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Posts Tagged ‘Physicist’

I suspect there are hundreds of physics classrooms across the country that have the following poster:

10314603This is the CENCO (Central Scientific Company) poster of the famous 1927 Solvay Conference. I’ve been to at least three universities that have this thing on the wall, including my own institution, Western Carolina University, and my alma mater, Wake Forest University. Strangely, I can’t date the poster, although if you read the descriptions of the 1927 Solvay attendees, the poster lists Dirac as being dead and De Broglie as being alive. Ergo, the posters were printed some time between 1984 and 1987. I suppose CENCO gave the posters away for free as a promotional during the Reagan administration, and I’d guess most of those freebies are still hanging on the wall today. (Physicists don’t update their décor very often.)

I’ve spent a fair amount of time looking at this poster (sometimes, the life of a lab instructor is dreary). And, in all my time staring at these giants of modern physics, I’ve formulated one burning question:

Which of these people was the dumbest?

[Note: I used this site for a listing of the attendees in the famous photo]

Don’t get me wrong; I’m not claiming anyone in the poster is dumb per se. And I would never compare myself to anyone on the list. But logic dictates that one of the people here was literally the dumbest attendee; I feel a moral obligation to identify this person for posterity.

Most of the names on the poster are familiar to physicists, and most of the attendees are therefore out of the running. No one would ever seriously consider Einstein, Curie, Dirac, Bohr, etc. as being the “dumbest.” On the other hand, some of the physicists aren’t so familiar, but they were obviously talented: Guye wrote over 200 papers; Knudsen had a bunch of crap named after him (Knudsen cell, Knudsen flow, Knudsen number, Knudsen layer and Knudsen gases). Piccard and Langmuir fall into this category as well.

And then there are the scrubs flanking Ehrenfest,

Picture1

Henriot, Ehrenfest, and Herzen

and the scrubs flanking Schrödinger,

Picture2

de Donder, Schrödinger, and Verschaffelt

These scrubs are so scrubby that the CENCO poster doesn’t even talk about them.

Surely one of these fools was the dumbest?

Let’s take them in order. Henriot was a chemist, so that’s a strike against him; he discovered that potassium is naturally radioactive, which is cool I guess, and figured out a way to make tops spin at high speeds. Woop-de-do. Herzen was a friend of Ernest Solvay, but didn’t really do anything else of note; I think we know how Herzen got an invite to the conference, don’t we?

Being a mathematician, de Donder probably gets a pass: he also wrote a shitload of books. The final scrub, Verschaffelt, is notable as having the shortest Wikipedia article of any Solvay attendee. Basically, all I can find out about him was that he was a physicist. Period.

Before we decide between Herzen and Verschaffelt, we should mention two other physicists in the poster. Compton once said, “the supernatural is as real as the natural world of Science,” so I’m tempted to list Compton amongst the scrubs. Anyone with so much woo in his veins can’t be listed amongst the top tier of physicists. Compton did win a Nobel prize though, and he was American…we have to disqualify him, then. America, fuck yeah! That leaves Ehrenfest, who was by all accounts a clever guy. But come on, the guy shot his own son and then killed himself. That’s hard to get past. I guess we’ll chalk that up to mental illness, not stupidity, but no one is ever going to make an Ehrenfest action figure.

Parents snub traditional action figures in favour of such as historical icons as Einstein and Van Gogh

None of these for Ehrenfest.

So who was dumber, Herzen or Verschaffelt?

Herzen wrote a book or two, and supposedly played a “leading role” in physics and chemistry. So I’ll give him the nod over Verschaffelt. Thus we can tentatively say:

Verschaffelt was the dumbest attendee of the 1927 Solvay Conference.

Scrub

“I’m still smarter than you.”

You’re welcome.

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thinker

I’ve had the following conversation at least a few dozen times:

“So where do you work?”

Me: “I’m a professor over at the university.”

“What do you teach?”

“Physics.”

“Physics?  Yikes!  Physics is hard.”

Mathematics and chemistry folks that I know get similar responses.  The unspoken assumption is, why would you want to study something so difficult?

