An image burbled up in my social-media feed the other day, purporting to be a list of “17 Equations that Changed the World.” It’s actually been circulating for a while (since early 2014), and purports to summarize the book by that name written by Ian Stewart. This list is typo-ridden, historically inaccurate and generally indicative of a lousy knowledge-distribution process that lets us down at every stage, from background research to fact-checking to copy-editing.
Continue reading 17 Equations that Clogged My Social-Media Timeline
Category Archives: Electromagnetism
Time Capsule
While looking through old physics books for alternate takes on my quals problems, I found a copy of Sir James Jeans’ Electricity and Magnetism (5th edition, 1925). It’s a fascinating time capsule of early views on relativity and what we know call the “old quantum theory,” that is, the attempt to understand atomic and molecular phenomena by adding some constraints to fundamentally classical physics. Jeans builds up Maxwellian electromagnetism starting from the assumption of the aether. Then, in chapter 20, which was added in the fourth edition (1919), he goes into special relativity, beginning with the Michelson–Morley experiment. Only after discussing many examples in detail does he, near the end of the chapter, say
If, then, we continue to believe in the existence of an ether we are compelled to believe not only that all electromagnetic phenomena are in a conspiracy to conceal from us the speed of our motion through the ether, but also that gravitational phenomena, which so far as is known have nothing to do with the ether, are parties to the same conspiracy. The simpler view seems to be that there is no ether. If we accept this view, there is no conspiracy of concealment for the simple reason that there is no longer anything to conceal.
Gbur’s Mathematical Methods
REVIEW: Gregory J. Gbur (2011), Mathematical Methods for Optical Physics and Engineering. Cambridge University Press. [Post also available in PDF.]
By golly, I wish I’d had this book as an undergrad.
As it was, I had to wait until this past January, at the ScienceOnline 2011 conference. These annual meetings in Durham, North Carolina feature scientists, journalists, teachers and students, all blurring the lines between one specialization and another, trying to figure out how the Internet can help us do and talk science. Lots of the attendees had books recently published or soon forthcoming, and the organizers arranged a drawing. We could each pick a book from the table, with all the books anonymized in brown paper wrapping. Greg “Dr. Skyskull” Gbur had brought fresh review copies of his textbook. Talking it over, we realized that if somebody who wasn’t a physics person got a mathematical methods textbook, they’d probably be sad. So, we went to the table and hefted the offerings until we found one which weighed enough to be full of equations, and everyone walked away happy.
MMfOPE is, as the kids say, exactly what it says on the tin. It begins with vector calculus and concludes with asymptotic analysis, passing through matrices, infinite series, complex analysis, Fourierology and ordinary and partial differential equations along the way. Each subject is treated in a way which physicists will appreciate: mathematical rigour mortis is not stressed, but when more careful or Philadelphia-lawyerly treatments are possible, they are indicated, and the ways in which their subtleties can become relevant are pointed out. In addition, issues like the running time and convergence of numerical algorithms are, where appropriate, addressed.
Continue reading Gbur’s Mathematical Methods
Freak Waves
No, they’re not just sonic effects from early Frank Zappa recordings. As Dr. SkySkull explains, rogue or freak waves are remarkable — and sometimes dangerous — phenomena in optics and on the high seas.
Colony Collapse Disorder
Bug Girl takes on a recent paper which claimed to find evidence that cell phones have it in for beehives. The punchline:
This paper (which for a student research paper would be questionable) should not have been in a journal. It definitely should not have postulated a connection to Colony Collapse Disorder.
And it should never have made the levels of press exposure that it did.
Two Slashdottings In One House
I got a little blip of a Slashdotting when I wrote about the Stuart Pivar incident, but my friend Brian Neltner — expert in genetically engineering viruses to his bidding, and black belt in a martial art which teaches eyeball extraction as a standard “defensive” move — has got the real deal. He designs LED artwork, you see, incorporating UV lights and other extra goodies to create colors which can’t be captured in a camera or reproduced on a computer screen. Imagine a room bathed in smoothly shifting wavelengths of vivid color, changing the appearance of everything they touch as pigments vanish or merge only to arise again in new, deceptive patterns.
