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What’s a wave?
Posted by Matt Springer on 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 one possible vague definition is “a disturbance of…
Sunday Function
Posted by Matt Springer on 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…
Dropping Rocks: Los Angeles
Posted by Matt Springer on 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 see the movie, I’m…
On Free Parameters
Posted by Matt Springer on 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…
Random Thoughts on a Trivial Lab Measurement
Posted by Matt Springer on 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…
Sunday Function
Posted by Matt Springer on 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 poles are smaller than the…
The Hydrogen Partition Function, or, How Matt Didn’t Pay Attention
Posted by Matt Springer on 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 just taking…
Sunday Function
Posted by Matt Springer on January 23, 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 treated in…
Sunday Function
Posted by Matt Springer on 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 acquisition or if the view of the sky is poor, it…
Quantum Bouncing Ball, Concluded
Posted by Matt Springer on 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, and from more modern work we…