Uncertain Principles

Weirdly, I'm the number two result on a Google search for "Jan Hendrik Schoen" (and the only page of the lot that's in English).

(I've also got two pages in the first ten results for "Orzel," despite sharing my surname with a famous submarine from the WWII Polish navy and a Polish textile manufacturer. Not that I'm keeping track, or anything...)

Of course, the strangeness of those results pales in comparison to some of the search requests that turn up in the referrer logs for steelypips (most of which go to Kate's nethack pages). I just don't really want to know what the people searching for "erotic dog stories" made of Kate's book log, though I am sort of curious as to why anyone would search for "drunks or ginghams or yet or economist or occlude" and what they thought of whichever Steelypips page that got them...

Posted at 12:09 PM | link | follow-ups | 2 comments

1) A photon with a wavelength of λ_i = 0.02 nm Compton scatters off a free electron, and the scattered photon moves off at an angle of 90 degrees to the original photon direction.

a) What is the wavelength of the scattered photon?

b) What is the kinetic energy of the electron after the scattering?

c) What angle θ_e does the electron move off at?

d) Scientists doing routine Compton scattering experiments annouce the remarkable discovery of a new type of particle. Using photons with a wavelength of 1.00 nm, they observed scattered photons with a maximum wavelength of 1.49 nm. What is the mass of the new particle in terms of the electron mass m_e = 9.1094 10^-31 kg?

2) A physicist sets up an idealized photoelectric effect experiment, shining light of different wavelengths on a metal plate, and measuring the maximum voltage difference developed between the plates as a result. Using light with a wavelength of 600 nm, he finds a maximum voltage of 0.23 V.

a) Using a different wavelength of light, he finds a voltage of 0.57 V between the plates. What is the wavelength?

b) What is the work function of the metal?

c) An ambitious young scientist from Bell Labs announces the discovery of a new metal called "unobtainium." He claims that, using an unobtanium photocell, he measured a stopping potential of 2.1 V for light at 600 nm, and a potential of 5.2 V for light at 400 nm. Being a sharp student of physics, you know immediately that he fabricated his results, and did a bad job of it. How?

3) For a laboratory experiment in quantum mechanics, you are given a proton (mass m_p = 1.673 10^-27 kg) which is trapped in an impenetrable one-dimensional. The box extends from x = 0 to x = L, and the potential energy is zero everywhere inside the box.

a) What is the normalized wavefunction of the proton in its lowest energy (ground) state?

b) What is the probability of finding the proton between x=0 and x=L/5?

c) What is the energy of the proton in the ground state if L = 100 nm?

d) What is the typical speed of the proton in the ground state for L = 100 nm?

e) As part of the lab, you double the size of the box, while keeping the proton energy the same. What is n for the proton in the new box?

Posted at 7:36 AM | link | follow-ups | 2 comments

Eric Olsen asked people to post "Top Ten" lists of some sort this week. Having posted a list of "Perfect Albums" a while back, I'm half tempted to just beg off. I like listening to myself type, though, so I'll post a slightly different list. Not a "top ten albums" list, but something like a "ten top albums" list-- top albums in various (mostly flippant) categories from my collection of CD's.