That’s our living room.
The total effect of these LED fixtures is a combination of both additive and subtractive color mixing. Oh, and if you look directly at the UV LEDs without the protective diffuser screen installed, well, you better not look again with your remaining eye. Normal people, when we tell them this, back away, but for some reason, MIT students always need to check for themselves.
What do you do with an Ultraluminous Illuminator of Doom? Well, you shine it on artwork! Brian and his mother Janet went to great lengths to find pigments which work well under polychromatic precision light:
Continue reading Two Slashdottings In One House
Intermezzo: The Dirac Equation
After you’ve been Pharyngulated a couple times, you develop a protective strategy to deal with the aftermath. “How,” you ask yourself, “can I get rid of the extra readers whom I’ve probably picked up?” The answer, for me at least, is clear:
Math!
RECAP
Science After Sunclipse has been presenting an introduction to supersymmetric quantum mechanics. This area of inquiry stemmed from attempts to understand the complicated implications of supersymmetry in a simpler setting than quantum field theory; just as supersymmetry began in string theory and developed into its own “thing,” so too has this offshoot become interesting in its own right. In a five-part series, we’ve seen how the ideas of “SUSY QM” can be applied to practical ends, such as understanding the quantum properties of the hydrogen atom. I have attempted to make these essays accessible to undergraduate physics students in their first or possibly second term of quantum theory. Having undergraduates solve the hydrogen atom in this fashion is rather unorthodox, but this is a safe kind of iconoclasm, as it was endorsed by three of my professors.
The posts in this series to date are as follows:
- Part 1: Superalgebra
- Part 2: Shape Invariance
- Part 3: Two-Body Problem
- Part 4: Separation of Variables
- Part 5: The Hydrogen Atom
Having solved the “Coulomb problem,” we have attained a plateau and can move in several directions. The solution technique of shape-invariant partner potentials is broadly applicable; virtually all potentials for which introductory quantum classes solve the Schrödinger Equation can be brought into this framework. We can also move into new conceptual territory, connecting these ideas from quantum physics to statistical mechanics, for example, or moving from the non-relativistic regime we’ve studied so far into the territory of relativity. Today, we’ll take the latter route.
We’re going to step aside for a brief interlude on the Dirac Equation. Using some intuition about special relativity, we’re going to betray our Vulcan heritage and take a guess — an inspired guess, as it happens — one sufficiently inspired that I strongly doubt I could make it myself. Fortunately, Dirac made it for us. After reliving this great moment in TwenCen physics, we’ll be in an excellent position to explore another aspect of SUSY QM.
REFRESHER ON RELATIVITY
Let’s ground ourselves with the basic principles of special relativity. (Recently, Skulls in the Stars covered the history of the subject.) First, we have that the laws of physics will appear the same in all inertial frames: if Joe and Moe are floating past each other in deep space, Joe can do experiments with springs and whirligigs and beams of light to deduce physical laws, and Moe — who Joe thinks is moving past with constant velocity — will deduce the same physical laws. Thus, neither Joe nor Moe can determine who is “really moving” and who is “really standing still.”
Second, all observers will measure the same speed of light. In terms of a space-time diagram, where time is conventionally drawn as the vertical axis and space as the horizontal, Joe and Moe will both represent the progress of a light flash as a diagonal line with the same slope. (This video has some spiffy CG renditions of the concept.) To make life easy on ourselves, we say that this line has a slope of 1, and is thus drawn at a 45-degree angle from the horizontal. This means we’re measuring distance and time in the same units, a meter of time being how long it takes light to travel one meter.
