Category Archives: Classical Mechanics

Behe on The Colbert Report

Last night, Michael Behe was Stephen Colbert’s guest on The Colbert Report. It was, shall we say, educational.

BEHE: Nobody was searching for the limits of Newton’s theory when Newton first proposed it. He thought that he had solved all of physics. But then when —

COLBERT: You mean about how — how apples fall?

BEHE: Apples fall, cannonballs go. But then —

COLBERT: Mm-hmmm.

BEHE: But then when —

COLBERT: He invented the cannonball? He invented the dive — the cannonball?

[audience laughs]

BEHE: Cannonballs fly.

Oh, yes. It’s nice to know that nobody checked to see if Newton was right, or if “universal gravitation” was really universal.

Wait. You say that it was Edmund Halley who used Newton’s laws to predict that comets travel in elliptical orbits, and that the comet seen in 1456, 1531, 1607 and 1682 would return in 1758? How could Halley say such a thing, after Newton had made his view clear that all comets travel in parabolic paths? It’s in the Principia, for Heaven’s sake! And you say that Halley was the one who realized that the stars are not fixed to a “celestial firmament” but instead move through space? How dare you imply that the views of one person are not the entirety of science! Sir, how dare you have the temerity to insist that people did not take Newton at his word but instead used his theories to make predictions about the world which they could then compare to observations to — I can hardly even articulate such a heretical notion — see if Newton was wrong.

What! Are you telling me it was the French, those wine-swilling, toad-munching surrender monkeys, who had the audacity to test Newton’s prediction that the Earth is an oblate spheroid? Sir, you could tell me all you want about the 1735 expeditions to Peru and Lapland under Charles-Marie de La Condamine and Pierre-Louis Moreau de Maupertuis respectively — the former of which incidentally brought back the first rubber and curare Europe had ever seen — but the mere suggestion that Newton’s word was not good enough is so repugnant I refuse to consider the matter further.

It gets better:
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The Physics of Nonphysical Systems

We just heard Steinn Sigurðsson complain that there’s no science in Harry Potter, and therefore the book title The Science of Harry Potter is a non-starter. Jennifer Ouellette then leaped to its defense:

I think in this instance, I’d conjure the spirit of Arthur C. Clarke: “Any sufficiently advanced technology is indistinguishable from magic.” :)

But then, that’s just the sort of viewpoint you’d expect from somone who wrote about the physics of the Buffyverse.

In a display of the kind of synchronicity one might expect whenever the system is large and the selection criteria are loose, Bee at Backreaction just pointed to a new paper on the arXiv, “Hollywood Blockbusters: Unlimited Fun but Limited Science Literacy” (9 July 2007). C.J. Efthimiou and R.A. Llewellyn declare their intentions as follows:

In this article, we examine specific scenes from popular action and sci-fi movies and show how they blatantly break the laws of physics, all in the name of entertainment, but coincidentally contributing to science illiteracy.

Movies under their microscope include Speed (1994), where projectile motion is thrown out the window; Spiderman (2002), which stretches Newton past the breaking point; Aeon Flux (2005), whose muscles really have to torque; The Core (2003), which just doesn’t float at all; Superman (1978), which ought to make a physicist’s head spin; X-Men: The Last Stand (2006), whose finale is cut loose from reality; and The Chronicles of Riddick (2004), which I haven’t seen.
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Lagrangian Mechanics is Intelligent Design?

Via Kevin Beck I just learned that Sal Cordova, famous (in some circles) for rank dishonesty and general lack of mathematical aptitude, has been claiming that Lagrangian mechanics was inspired by Intelligent Design. For those who are not au courant with physics, Lagrangian mechanics is an alternative take on the classical physics — think billiard balls, pendulums, planets orbiting the Sun — studied by Newton. The enterprise is named for Joseph-Louis Lagrange, who along with Euler and others laid the groundwork. It’s equivalent to Newton’s F = ma approach, but more convenient for some problems, and because it talks about the same physics in a different way, it provides a different and useful starting point for developing new theories. (For example, Barton Zwiebach’s First Course in String Theory generalizes the Lagrangian description of zero-dimensional objects, particles, to invent a theory of one-dimensional objects, strings. This is much easier to do in a Lagrangian rather than a Newtonian formalism.) Phenomena in relativity and quantum field theory are also often studied via a Lagrangian approach.

