“Like the microscopic strands of DNA that predetermine the identity of a macroscopic species and the unique properties of its members, the modern look and feel of the cosmos was writ in the fabric of its earliest moments, and carried relentlessly through time and space. We feel it when we look up. We feel it when we look down. We feel it when we look within.” ~Niel Degrasse Tyson There was some very big news today! If you haven’t already heard, the BICEP2 research group at Harvard has found evidence of ancient gravitational waves in the sky. A lot
quantum mechanics
abstract algebra / History / Mathematics / etc.
International Women’s Day Spotlight: Emmy Noether
The connection between symmetries and conservation laws is one of the great discoveries of twentieth century physics . But I think very few non-experts will have heard either of it or its maker[:] Emily Noether, a great German mathematician. But it is as essential to twentieth century physics as famous ideas like the impossibility of exceeding the speed of light. It is not difficult to teach Noether’s theorem, as it is called; there is a beautiful and intuitive idea behind it. I’ve explained it every time I’ve taught introductory physics. But no textbook at this level mentions it. And
optics / Physics / Quantum Mechanics / etc.
How Things Work: Lasers
You know, I have one simple request. And that is to have sharks with frikkin laser beams attached to their heads! ~Dr. Evil Always look on the bright side …unless you’re holding a laser pointing device. ~Unknown The laser is, without a doubt, one of the most ubiquitous, archetypal technologies of modern times. And it is one of the most direct applications of quantum mechanics. But how do lasers work? It All Starts In The Atom The story starts deep within the atom. I’ve previously discuss the fact that particles are waves and that this forces electrons to have
Physics / Quantum Mechanics / Science And Math
Between the Two Shores: Covalent Bonding
But let there be spaces in your togetherness and let the winds of the heavens dance between you. Love one another but make not a bond of love: let it rather be a moving sea between the shores of your souls. ~Kahlil Gibran Two weeks ago now, I flew to Conway, Arkansas to attend the wedding of my very good friends Vincent and Mary. This and an academic conference got in the way of blogging for a little while but I’m back. As such I decided to a post in their honor about bonding. Not human bonding, mind you,
Physics / Quantum Mechanics / Science And Math
Reality Is—The Feynman Path Integral
Will you understand what I’m going to tell you? …No, you’re not going to be able to understand it. … I don’t understand it. Nobody does. ~Richard Feynman on the Path Integral The “paradox” is only a conflict between reality and your feeling of what reality “ought to be.” ~Richard Feynman, in his lectures on physics Quantum mechanics is a very strange beast. Things tunnel and ooze. You can’t know both position and momentum at the same time. These strange properties come from the amazing realization that particles are waves. Not only that, but the amplitude of the wave
Condensed Matter / Physics / Quantum Mechanics / etc.
How Things Work: The Field Effect Transistor
I don’t know how to do this on a small scale in a practical way, but I do know that computing machines are very large; they fill rooms. Why can’t we make them very small, make them of little wires, little elements – and by little, I mean little. ~Richard Feynman (1959) As of 2012, the highest transistor count in a commercially available CPU is over 2.5 billion transistors. ~Wikipedia In my article on quantum tunneling, I mistakenly claimed that diodes and transistors made use of this phenomenon. In an effort to correct my mistake, I’m going to explain
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
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
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