Continue reading Intermezzo: The Dirac Equation
Teh Burning Stupid: Relativity Edition
To put the “moral” at the beginning, let’s summarize. If you want to raise my blood pressure, one good way to do it is to write a completely wrong, back-to-front absurd tirade against all of twentieth-century physics. Anyone can slip a few errors into an essay, or even a few “fundamental” errors, but if you want the brass ring, you need at the very least to misrepresent the special theory of relativity, the general theory of relativity, quantum mechanics, the use of mathematics in physics and the scientific method. Bonus points if you confuse general relativity with quantum physics; a woop-woop-woop special prize for taking a non-true assertion and calling it a “fundamental premise” of quantum mechanics; and an extra cherry on top if you take three famous observations which support general relativity, lie about two of them and forget the third.
The story so far:
- 14:06: PZ Myers finds a kook with some dumb things to say about Einstein.
- 14:09: I make a snappy remark,
- and then (14:33) I get kind of angry.
- No, wait, 14:49 is when I got really angry.
- 14:54 — have I calmed down?
- 15:56: maybe. . . .
- 16:06: Nope.
- 17:41: Dave Bacon reminds me to have a little fun in life.
- 18:10 An assistant professor by the ‘nym of “gg” writes a nice post on the matter, and promises more to come.
I might write an actual, non-linkfesty post about this. . . but then again, other corners of the Network are calling to me and reminding me of overdue obligations, so I might leave it to my colleagues.
UPDATE (6 December): gg now has Part 2 out on the blogonets.
UPDATE (16:47 o’clock): Tyler DiPietro dons the asbestos and joins the fun, followed quickly by Mark Chu-Carroll.
UPDATE (9 December): Flavin of the St. Louis Skeptical Society offers an essay.
I Get E-Mail
Below the fold is an e-mail I received this morning from Victor Senchenko, human space navigator, and his “Media Team.” According to his website, Senchenko can explain why homosexual humans exist (OK), why God doesn’t exist (not clear whether this is the Abrahamic tantrum-tosser or something more sophisticated) and why time also does not exist (and right there, we hear the fuses blow).
Greetings Blake,
Considering your involvement with science, the following Press Release may be of interest to you.
As an astute person, you probably would agree that for a long while humans – especially the scientists – had been claiming that they wanted to solve all the mysteries of physical existence. They have also repeatedly indicated that they wanted to understand the causes of human behavior.
I don’t know many scientists who’ve claimed they want to solve all the “mysteries of physical existence.” We’ll settle for solving one mystery big enough to get us tenure; the others are left as an exercise to the interested reader.
Continue reading I Get E-Mail
Rob Knop on Supernovae
Rob Knop, having decided to leave ScienceBlogs.com, has discovered that the SB Overlords will remove the archives of his blog sometime during the next couple months. Rather than let them vanish entirely into the memory hole like a factual comment on a creationist blog post, I thought I’d mirror a few here at Sunclipse. (In no way will Dr. Knop be responsible for answering comments on these mirrors, or anything like that; I’d just like to preserve the information.) First up is an essay from 10 October 2007, “Supernovae: the source of cosmic rays.” I have something of an interest in big stars going boom — check the SNEWS link over in the sidebar and say hello to my old colleagues — so I don’t want to see good explanations of this stuff slip away into the aether.
Continue reading Rob Knop on Supernovae
Nine Minutes of Science
OK, this is too good to pass up. Jim Blinn, the computer-graphics expert responsible for the Mechanical Universe animations — and therefore, responsible for filling my childhood with arrows — summarizes The Mechanical Universe in nine minutes. Watch all of first-year physics packed in a single morsel:
Blinn also worked on Caltech’s Project MATHEMATICS! series. I’m a little surprised that so few of the Project MATHEMATICS! videos have found their way onto the Intertubes yet. Here’s a “teaser trailer” of sorts, made from clips of “The Story of π”:
Continue reading Nine Minutes of Science
Superconductors via Superstrings
Nature has an article about a nifty and relatively new application of ideas born out of string theory: to understand what happens in high-temperature superconductors! The story goes something like this.
Take a sample of some material which can conduct electricity, and apply two kinds of outside influence upon it. First, stick it in a magnetic field pointing in some direction, and second, apply a temperature gradient in a direction perpendicular to the magnetic field. In some substances, an electric field will appear, perpendicular to both the magnetic field and the temperature gradient. This is called the Nernst effect. It doesn’t happen very much with ordinary metals, but in semiconductors — like silicon or germanium — it can be quite noticeable. It also appears in some superconductors, like Y-Ba-Cu-O and CeCoIn5 to name but two.