Well, why wouldn’t you?

This leads me to my main point.  When asked why I decided to study physics in the first place, my response is usually “Because physics is hard.”  To me, that’s a sufficient reason.  Not necessary, but sufficient.  I can’t imagine having a job that wasn’t mentally challenging.  Well, unless they paid me enough.

My first exposure to physics (not just science but physics) was in high school, 10th grade I think, when I read a copy of The Dancing Wu Li Masters.  Today I know this book is full of new age nonsense, Deepak Chopra-esque mumbo jumbo, but of course I couldn’t know that at the time.  All I could see at the age of 15 was this great bizarre world of quantum weirdness, and what’s more people were still investigating it.  There was work to be done.  Any copy of Bullfinch’s mythology, or any religious text for that matter, was full of similar bizarre weirdness, but those fields of study seemed static and dead.  But quantum mechanics?  You mean people get paid to think about this shit, and study it in a laboratory?  Count me in!

I was lucky enough to recognize at the time that I didn’t yet have the toolkit for thinking about these kinds of things.  Without a working understanding of calculus, without following the trajectory of physics history into the early 20th century, without seeing the careful, subtle arguments of the physics greats, one can’t really get a handle on quantum mechanics at all.  I wish I had a dollar for every time I met someone who claimed to know “all about” quantum mechanics because they watched a Nova episode about Schrödinger’s cat.  But sorry, quantum mechanics is primarily (arguably entirely) a mathematical theory and as such there are no shortcuts to understanding.  Read as many Brian Greene books as you like…read my book, while you’re at it…but all that can really do is whet your appetite for more advanced study.

That’s what happened to me.  I read a new age book filled with nonsense, but that had enough physics to get me interested.  I wanted to learn more than the author; I wanted to be able to tell him where he was wrong.  (I can certainly do this now.)  And I stuck with physics because it’s maddeningly difficult.

Don’t be afraid of learning difficult things.  Study physics.  Take up quilting.  Learn to play the violin.  Learn how to fix a boat.  Read a book about the Crimean war.  Invent a recipe for Baked Alaska.

If it’s not difficult, then why are you bothering with it?

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War is nothing like chess.

War is nothing like chess.

I am a big chess fan.

I can name every chess world champion since Morphy; I could probably name around 17 of the world’s current top 20; I can checkmate a lone king with two bishops and a king; I have a good working knowledge of just about every opening there is.

(And by working knowledge, I don’t just mean I’ve “heard” of the Sicilian defense.  I don’t just mean that I know that 1. e4 c5 2. Nf3 Nc6 3. d4 cxd 4. Nxd4 Nf6 5. Nc3 e5 is the Sveshnikov.  I mean that I am fully aware of the differences between the 9. Nd5 and 9. Bxf6 Sveshnikov, and prefer the former.)

The problem is, I’m just not that good.

Oh, I can beat most casual players…the ones that begin a game by moving a rook pawn (to a4, say) and then move their rooks out vertically (to a3, say).  In USCF rating terms, my rating is around 1800, which (to my own surprise) is about the 85th percentile for tournament players.  So objectively, I am not bad at all.  But I am good enough to be aware of just how much better other players are.  I have a friend Shawn who is a master (here he is drawing a grandmaster).  I am in awe of his tactical strength, and his fine sense of dynamics.  I have beaten him dozens of times in speed chess, but for every game I win, he wins 10.

It has taken me a while to get to the point of this blog post, which is this: I like chess because of its icy logic and its mathematical purity.  For this reason, chess is a horrible metaphor for war, or for life.

Chess is used in books and movies for two basic purposes.  The first is to establish the intelligence of a character.  For example, Lisbeth Salander (in The Girl with the Dragon Tattoo) is an expert at chess.  This was a bad choice on the author’s part: Lisbeth is also an expert hacker and financial genius, has an eidetic memory, and is an incredible detective—why stretch credulity even further?  A lot of great chess players are certainly smart, but the correlation doesn’t go the other way: many smart people are terrible at chess.  Einstein was probably weaker than me.  Oppenheimer was even worse.  Comedian Howard Stern, a player of about my strength, would crush either one.