Many people are familiar with basic characteristics of light. We know, for instance, that light travels in straight lines; when light bounces off a mirror, the angle of incidence equals the angle of reflection; light can be spread out or focused together using lenses; and so forth. When we study optics, we can derive all these disparate facts from a very simple, central premise: when traveling from point A to point B, a light ray takes that path for which the travel time is a minimum. (A more precise statement is that the physical path taken by the light ray is such that a small perturbation to the path does not significantly change the travel time; this is connected to the calculus idea that the slope of a curve at a minimum or maximum is zero. For our purposes, we won’t have to worry about these details.) If there’s nothing in the way to change the light’s propagation speed, or if the material through which the light travels is uniform, then the path of minimum time is a straight line. Requiring that the light go from A down to a mirror and bounce back up to B means — I leave the geometry as an easy exercise to the interested reader — that the angles of incidence and reflection will be equal.

Lagrangian mechanics takes a similar approach, taking the idea of a “minimum principle” and applying it not to light, but to the motion of matter — balls, planets, frightened cats and so forth. Instead of calculating the travel time, as we did with light, we consider the energy of the moving objects; more precisely, our calculations involve the difference between kinetic and potential energies. The “Lagrangian” for classical problems — remember, we can generalize the ideas later — is the difference between the kinetic energy and the potential, and we find the path through space an object will take by adding up, or integrating, the Lagrangian along all possible paths. The physical path, the one the object really follows, is the one whose total Lagrangian, or “action,” is a minimum.

Now, what in blazes does any of this have to do with Intelligent Design?
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Missing No More

Richard Feynman’s second Messenger Lecture, on the relation between physics and mathematics, is missing no more:

[VIDEO REMOVED FROM GOOGLE’S ARCHIVES]

This is the lecture in which Feynman presents an example I have appropriated before, concerning the necessity of knowing math before being able to do science, and how popularizations of physics often fail because they leave out the mathematics.

Feynman’s example goes like this: I can say that when a planet travels in its orbit, a line from the planet to the Sun sweeps out equal areas in equal times. I can also say that the force pulling on the planet is always directed toward the Sun. Both of these statements require a little math — “equal areas,” “equal times” — but it’s not really math, not a kind to give the layman heebie-jeebies. Given some time for elaboration, one could translate both of these statements into “layman language.” However, one cannot explain in lay terminology why the two statements are equivalent.
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Video Physics Resources

I’ve mentioned both of these items before, but I figured I should bring them up explicitly. (A nasty stretch of PHP coding lies in my near future, and the need to procrastinate is becoming almost a physical pain.) First is Caltech’s series The Mechanical Universe (1985), which I first saw on PBS many years ago and is now available online for free. If you want a year’s worth of freshman physics, you can now get it in moving-picture form. Early episodes also cover some necessary math: derivatives, integrals and vectors. The videos require a free login before use.

Second in the video department is Barton Zwiebach’s String Theory for Pedestrians (2007). The content should be comprehensible to advanced undergrads. Summary:

In this 3-lecture series I will discuss the basics of string theory, some physical applications, and the outlook for the future. I will begin with the main concepts of the classical theory and the application to the study of cosmic superstrings. Then I will turn to the quantum theory and discuss applications to the investigation of hadronic spectra and the recently discovered quark-gluon plasma. I will conclude with a sketch of string models of particle physics and showing some avenues that may lead to a complete formulation of string theory.

Unfortunately, the CERN people haven’t yet figured out this neat “embedding video” thing. RealMedia is so, like, 2001 (and sucks besides). I was able to use Real Alternative to play the Zwiebach videos on Windows and MPlayer to watch them on Linux.
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Chaos, Phase Transitions and Topology

Ben has suggested the following paper as a target for our discussion. We should, he says, have the necessary background by the end of the summer.