Sean A. Hartnoll et al. have cooked up a theory to explain the Nernst effect and other behaviors seen in the cuprate superconductors, ceramic compounds containing copper. Looking at the situation near the phase transition, where a substance is “on the verge” of changing from insulator to superconductor, they developed a theory involving the magnetic field, call it [tex]B[/tex], and fluctuations in the material’s density, [tex]\rho[/tex]. Then they looked at this theory in the conceptual mirror known as the AdS/CFT correspondence. This connection between seemingly disparate ideas takes you from a “conformal field theory,” the sort of math involved with the superconductor problem (among other things), to a theory of gravity in a type of universe called anti-de Sitter space. In this mirror-world description, the perturbations in [tex]B[/tex] and [tex]\rho[/tex] become magnetic and electric charges of a black hole sitting in the AdS universe!
Continue reading Superconductors via Superstrings
Link-Love
In the brief interlude between my morning of debugging PHP code — Semantic MediaWiki isn’t compatible with Cite.php, the bastards! — and my afternoon of category theory, I’d like to call attention to a few items.
First, an observation: for some reason I can’t quite fathom, I was able to adapt myself to using HTML entities for punctuation marks, writing — for — and the like, but my brain didn’t process the fact that HTML entities also exist for accented letters. Instead of typing, say, à to get à, I would hit Ctrl+T to open a new Firefox tab, hit the Tab key to move to the Search bar, type a French phrase which I knew had the accented characters in question, copy the characters I needed from the search-result summaries, and paste them where I needed them.
Searching was easier than typing. Now, that’s either a sign of advanced Internet-induced brain rot, or an indication that our interconnected world has definitively left TwenCen far behind.
OK, it could be both.
Next, interesting items recently spotted on the Weboblagospherenet:
Continue reading Link-Love
Detailed Calculations on the “EmDrive”
Last September, New Scientist magazine published a story about the “EmDrive,” a machine designed and built by the British engineer Roger Shawyer, who claimed that his contraption could produce a net forward acceleration by bouncing microwaves around inside a metal cavity. Onward to the stars, etc. Now, nobody else has been able to reproduce what Shawyer claims he’s seen, and Shawyer’s assertion that standard relativity and electromagnetism predict such an acceleration is, to put it mildly, nonsense. The conservation of momentum is built deeply into the mathematical structure of these principles, and so whatever the fine details of Shawyer’s machine, his claim is wrong.
It’s always possible that some new physics came raining out of the sky and landed in Shawyer’s garage, but if nobody can reproduce his “result,” there’s no reason to speculate about it.
Although basic tenets of E&M imply that radiation pressure can’t impart a net thrust to a closed cavity, it’s fun to see the details for how this works out, particularly in the sort of asymmetric conical shape which Shawyer built. Greg Egan has written up the details, in an essay I didn’t know about till now:
- Greg Egan, “Resonant Modes of a Conical Cavity” (29 March 2007)
He has pictures, too!
Scraping the Bottom of the Garden
Last Thursday night, while a bunch of us were eating sushi, we realized that something had to be done about our excessive indulgence in nerd humor. It was consequently declared, “Every time you tell a geek joke, God kills a fairy. Thus, you must after each such joke clap your hands and proclaim, ‘I believe in fairies! I believe in fairies!'”
For example, suppose I asked, “How do Communist electrical engineers study capacitors?”
“I don’t know, Blake, how do Communist electrical engineers study capacitors. . . Sigh. . .”
Continue reading Scraping the Bottom of the Garden
LOLScience!
Makyo picked up on my LOLCategory picture (“This category macro will, I suspect, make no sense to any of you, but amused me tremendously”). In the comments there, currytastegrit pointed to the lolscience LiveJournal community. My favorite there, I think — the one which truly made me “LOL” — was the following:
