electrons: treating electrons as waves completes the Bohr Model of the atom and explains the Rydberg Formula. However, legendary physicist Richard Feynman once said: It doesn’t matter
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
Uncategorized
No Cat
Sorry everyone, but some family stuff came up this week. For this reason, I’ll be posting on Monday instead of Sunday. 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.