As the abstract says, the paper is divided into two main parts:
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Entropy for Non-Majors

Every once in a while (well, actually, pretty frequently) I see a post out there in the Blagopelago which makes me feel bad about ranting so much and discussing science so little. Today’s entry in this category is Jacques Distler’s treatment of Boltzmann entropy. He explains his motivation as follows:

This semester, I’ve been teaching a Physics for non-Science majors (mostly Business School students) class.

Towards the end of the semester, we turned to Thermodynamics and, in particular, the subject of Entropy. The textbook had a discussion of ideal gases and of heat engines and whatnot. But, somewhere along the line, they made a totally mysterious leap to Boltzmann’s definition of Entropy. As important as Boltzmann’s insight is, it was presented in a fashion totally disconnected from Thermodynamics, or anything else that came before.

So, equipped with the Ideal Gas Law, and a little baby kinetic theory, I decided to see if I could present the argument leading to Boltzmann’s definition.

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New Scientist, the EmDrive and the Wobosphere

shnood: (roughly) an imposter; a person oblivious to just how trivial or wrong his ideas are.

“Were there any interesting speakers at the conference?”
“No, just a bunch of shnoods.

“The magazine New Scientist loves to feature shnoods on the cover.”

Note: someone who’s utterly contemptible would not be a shnood, but rather a schmuck.

— Scott Aaronson (27 May 2006)

Those of you interested in the way the Wobosphere functions as a disputation arena (“We Can Fact-Check Yo’ Ass!”) may be interested in the following sordid tale of intrigue and skullduggery. I originally wrote most of this last October, in a lengthy comment on David Brin’s blog. The moral of the story, insofar as I can find one, is this: if you say that you can move your car forward by bouncing a soccer ball back and forth inside it fifty thousand times, you’ll get a quizzical look (at best). If you say the same thing but with “microwave photons” instead of soccer balls, you’re reporting on cutting-edge science!

Back in September, New Scientist magazine published an article on the “EmDrive”, a machine purportedly able to propel itself using microwaves bouncing inside a box. Those of us who remember the Dean drive and umpty-ump other wonder machines have no trouble recognizing this as the same old stuff: like all the wonder-powered spacedrives before it, it can only putter forward by violating the conservation of momentum. New Scientist‘s reportage provoked science-fiction writer Greg Egan to write an open letter saying he was “gobsmacked by the level of scientific illiteracy” the magazine showed.

So it goes, as they say on Tralfamadore. Claims of exotic spacedrives fuelled by violations of fundamental physics are, sadly but understandably, about twopence a dozen. The aspect of the affair which Egan found truly disturbing — indeed, reprehensible — was the way New Scientist glibly provided a “news” piece full of pseudoscientific gibberish purely to justify how the EmDrive might work. (Their argument really pushed the limits of the absurd, too: Einstein’s relativity has momentum conservation built into its mathematical structure, so you can’t use relativity jargon like “reference frames” to sidestep the conservation law.)

Egan posted his letter to the moderated Usenet group sci.physics.research, and the physicist John Baez put a copy on the blog he co-hosts, The n-Category Cafe. This spurred enough people to write New Scientist that the magazine opened a blog thread to discuss the issue, opening with a self-exusing note from the editor, Jeremy Webb. (Said note, as far as I can tell, satisfied nobody.)
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I Guess It’s a Deuteron

Seed has just offered the world a “Cribsheet” on string theory. It looks pretty slick, although their portrayal of a “hydrogen atom” seems to have an extra nucleon (as Wolfgang notes in the Cosmic Variance thread). I’m inclined to forgive the multiple electron orbits, since they only show one actual electron — and besides, ellipses aren’t that great a way of drawing orbitals anyway.

(Incidentally, if you want to see orbitals in video, check out episode 51 of The Mechanical Universe, available for free online via Annenberg Media.)

They do cite Barton Zwiebach’s First Course in String Theory (2004), which gives me a slight tinge of pride. I mean, somebody had to work the problems in the last five chapters to see if they were solvable by students and not just professors.

The portion of this post below the fold is a rough draft of several different rants, developed in embryonic form and smushed together. Read only if you’re exceptionally curious.
Continue reading I Guess It’s a Deuteron