• Top Album That Should've Sold a Billion Copies, But Didn't No question here, it's 1965 by the Afghan Whigs. This is the only overlap with the "Perfect Album" list. Featuring their trademark mix of blue-eyed soul crooning and alternarock skronk, with the angst turned down from 11, this is the Afghan Whigs party album, if you can believe such a thing. Greg Dulli's got a little wine, some Marvin Gaye, and a kick-ass backing band-- buy the album, enjoy the party.
• Top Album That I Was Faintly Embarrassed to Buy in a Store. Take Off Your Pants and Jacket by Blink-182. I'm over thirty, and never did own a skateboard, which puts me outside this band's demographic by about fifteen years, but for some reason, I really enjoy a lot of the pop-punk bands that I end up associating with annoying skateboarders (an association that's also probably five years out of date. Whatever.). These guys are really good at what they do-- "Rock Show" is pure pop gold-- but they always throw one cringe-worthy song on for the amusement of their fourteen-year-old core audience ("Happy Holidays, You Bastard," which appears to exist solely for the amusement value of saying "I'll never talk to you again,/ Unless your dad will suck me off"), and I hate the "So, you're buying this for... your kids?" look from the tattooed high-schooler at the record store. I'll order the next one of these I buy on-line.
• Top Obscure Album Bought Due to Vague Personal Connections. This one's a tie, between an Acoustic Junction album that appears to be titled Acoustic Junction (which I can't find on Amazon), and Play Each Morning Wild Queen by the Flash Girls. The former I bought in a Borders in DC, having seen the band play a couple of times back when I was in college, once in an art museum (one of the band members was also a cousin of somebody I played rugby with). The second Kate bought after we saw the Flash Girls perform at Boskone, and is notable for featuring a couple of funny songs written by Neil Gaiman. Also, noted fantasy author Emma Bull is one-half of the Flash Girls...
• Top Album Bought Because of an In-Store Performance. Awake by John Wesley Harding. I wandered into Borders looking for something else, and John Wesley Harding was playing in the record section, down in the basement. I was curious to see what sort of music you'd get from a guy who named himself after a Dylan album, so I went and listened. He was a very funny guy, and didn't seem at all distressed by the fact that he was playing to a crowd of about fifteen people in the basement of a bookstore in Gaithersburg. It's a good album, too, but I would've bought it just for the show, and the rant about how Titanic is the dumbest movie ever.
• Top Obscure Album Bought on the Strength of One Song and an Interesting Band Name. A very competitive category, this-- Fountains of Wayne are strong contenders (though I was tipped into buying that one by the song titles "Leave the Biker" and "Please Don't Rock Me Tonight")-- but I'll give the nod to Mono by the German band Fury in the Slaughterhouse (which is probably all one big word in German), because I can also give them Worst Follow-Up to an Obscure Album I Liked for The Hearing and the Sense of Balance. The former, I bought because WHFS was playing the single "Every Generation Got Its Own Disease" quite a bit, and it was a nicely moody generic-alternative song that fit my mood well at the time. The rest of the record turned out to be pretty good, so I bought the follow-up, which was really dire (or at least I remember it that way-- I haven't listened to it since just after I bought it).
• Top Album Bought on the Strength of One Song That Sounded Nothing Like the Rest of the Album, Damnit. In the same vein, this award goes to Rocket by a guy who billed himself as "Primitive Radio Gods." You know the song I mean-- that one with the B.B. King sample ("I been downhearted, baby/ Ever since the day we met") and the faintly dream-like lyrics. The rest of the album is nothing like that, and is, in fact, amazingly awful. The "Parental Warning-- Explicit Lyrics" sticker should've been a tip-off. Buying this was a huge mistake, but still, the one song is really good...
• Top Album Bought On the Strength of a Recommendation in the Back of a Book. Shoot Out the Lights by Richard and Linda Thompson. At the end of my copy of War for the Oaks by the aforementioned Emma Bull, there's a list of albums that she listened to while writing the book (which is about a rock band's battle with Faerie). I liked the book, and it had some great bits about music in it, so I looked for some of the items on the list the next time I was in a record store. This was the only one I found, but it's very good indeed. Weirdly, I still haven't bought any other albums by the two of them. I really ought to. (OBHookForComments: Which one?)
• Top Fifty-Dollar Box Set. Hitsville U.S.A.: The Motown Singles Collection 1959-1971. OK, this is cheating a bit, as I don't own a lot of box sets, but I really ought to have one vaguely serious category on the list. Plus, I've been listening to some of it in the car for the last few days, in an effort to improve my mood (Animals, exam grading, and electoral politics had increased my normal level of bitter cynicism to dangerous levels). And really, sometimes a little Motown is just what you need-- a flash back to a time when pop music was just pop music, a celebration of (mostly teenage) love (requited and otherwise), without the need to make an Important Statement in every song. And there aren't many people who can raise dippy pop songcraft to the level of Art the way Motown's team of writers and performers could.

And that's probably enough albums, Amazon links, and weird personal confessions to make a point of some sort, so I'll stop there.

Posted at 9:51 AM | link | follow-ups | 2 comments

I kinda-sorta feel like I ought to say something about the election, but, well, I gave an exam recently, and I've got a $50,000 term paper due next week, and I'm buying a house, and it's all just too depressing to spend a bunch of time ranting about the foolishness of the Democrats and the perfidy of the Republicans. My main reaction has been "Well, at least I won't have to listen to another annoying goddamn Tom Golisano spot..."

Happily, Teresa Nielsen Hayden had some things to say, and said plenty.

I think she has a bit too much faith in the inherent Power of Being Nice-- Aaron "Blogspot Sucks" Bergman (his permalinks are broken at the moment-- it's the Nov. 6th entry) has a point, too-- but much of what she says is spot-on. And she writes really well. Go read it.

Posted at 8:28 AM | link | follow-ups | 1 comment

So, why "relativity" as a name for all this?

Formally, Einstein's theory comes from two principles. The best-known one is the idea that the speed of light is a constant, that all observers regardless of their velocity see exactly the same speed of light. Only slightly less well known is the principle which gives the theory its name, the Principle of Relativity.

As noted earlier, the basic idea pre-dates Einstein by quite a bit. The idea that there's no way to distinguish between a situation where you're moving past stationary objects at constant velocity and a case where you're stationary and the rest of the world is moving past you at constant velocity traces back to (or at least is attributed to) Galileo. Prior to Einstein, though, it was only applied to the motion of objects-- "Galileian Relativity" is the statement that the laws of motion (F = ma and all that) are the same for all observers moving at constant velocity.

Formally, Einstein extended this to all the laws of physics, including things like Maxwell's Equations. Einsteinian Relativity is the idea that all the laws of physics are the same for all observers moving with constant velocity; or, stated another way, that there's absolutely no way to distinguish between frames of reference. You're not allowed to determine unequivocally that one person is moving, while another is stationary-- relative motion is all that matters.

Everything else follows from this, including the constancy of the speed of light (which Einstein listed as a second principle just to hammer home the point). If light moved at different speeds for different observers, then you could determine which person was moving by having each of them measure the speed of light and compare the results. Since that would violate the Principle of Relativity, it's not allowed, and every observer must measure the same speed of light.

It's an incredibly simple idea, but also an amazingly powerful one. It leads to all sorts of amazing consequences, from time dilation (moving clocks run slow) and length contraction (moving objects seem to shrink), to the unification of electricity and magnetism (what Brad DeLong was talking about), to E=mc² and all the rest.

It's also a philosophical revolution of sorts, attacking the idea of an absolute universe whose properties could be determined by sufficiently clever scientists. That idea was a cornerstone of scientific thinking up through the 1800's, so relativity, with its idea that only relative motion, never absolute motion, could be determined shook science to its foundations. In a sense, it was the first step in a process of creative destruction that quantum mechanics, which showed that even relative motion is fundamentally indeterminate, finished off.

But that's a weighty subject, and one for another day.

Posted at 7:40 AM | link | follow-ups | no comments

A post on Brad DeLong's weblog reminded me that I still haven't finished my discussion of relativity, begun a month and a half ago. If you want to understand the rest of this post, go back and read that one. Go ahead, I'll wait.

OK. Toward the end of that whopping huge post, I wrote:

It turns out that the common-sense argument is like one of those joke proofs that 1=2. They look convincing for a little bit, but there's always a step in there where you divide by zero, and all bets are off after that. It's not a divide-by-zero error, but there's a subtle mistake in the argument that leads to the conclusion that light should move at different speeds-- a mistaken assumption so basic that most people don't even notice making it.

And said that Einstein's theory of relativity is, in large part, about what happens when you stop making that assumption. So what was the assumption in question?

Fundamentally, the question here is one about relative motion, and how the same events are perceived by observers moving at different velocities. The perceptions of different observers can be very different indeed: if you're standing on the side of the road watching a little old lady drive by, it looks like she's moving from left to right at 30 miles per hour; on the other hand, if you're in a car coming up behind her, not only is she going too goddamn slowly, she appears, from your perspective, to be moving back toward you (from right to left) at 30 mph. As an aficionado of driving games could tell you, there's no perceptible difference between a case where you're moving forward, and a case where you're sitting still and the rest of the world is rushing toward you. In physics, this indistinguishability is referred to as the "principle of relativity," which actually pre-dates Einstein by a couple hundred years.

So how do we describe this situation? Well, in the classical world, we can describe the position of an object at any given instant with four numbers: three space coordinates (measuring position along axes running East-West, North-South, and Up-Down for example) and one time coordinate. For convenience, we can choose the motion to be along one of the axes, traditionally called the x-axis. We can track the position of moving objects by following x,y, and z coordinates over time.

If we've got a track through space describing the motion of some object as measured by a stationary observer, then, how do we convert that to what would be seen by a moving observer? Well, classically, if you're moving along the x-direction, nothing changes along y and z-- the person standing by the side of the road and the person driving the second car both agree on the height and width of the little old lady's car. Only the x-values change, and in a very straightforward way-- if you want to know the velocity of some moving object seen by a moving observer, you just take the difference in their velocities, to get the relative velocity. Somebody who's stationary sees a little old lady moving in one direction at 30 mph, while somebody moving at 60 mph sees her going in the other direction at 30 mph. And, of course, all three of these people agree on what time it is.

Or do they? It turns out that that last assumption-- that everybody agrees on the time-- is the mistaken one. That's the stumbling block that trips everybody up, and it's such a basic assumption that most people don't even notice making it. When I said "Everybody agrees what time it is, right?" in class, I got a collection of looks that said, basically, "Who let this clown out of the nuthouse?"

To fix the conflict between Maxwell's Equations and common sense, though, that's the assumption you need to lift. People knew this before Einstein came along-- Lorentz and FitzGerald had pointed out that a different sort of transformation between stationary and moving frames of reference could explain the Michelson-Morley results (It's called a "Lorentz transformation" in their honor. Why FitzGerald gets screwed out of a named equation, I don't know)-- but it never really went anywhere, in part because the idea of universal time was so deeply entrenched. Part of Einstein's great achievement was not just realizing that this was the case, but managing to convince everybody else that it not only was true, but had to be true.

The classic explanation of this is to consider an odd sort of "clock." Take two mirrors, separated by some distance (one above the other, for example), and set a short pulse of light bouncing back and forth between them. Whenever the light hits one of the mirrors (the bottom one, say), we record that as a "tick." It's an odd sort of clock, and it'll "tick" very rapidly, but there's no reason why you couldn't use that as your clock.

Now, let's think about what happens with the clock as seen by two different observers. An observer moving with the clock will see it as stationary, and it'll behave just like a stationary clock. The light bounces straight up and down between the mirrors; if we call the distance between the mirrors "L," the total distance traveled by a light pulse is "2L," and the time between "ticks" is just the round-trip distance divided by the speed of light (2L/c).

Now, think about what an observer watching this clock go past sees. If the light leaving the bottom mirror went straight up, by the time it got to the top mirror, it would actually miss the mirror, which moved during the time of flight. So the light really needs to be directed at an angle, as seen by the stationary observer-- it's tilted toward the direction of motion. Likewise, on the return trip, the light can't go straight down, but again, must be tilted in the direction of motion. The light path seen by a stationary observer watching a moving clock isn't a straight up-and-back track, then, but rather a triangular path, like the legs of a capital "A."

(This might make more sense if you think about material objects. Somebody moving in a car can toss a ball up in the air, and they'll see it go straight up and come back down. A stationary observer watching this will see a parabolic arc, as the car moves by.

