August 12, 2011
Boy howdy do we love spheres in physics. Sure we might tell you that the reason involves deep truths in topology, and symmetry, and group theory, and all that mathematical arcana, and in fact there's a lot of truth to that. But if we're completely honest, or at least if I'm completely honest, I…
August 1, 2011
A reader asked me about the hyperbolic trig functions, sinh(x) and cosh(x). What are they for, and do they have an intuitive interpretation in physics?
That's a pretty good question. After all, most of the time you first meet the hyperbolic trig functions in intro calculus, where their rather odd…
July 29, 2011
Our department here at Texas A&M has a student chapter of the Optical Society of America, and each week a student or professor gives a talk about something interesting while the rest of us eat pizza. I've been working on and off on a talk I'm going to give, tentatively titled "Just what the…
July 8, 2011
By the 1860s, the classical theory of electricity and magnetism was on a very solid theoretical footing. Maxwell's equations describing the interplay of charges and currents with electric and magnetic fields were on paper by 1862, and with some changes in notation they're the exact same today.…
June 27, 2011
Phil at Bad Astronomy opined (and it is a common opinion) that the supernatural is incoherent:
If you posit some thing that has no perceivable or measurable effect, then it may as well not exist. And as soon as you claim it does have an effect -- it can be seen, heard, recorded, felt -- then it…
June 26, 2011
Head down to Box Office Mojo and pull up the list of the top grossing films of the year thus far. Seven of the top ten have a dollar gross beginning with the number 1. Okay, that's not too weird. Big films tend to pull down somewhere between $100-200 million, while only the real monsters have high…
June 11, 2011
Here is a picture of (I think) Maru the cat playing in a bag. He loves bags.
Here is the same picture of Maru, at half the size:
Now imagine that Maru is a physicist and the pictures are not pictures but instead windows into the universe he occupies, separate from ours with (possibly) its own…
May 17, 2011
Just though I'd try writing a post title in the style of a crank. Kinda fun!
Gauss' law, of course, is not wrong. But I got a question from a reader that deceptively simple and an interesting example of a theorem not quite working the way you'd expect. I've gone over Gauss' law before, so as a…
May 2, 2011
Some initial thoughts, on a beautiful day in a palpably better world without Osama:
1. I'm astonished he was still alive. I was certain he died from an anonymous bomb or health problems sometime between '01 and '04. He hadn't released any tapes or videos with unambiguous confirmation of when they…
April 27, 2011
Last time we took a pulse of light and shot it through a medium with a frequency-dependent refractive index. The particular form of the refractive index was sort of interesting - for some frequencies, it was less than 1. That implied that the phase velocity of a sine wave would be faster than the…
April 20, 2011
Last time, we did some slightly boring groundwork. This time, we're going to look at something more interesting: the way a pulse of light propagates in something (like a piece of glass) with a frequency-dependent refractive index. As we discussed, the refractive index is just a way to express the…
April 13, 2011
So we left off with the most basic mathematical description of a wave. It's a function of the form f(x - vt), or in words a disturbance that moves from one place to another at a constant speed without changing shape.
This is a nice start, but it's both too general and not general enough to be…
April 7, 2011
So, what's a wave? In his deservedly ubiquitous undergrad electrodynamics textbook, David Griffiths emphasizes the fact that the whole idea is pretty nebulous. Any rigid definition is likely to exclude things that are usually thought of as waves or to include things that aren't. He suggests that…
March 14, 2011
A while back I was driving in my car listening to the radio and was gobsmacked to hear a song (What's My Name? by Rihanna and Drake) in which the singer's rap involved accurately estimating a square root. Unfortunately it was in the context of a rather vulgar play on words ("the square root of…
March 12, 2011
So there's this alien invasion flick called Battle: Los Angeles. It's getting mixed reviews. Ebert hates it - "an insult to the words "science" and "fiction," and the hyphen in between them." With the caveats that his judgment is usually questionable, I haven't seen the movie, and I don't plan to…
March 11, 2011
In the last post I talked about a measurement we did in our lab to characterize some properties of two parallel laser beams. The theory, if you want to dignify that equation with such a title, gave the power of the two beams as a function of mow much of the beams we cut off with a moving opaque…
March 4, 2011
A while back in the lab we were conducting an experiment that involved passing a laser beam through a narrow iris, using a beamsplitter to take half the intensity of the beam and send it one way, with the remaining half passing through undisturbed. Then we arranged our mirrors in such a way as to…
February 27, 2011
Here is a picture of the earth, with latitude and longitude lines in ten-degree increments:
Despite the fact that each vaguely rectangular area formed by the intersection of those lines forms a 10 degree by 10 degree region, the actual square-mile area of each rectangle varies. The ones near the…
January 25, 2011
I always tell my students that they should never just write down an equation blindly and start plugging things in. If you don't understand what you're doing, you're much more likely to make a mistake.
Sometimes I don't take my own advice. On a science forum I read occasionally, a person who was…
January 22, 2011
In my free time during data acquisition runs and the like, I've been paging through Hardy and Wright's famous textbook An Introduction to the Theory of Numbers. It has something of a legendary reputation among pure math textbooks, and so far as I can tell it is entirely deserved.
One of the topics…
January 17, 2011
This Christmas I got a little handheld GPS, which I've been using mostly for geocaching. As the device acquires signals from the various satellites dutifully orbiting overhead, it displays your position coordinates and a figure indicating the estimated uncertainty. At the beginning of the…
January 14, 2011
Well, last time we were looking about the classical probability density for a bouncing ball, and the quantum mechanical probability distribution for the same. They looked not even a little bit alike. This is kind of a problem, since we know from experience that classical physics works pretty well,…
December 16, 2010
All right, I'm gonna delay the next installment of the quantum bouncing ball for a brief diversion. I have a friend who's also a physics grad student, and he suggested that we along with a few other fellow students form a yet-to-be-named unofficial club whose raison d'etre is to get together every…
December 13, 2010
Right now I'm on the 4th floor of the physics building. If I walk down the hall to the balcony overlooking the atrium, I could drop a bouncy ball and watch its trajectory. It'll fall to the ground, bounce up to some fraction of its initial height, and repeat the process with a loss of energy each…
December 3, 2010
Isaac Newton, when he wasn't revolutionizing mathematics and almost single-handedly inventing physics as a systematic discipline, wrote some really ridiculous stuff. Alchemy, occult esoterica, you name it. In his defense, it was the 1600s. He didn't have a whole lot of prior scientific…
November 21, 2010
In pure mathematics there's not too many function studied more than the Riemann zeta function. For reasons of historical tradition, the generic variable name that's usually used is s instead of z. (The function is mostly interesting in terms of complex analysis, so x would be a bit unorthodox too…
November 13, 2010
Shortly after the invention of the laser, a torrent of discoveries began pouring in thanks to the previously unreachable intensities that became available. Many of these discoveries fall under the general category of "nonlinear optics", which you could more or less say is the study of the behavior…
November 10, 2010
There was some dissension in the comments of my post on solving the Schrodinger equation with a linear potential. What the post boiled down to was that the solution was Ai(u), where we found that u was:
The point of the post was to work through and get that coefficient that's in front of the (Fx…
November 7, 2010
Most textbooks, especially ones not aimed at college math majors, give a definition of "function" that seems quite intuitive. They'll say something along the lines of: a function is a rule that takes an input x and turns it into an output f(x). Formally this isn't quite right - the essence of a…
November 5, 2010
So consider the one-dimensional time-independent Schrodinger equation:
In some ways it's not really an equation as such, because you have to plug in some function V(x) that describes the potential in the problem you're solving. When you first learn quantum mechanics you'll learn the big ones: V(x…