The other use for chess in books and movies is as metaphor.  In The Seventh Seal, Antonius Block plays a game of chess against Death.  In Harry Potter and the Philosopher’s Stone (the original title; not the dumbed-down American version) someone plays chess with someone else (like I remember?)  In both cases the chess itself is ludicrous.  For example, at one point Death captures Block’s queen; Block says that he “didn’t see that”.  (Really?  Did Block just learn the rules the day before?)  But I don’t want to evaluate the chess in such works per se; rather, I want to see how well chess works as a metaphor.

First, chess as war.  I can’t think of any examples off the top of my head, but there seems to be an assumption that skill at chess somehow equates to skill at war.  But this is ludicrous: in chess, every move is transparent; you can always see what your opponent is doing, and everyone starts on a level playing field.  In terms of game theory, chess is a perfect information game.  I’m no Colonel Dax, but I don’t think war works that way.  There is always a fog of war, and an element of chance, so war is about contingencies, and adaptability, and bluff, and extrapolation.

Second, chess as life.  I have to admit, I don’t really get this metaphor at all.  Is life therefore a game?  A perfect information game?  If chess represents life, does that mean that I struggle throughout my life against an opponent (Satan?  Howard Stern?) who is trying to thwart me at every turn?  And if I play well, but my opponent does too, then am I destined for a draw?  What is a draw, in life?  Is it retiring at 65 to play shuffleboard in Orlando?

As much as I like chess, I think backgammon is a much better metaphor for war or for life.  In backgammon, there is an element of chance, and so the “the best laid schemes o’ mice an’ men” will often go awry.  That is why a good backgammon player will weigh contingencies.  What move leaves me in the best position, based on what dice rolls are possible, and what might happen?  In backgammon, you’re not just playing against an opponent, you’re playing against the fates themselves (in the form of the dice) and this makes the game feel more “real” to me.

People who don’t play backgammon often think that luck is a major part of the game.  This is true, on the level of a single game, but backgammon is played in matches of multiple games, and luck is much less important at that level.  This is because of the doubling cube.  With the doubling cube, a master will almost always defeat a weaker player, in the same way that a Napoleon will almost always win a war against a General Mack, even if an individual battle is lost here or there.

And so, life.  The dice aren’t always going to go your way.  You should plan with that in mind.  Look at your current position, figure out the possible contingencies—the possible ways God might play dice with your universe—and set up your pieces accordingly.  Even if you get gammoned, tomorrow’s another day.

[Note: I subconsciously chose an inept Austrian general to be the foil against Napoleon’s military genius.  But I want to be balanced in my portrayal of Austrians.  So I will remind everyone that Lise Meitner was Austrian, and she was a super-smart physicist.  And strangely, her father was Philipp Meitner, a chess master and part of the immortal draw.]

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As a physics professor, I have certain pet peeves.  For example, I cringe when someone says that “gravity” is 9.8 m/s2 when they mean the acceleration due to gravity.  I’m annoyed if someone says that an object “weighs” 7 kg.  And I stifle a laugh if someone says that a roller coaster is exciting because it goes so “fast”—humans can only detect acceleration, not speed, which is why we don’t notice that we’re traveling something like 67,000 mph right now in our orbit around the sun.

goose

“I feel the need for acceleration!”

But my biggest pet peeve may be students doing algebra with numbers.

Fellow physics professors will know exactly what I’m talking about, but for the uninitiated, here’s an example:

If you drop an object from a height of 20 m, how long will it take to hit the ground?

A student knows that a kinematics equation is needed, hits upon the correct one, Δyvi Δt + (1/2) a Δt2, and then correctly identifies Δy = –20 m, a = –9.8 m/s2, and vi = 0.  So far, so good.  They’ve studied their physics, right?  What happens next is sheer madness:

algebra_with_numbers

Sigh.

Over and over again I tell students, “don’t plug numbers in until the end.”  But students love plugging in numbers.  They feel they’re actually getting closer to the answer if they’re manipulating numbers.  On some level, they still feel uncomfortable with letters—as if manipulating letters isn’t really “math”.