(It actually occurred to me that there's a decent sports example of this, which sadly makes no sense to most of my countrymen: you'll sometimes see very good rugby players loft a little kick over the head of a defender, and run under it to catch it. From the sidelines, it looks like the ball follows an arched path, and the runner has to be pretty clever to end up directly underneath it, but from the runner's perspective, the kick is more or less straight up, and there's no trick to it at all-- what goes straight up, comes straight back down...

(Not that I lofted a lot of clever little pop kicks in my playing days. If I was involved in such a play, I was usually the befuddled defender watching the ball sail over my head. But I digress...)

Now, think about how much time is involved in this process. The light in the moving clock, according to the stationary observer, actually travels a distance greater than 2L, and thus takes longer than 2L/c between ticks (exactly how much longer depends on how fast the clock is moving). But the moving observer sees it take exactly 2L/c-- they disagree on the time between "ticks," and thus they don't agree as to what time it is. Weirder still, the moving observer looking at a stationary clock will see it running slow.

You can't fix this disagreement in any simple way, and part of what Einstein did was to say that you shouldn't even try. If you look at how much the clocks differ in their "ticking," it turns out to be exactly the amount needed to fix the problems with Maxwell's Equations-- this difference, then, is something fundamental to the way the Universe works. Moving clocks appear to run slow, and observers moving relative to one another will disagree about the timing of events.

This seems bizarre, but has been experimentally verified. The shifts involved are tiny-- clocks in supersonic jets run slow by nanoseconds (one-billionths of a second) over trips measured in hours-- but people have done the most obvious experiment to test this, flying a sensitive atomic clock around the world, and then comparing it to one that remained stationary, and they found a difference between the clocks that agreed exactly with the predictions of relativity. Numerous other tests of relativity confirm this prediction, and others even stranger.

Why don't we see these shifts in daily life? We don't notice the difference between moving clocks because the shift is extremely small unless the clocks are moving at a good fraction of the speed of light (2.9979 10⁸ m/s, or 186,000 miles per second). Newtonian mechanics is an excellent approximation to reality at everyday speeds. But when you start talking about light, or even electrons moving around in ways described by Maxwell's Equations, you need to take relativity into account, and the world is a much stranger place than you think.

Posted at 7:39 AM | link | follow-ups | no comments

Aaron Bergman responded to my earlier snarky comments about the Bogdanov scandal in high energy physics. One thing Aaron notes, which I should've noted, is that, claims to the contrary aside, the journals the Bogdanovs were publishing in were hardly the most prestigious journals in physics-- I've read the occasional article from Annals of Physics, and seen some citations from Il Nuovo Cimento, but the Chinese Journal of Physics is one of those journals that non-Chinese physicists send publications to primarily when they're trying to pad out their CV before tenure review. These are journals that probably don't see a whole lot of string theory, and probably have a hard time getting anybody to referee anything, so a breakdown of refereeing there is marginally less scandalous than a similar breakdown at the Physical Review would be.

(I have no idea how those journals choose referees-- I've refereed papers for Physical Review A and Physical Review Letters, because I've published in those journals, which means they have my address. I also refereed a paper for the Journal of the Optical Society of America B once, because I used to borrow equipment from the editor, and he asked me to take a look at it. I doubt I'd turn down a request from Annals of Physics, but I'm not sure how they'd know to ask. Unless they read this blog, in which case I can probably expect a veritable flood of string theory papers from them soon...)

Aaron also takes issue with my concerns about the preprint server in general, saying:

I'm less clear, however, on how Chad thinks that someone is going to defraud the community. One important distinguishing fact about high energy theory right now is that we don't have any data to make up. The papers are all ideas and math.

Of course, a few months ago, most scientists probably would've said something along the lines of "I don't know how somebody would defraud the scientific community. The data have to be replicated before anybody will believe them." That's what produces the smugness that leads to the Sokal hoax, after all-- science is superior to postmodernism, because science is continually checked against reality.

That failed pretty miserably in the Schoen case. In some limited, unhelpful sense, the system did work, as it was the failure of numerous groups to replicate the data that finally called the papers into question, but people bought into his supposed work right away, without any of the skepticism they should've had. Schoen succeeded in part because his fraud was so brazen. Nobody could really imagine that anyone would so blatantly fabricate data, so they accepted the fraud until a preponderance of evidence changed their minds.

I have a hard time believing that a lack of data is any surer grant of invincibility than a reliance upon data was (but then I'm an experimentalist by nature, and don't believe anything without data). I don't know exactly how somebody would defraud theorists, but then I wouldn't've known how anybody could defraud experimentalists a few months ago. Never underestimate the ingenuity of the corrupt.

In the end, what we're seeing here is largely a result of years of complacency. Lots of shoddy stuff has snuck into print over the years, and I'd wager that Schoen's wasn't the only blatant fraud published, either. Everybody had too much faith in the process, and people stopped putting in the careful work that is required to make the process work. If I had to make a prediction based on recent events, I'd say that we can expect several more revelations of scientific fraud through shoddy fact-checking before things get back to normal. And I expect it'll be a lot harder to get papers through the refereeing process for the next few months-- I know I'll be looking more closely at whatever they send me. (OK, that's two predictions. Nobody expects the Polish Inquisition!)

In the end, I'm still more comfortable with the idea of peer review before publication. I like having a system in place that provides at least some checks on the dishonest, even if it doesn't work all the time. I've installed (or, rather, given up after trying to install) too much crappy open-source software to be happy with the preprint server model.

Posted at 7:39 AM | link | follow-ups | no comments

Having taken a couple of shots at Jim Henley, I should give a positive mention to the new collaborative weblog he's part of. Stand Down aka "No War Blog" is a collection of people from all across the political spectrum posting in opposition to the seemingly inevitable war with Iraq. There's some interesting reading on the site, as people from widely divergent ideologies give careful, principled statements of why they oppose the war.

They've got a "join us" link there, for those who are interested. I'd add my name to the list, but it doesn't feel quite right, as my objection to the war isn't really founded in deep political principle, so much as a conviction that the people currently planning the war are fundamentally dishonest and undemocratic. I could support (and happily would support) a different war on Iraq, but I can't support one arranged by a pack of dangerous lunatics.

Posted at 7:28 AM | link | follow-ups | 1 comment

Jim Henley responds to my vigilantism comments:

Chad seems to argue that any heavy- handedness by government law enforcement merely reflects baleful tendencies in the population. He also avers that, if anything, government law enforcement acts as a damper on public mania. It apparently never acts as an amplifier, or forms self-contained institutions that channel and cultivate the worst impulses of the populace for its own benefit.

I wouldn't be fool enough to claim that government law enforcement never acts as an amplifier for the ill will of individuals. Government is too complicated a system for such a simplistic description to be right-- indeed, in the specific cases being argued about, it almost certainly acted as both amplifier and damper. The recovered-memory sex scandals sprang in part form the over-zealousness of a handful of prosecutors who were able to use the system to amplify the affects of their misapprehension, while in other places, the general inertia of the legal system prevented some cases from coming to trial before the whole thing had been debunked, sparing some people legal sanction as a result of public hysteria.

My point is that I don't think that situation (or some of the other cases mentioned) would automatically have been much less of a debacle under a system where the government had less power, and private citizens were encouraged to take on law-enforcement duties. It's not hard to imagine ways in which it could've been worse than it was. Part of the reason we don't have vigilante mobs running around killing people is precisely the fact that the government can be made to do the work instead (albeit more slowly). A reduction in the power of government law enforcement might well reduce the incidence of formal abuse by government agents, but a shift of that power to the "pack" might not be a real improvement.

There's probably some middle ground between what we have now, and a pure "pack" system that would be an improvement, but ultimately, if you want to get rid of the problem of heavy-handedness in law enforcement, by government or otherwise, you're really asking for a change in human nature. These problems really arise from a combination of gullibility and ill will, and we're pretty much stuck with those.

(I also thought I qualified my statements more than Jim seemed to think, but then my inability to precisely calibrate what I write to ensure that it comes across the way I intend has been amply demonstrated before this...)

Posted at 7:15 AM | link | follow-ups | no comments