Nov
30
Posted by jns on
November 30, 2007
I learned about it from Science News Online (here), but evidently it has been on its way to becoming a mini-phenomenon since it was posted on YouTube in June, 2007.
It’s a short animation of some mathematical concepts, called “Moebius Transformations Revealed“. To quote from the creators’ website (here):
Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity.
It does do what it claims it does, although it doesn’t go so far as to suggest what we learn from understanding their essential unity, nor what we might do with our new understanding. Perhaps I’ll have that “aha!” later on.
Nevertheless, it’s a very pretty little film (2:32 long), and the music (Robert Schumann, a movement from Kinderscenen, for piano) seems unusually well suited.
But it’s better that you just have a look rather than listen to me talk about it.
Nov
21
Posted by jns on
November 21, 2007
From this week’s Physics News Update* a note about physicist Luis Alvarez, to whom all things were interesting. In case you’ve ever wondered about the source of the hypothesis that the dinosaurs were wiped out by a meteorite, read on.
EGYPTIAN PYRAMIDS, DINOSAUR EXTINCTION, THE JFK ASSASSINATION: all were studied by Berkeley physicist Luis Alvarez. Alvarez won a Nobel Prize for his discovery of new particles using a bubble chamber, but some of his fame comes from his work applying physics principles and methods outside the normal physics-research world. In the November issue of the American Journal of Physics, Charles Wohl of the Lawrence Berkeley National Lab looks at three notable examples of Alvarez*s extracurricular effort.
(1) To search for possible hidden chambers in the Chephren pyramid in Cairo-one of the three great pyramids built in the third millennium BCE-Alvarez designed an experiment in which cosmic rays would strike a detector set up inside a known chamber beneath the pyramid. Observing the penetrating muons from cosmic-ray showers, this detector would discern any intervening empty spaces in the overlying pyramid structure. The upshot: no hidden chambers.
(2) In scrutinizing the so called “Zapruder film”, a short filmed sequence that caught the assassination in progress, experts had been puzzled by the backwards jerk of President Kennedy’s head after one of the bullet impacts. Some took this to be evidence for another assassin shooting from in front of the president’s car. Alvarez and some of his colleagues performed impromptu experiments at a shooting range, and also considered the conservation of momentum and the forward-moving matter from the wound. From this they concluded that the movie sequence was consistent with a shot coming from the rear.
(3) Most famous of all was Alvarez’s hypothesis, made in collaboration with his son Walter Alvarez, that a thin but conspicuous layer of the otherwise rare element iridium in numerous places around the world, all at a geological stratum corresponding to the era just around the boundary between the Cretaceous and Tertiary periods (the KT boundary), signified a large asteroid impact at that time. This impact, it was further thought, cast enough dust into the air from a long enough time as to kill off many living things, including a large portion of dinosaurs.
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* Phillip F. Schewe, Physics News Update, The American Institute of Physics Bulletin of Physics News, Number 847, 20 November 2007.
Nov
01
Posted by jns on
November 1, 2007
While some vaguely scientific notions are passing through my head, here’s a clipping from Physics News. It came as a bit of a surprise to me. I spent most of my laboratory research life doing stuff that came, in one way or another, under the general heading of “thermodynamics”, and yet it never occurred to me to wonder whether we needed to develop a relativistic theory of thermodynamics. Relativistic electrodynamics, sure. Relativistic quantum mechanics, obviously. But relativistic thermodynamics? I guess the worm goes to the bird who thinks of worms first.
What would relativistic thermodynamics be about? The main question would be whether the temperature of some mutually observed object would be measured the same by two different observers, each in a different inertial (i.e., unaccelerated) reference frame. Care to make a guess?
RELATIVISTIC THERMODYNAMICS. Einstein’s special theory of relativity has formulas, called Lorentz transformations, that convert time or distance intervals from a resting frame of reference to a frame zooming by at nearly the speed of light. But how about temperature? That is, if a speeding observer, carrying her thermometer with her, tries to measure the temperature of a gas in a stationary bottle, what temperature will she measure? A new look at this contentious subject suggests that the temperature will be the same as that measured in the rest frame. In other words, moving bodies will not appear hotter or colder. You’d think that such an issue would have been settled decades ago, but this is not the case.
Einstein and Planck thought, at one time, that the speeding thermometer would measure a lower temperature, while others thought the temperature would be higher. One problem is how to define or measure a gas temperature in the first place. James Clerk Maxwell in 1866 enunciated his famous formula predicting that the distribution of gas particle velocities would look like a Gaussian-shaped curve. But how would this curve appear to be for someone flying past? What would the equivalent average gas temperature be to this other observer?
Jorn Dunkel and his colleagues at the Universitat Augsburg (Germany) and the Universidad de Sevilla (Spain) could not exactly make direct measurements (no one has figured out how to maintain a contained gas at relativistic speeds in a terrestrial lab), but they performed extensive simulations of the matter. Dunkel (joern.dunkel@physik.uni-augsburg.de ) says that some astrophysical systems might eventually offer a chance to experimentally judge the issue. In general the effort to marry thermodynamics with special relativity is still at an early stage. It is not exactly known how several thermodynamic parameters change at high speeds. Absolute zero, Dunkel says, will always be absolute zero, even for quickly-moving observers. But producing proper Lorentz transformations for other quantities such as entropy will be trickier to do. (Cubero et al., Physical Review Letters, 26 October 2007; text available to journalists at www.aip.org/physnews/select)
[The American Institute of Physics Bulletin of Physics News, Number 843 October 18, 2007 by Phillip F. Schewe]