How does this problem look in my answer key?  Like this:

algebra 2

You can now plug in values if you like…and get Δt = √[2(-20)/-9.8] = 2.02 s.

Which of these approaches is more beautiful, more powerful?  The approach you pick indicates whether you “get” algebra or not.  If you do algebra with numbers, the answer you get is very narrow and very specific, even if you do it correctly.  That hypothetical student could have gotten 2 seconds as an answer, and I would have given them full credit.  But their answer would have been ugly.

The second approach is beautiful, because it is completely general and applicable to multiple situations.  I try to tell students “Look!  You found the time to fall a certain distance.  You now know the answer no matter what the height is, and even no matter what planet you’re on, since g doesn’t have to be 9.8 m/s2.”  This is usually followed by a blank open-mouthed stare, much like Kristen Stewart in a Twilight movie.

There is a more practical reason to avoid doing algebra with numbers.  It’s simply that when you do algebra with numbers, other people cannot follow your work as easily.  And then, if you make a mistake, it’s harder for someone else to spot.  Quick: what algebra error did the student make above?  It takes a while to find the mistake.

My ultimate point is that students need experience seeing the power of algebra.  It’s all well and good that algebra classes stress real-world applications—else, why teach algebra in the first place?  But real-world doesn’t only mean with numbersE=mc2 is certainly a real-world application of algebra, and it’s a lot more elegant than saying that 378,000,000,000,000 Joules is released when a teaspoon of sugar with mass 4.2 grams  is converted to pure energy, given that the speed of light is 300,000,000 m/s.  The hard part, for us physics professors, is to help this spoonful of algebra go down.

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Einstein circa 1905

There are a lot of people who, to this day, deny the truth of Einstein’s special relativity (SR).  I’m not even referring to the OPERA superluminal neutrino debacle—an anomaly that was eventually found to be caused by a misconnected fiber optic cable.  No, I’m referring to laymen who deny SR because it goes against common sense.

A Google search will find such people readily.  Most of the time, their arguments aren’t even worth refutation, since it’s obvious in most cases that they haven’t mastered even the simplest algebra, much less sophomore-level physics.  (I am planning to use this gem in my Modern Physics class in the spring as a homework problem: for 20 pts., find the elementary flaw in this person’s logic.)  However, as a working physicist, I sometimes find myself dismissing such people too readily: it is easy, and self-gratifying, to call such people cranks.

A person who doubts SR is not necessarily a crank.  After all, relativity is very counter-intuitive, and our brains have been exquisitely fine-tuned by natural selection to perceive the world as inherently classical.  In fact I will go so far as to say that if you accept SR whole-cloth, without any mathematical or scientific background, then you’re basically showing a blind faith in science in the same way that Iotians have a blind faith in “The Book”.  I would rather beginning physics students showed some skepticism; it makes their final “conversion” that much more intellectually pleasing.

I think the main problem with perceptions of SR is the way it is normally presented.  My thesis is this: most physicists are teaching it wrong.  And as a consequence, many people who have studied SR come away with a misguided notion of what SR is all about.

The old way to teach SR begins with Einstein’s two postulates.  The first is that the laws of physics should be the same, in any inertial reference frame.  The second is that the speed of light is the same for all inertial observers.  There is then an obligatory picture of a train and lightning bolts, and talk about how simultaneity isn’t preserved in SR.  This leads (usually after a lengthy derivation) to time dilation and length contraction.  And then, out of the blue, there might be talk of the twin paradox and the obligatory pole vaulter in the barn.

Shudder.  Such a pedagogically confusing approach!  No wonder very few first-time SR students “get it” at all.

The original train picture from Einstein’s 1916 book

This approach has a long history.  In Relativity: The Special and General Theory (1916), by Einstein himself (!) the discussion begins with the two postulates, and there is then a diagram of a train and a discussion of simultaneity (see above).  Seriously?  I’m not blaming Einstein, mind you; I’m blaming the textbook authors today who can’t let go of that stupid train.  It’s been almost 96 years.  Get over it.  Hop off that train, please.  There are more intuitive approaches that are easier for the layman to grasp.

