Your hand opens and closes, opens and closes. If it were always a fist or always stretched open, you would be paralysed. Your deepest presence is in every small contracting and expanding, the two as beautifully balanced and coordinated as birds’ wings. ~Rumi Although we don’t usually notice them, ultrafast pulsed lasers are all around us. They are keep time in the atomic clocks on GPS satellites. Metrologists and chemists use them to measure the properties of atoms and molecules. Astronomers use them to measure the color of light from distant stars. Particle physicists use them in supercollidors. Materials
Quantum Mechanics
Physics / Quantum Mechanics / Science And Math
Quantum Field Theory in A Cavity
So I’m still mired in final exams–this time a final project for my quantum field theory course. The downside is that it will be yet another week before my next “real” post. The upside is that I still have a little something for you all this week. The above image shows part of what I’m working on for my project. Imagine that you make a square box of mirrors, and with some magic quantum tweezers, you put exactly fifty-one photons into your box. Light is a special oscillation in an electromagnetic field, which we usually describe classically. But if
optics / Physics / Quantum Mechanics / etc.
Scattering Part Two: A Quantum of Scattering
We come spinning out of nothing, scattering stars like dust! ~Jalāl ad-Dīn Muhammad Rūmī Last week, I explained Rayleigh and Raman scattering from a classical point of view. In the process, I explained why the sky is blue and introduced Raman spectroscopy, a powerful tool for studying the structure of molecules. This week, I fill in the gaps and explain scattering from a quantum-mechanical point of view. Before we can talk about scattering, though, we need to review some important ideas from quantum mechanics: energy levels and the Heisenberg uncertainty principle. Energy Levels The story of energy levels starts
optics / Physics / Quantum Mechanics / etc.
Why The Sky is Blue: Lord Rayleigh, Sir Raman, and Scattering
The Sky is the Daily Bread of the Eyes ~Ralph Waldo Emerson At some point in his or her life, almost every child on Earth asks, “Why is the sky blue?” The question is so prevalent that, to me, it has come to represent the wonder that the world holds for a a child. Adults don’t ask such questions… at least, not unless they’re scientists. Part 1: John Tyndall In 1859, physicist John Tyndall thought he’d found the answer to the sky’s color. His studies of infrared radiation required him to use containers of completely pure air. He
Condensed Matter / cosmology / Physics / etc.
BICEP2, Primordial Gravity Waves, and Cosmic Inflation
“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
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,
cosmology / Discrete Math / Geometry / etc.
Quantum Geometry: Causal Dynamical Triangulations
A “quantum gravity expert” is presumably someone well acquainted with the details of our immense ignorance of the subject. I suppose I count. ~John Baez I long ago promised that I would discuss some of my own research. Here’s the first post that makes good on that promise. Today I’ll discuss a theory of quantum gravity. Why Quantum Gravity? Without a doubt, the two greatest advances in physics in the last 120 years were the advent of general relativity and quantum mechanics. These two amazing theories have totally changed the way we see the world. Quantum mechanics describes the
Analysis / Mathematics / Physics / etc.
Between Being and Non-Being: Imaginary Numbers
Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being ~Gottfried Wilhelm Liebnitz One of the first things we learn how to do is multiply numbers. . That sort of thing. But what if we multiply a number by itself? This is the familiar operation, which we call squaring a number. and . That sort of thing. You can take a number to a power by multiplying it by itself some number of times equal to the power. So if you square a number, you’ve taken it to the second power.