Here’s the approach I use in my classes.  This is not the only approach, of course, nor do I claim it is the best approach.  However in my experience (admittedly, just one data point) this approach is a better way to get students to gradually accept SR.  The trick is to present information one plausible chunk at a time, and then only gradually derive all the weird stuff.  Thus, without realizing it, the students have been convinced of the truth of SR despite themselves.  If you start with simultaneity and time dilation and length contraction then half of the students will get turned off immediately (because their common-sense alarms will be blaring full-force).

  1. Talk about classical (Galilean) relativity.  That is, discuss how the laws of physics should be the same in any (inertial) reference frame you choose.
  2. Talk about coordinate transforms: how you can take the spatial coordinates of an object (x,y,z) and find what the coordinates (x’,y’,z’) would be in a different coordinate system.
  3. Talk about how some coordinate transforms are “good” and some are “bad”.  For example, a translation in space such as x’ = x – L preserves distance, but a rescaling transform like x’ = ax does not.
  4. Mention how the good ol’ Pythagorean theorem s2 = x2 + y2 + z2 gives you an invariant quantity (s2) that is preserved under “good” transforms.
  5. Mention that the (experimental) behavior of light throws a monkey wrench into this analysis.  For whatever reason, all observers measure the same speed c for light, and this actually makes things a little harder.  (Don’t do any math at this point!)
  6. Here you should start talking about time as being a 4th dimension.  The earlier you introduce the idea of an event P as a point P=(x,y,z,ct) in space-time, the better.
  7. State Einstein’s postulate about the speed of light.
  8. Show that the light postulate implies that s2 = x2 + y2 + z2 is no longer an invariant quantity, when talking about transforms as applied to space-time.
  9. If s2 = x2 + y2 + z2 is no longer invariant, can we modify the formula in any way so as to make s2 invariant, while still preserving the light postulate?  The answer is yes; and so you should derive the 4D version of the distance formula, s2 = x2 + y2 + z2c2t2.

To me, this is the core idea of SR.  Everything else follows from the invariant interval s2.  One should no longer think of our existence as being 3D; time represents another “direction”.  And it turns out that the time you perceive depends upon your vantage point (time is “relative”), just like position.

For example, suppose you are looking at a row of trees.  From one location, the trees are lined up in front of you (they all share the same x-coordinate).  From another vantage point, they are separated by 1 m each (x=0, 1m, 2m, 3m, etc.)  No one, not even Galileo, would find this controversial.

But now imagine that you think of time as just another “direction”.  Why is it so hard to believe that your time coordinate could have one value in one reference frame, and another value in a different frame?  Why is it so hard to believe that events that are simultaneous in one frame are not simultaneous in another?

Time dilation and length contraction follow from this in a straightforward way.  And they are much easier to visualize if you buy into the paradigm (I’ll say it again) that time is another “direction”, and therefore relative just like position.

[Caveat: I do know that time is special, in the sense that there’s a minus sign in the s2 = x2 + y2 + z2c2t2 formula.  That minus sign is crucial.  But discussing its importance should be deferred to a later (pun-intended) time.]

If you’re interested, here’s the rest of my SR program:

10.  Discuss space-like, time-like, and light-like intervals, and the ideas of proper length and proper time.
11.   Show how the Galilean boost (which is a “good” transform in classical relativity) must be modified into the Lorentz boost in order to preserve s2.
12.   Show how the Lorentz boost implies length contraction and time dilation.
13.   Discuss relative velocity in SR.
14.   Discuss so-called paradoxes like the twin paradox and the pole vaulter paradox.

The discussion can then go into advanced topics: momentum, energy, E=mc2, forces, etc.  However, with the foundation I have described, I believe these topics are much easier to present.

I’m sure there are some great professors out there who have had great success with the “traditional” program of SR instruction.  I’m sure Feynman could teach circles around me, even with the train and lightning bolts.  But I prefer this different approach, as I have presented it, and I hope others will realize that there’s more than one way to explain special relativity.

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Physicist

My contribution to the “What I Really Do” meme, back in February 2012.

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