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Teaching Quantum is fun

steuard: (physics)
Friday, February 25th, 2011 09:03 pm
I'm really enjoying teaching Quantum Mechanics this year. I've got some fun and interested students, and it's an absolute thrill to watch them figure this stuff out (and to completely blow their minds with quantum weirdness from time to time).

Today's class was a great example: I spent half an hour carefully explaining what a "hidden variables" theory is and why that approach is so much more sensible than the usual interpretation of quantum mechanics. I showed them how they could use very general statements about all possible hidden variable theories to make predictions about the results of various experiments. And then at the end of the class period, I got to see them exclaim in frustration when I did a calculation and showed them that those predictions are inconsistent with the predictions of quantum mechanics, and told them that the quantum prediction is confirmed every time someone tries that sort of experiment.

One of my favorite things about the way Townsend approaches this subject in his book is that students are confronted with the crazy aspects of quantum mechanics right from the start and then repeatedly along the way, so that they have just as much time to improve their mistaken intuition as they do to master the technical details of the calculations. It's a real joy to see them go from disbelief to furious concentration to dawning understanding. I like my job.
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Whew

steuard: (physics)
Saturday, October 16th, 2010 10:55 pm
I've just made it through a horribly exhausting week. I had an exam to grade for the 55 students in my intro physics classes, and I was also giving a "faculty forum" talk about my highly specialized research to a very much non-specialist audience. The week was made harsher by what Kim too kindly described as me "failing my time management roll": I didn't accomplish much last weekend, and I wasn't entirely on-task during the week, either. (I unwisely spent a significant block of time one night looking into possible hardware and software to upgrade our college's planetarium.)

But I did finally get the exams graded and returned, and I somehow managed to prepare a halfway decent talk. I felt pretty good about it, and I think it was well received, though several people have mentioned that everything I said made perfect sense, but only until the talk was over and they left the room. I guess I need to figure out how to make a more lasting impact. (Well, maybe that's clear: Step 1 is probably "don't try to describe all of modern physics in an hour." Not that I was quite that bad.)

But now, thank goodness, I've got a little chance to rest and recuperate, and this coming week is shortened for fall break. I'm happy about that.
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Quantum histories, time travel, and free will

steuard: (physics)
Thursday, June 24th, 2010 09:06 am
Even back when I wasn't happy about quantum mechanics, I recognized a significant point: it provided perhaps the only way for traditional notions of free will to sneak into our description of the universe. Before quantum mechanics, the universe seemed to run like clockwork: once you'd set up the initial conditions, every moment of the future was uniquely determined.

But quantum mechanics brings fundamental uncertainty into the mix: only probabilities could be predicted, so one could hope that "free will" could somehow slip into the picture. In particular, as I've discussed before, quantum mechanics implies that every possible history "happens" and gets an equal vote to determine the probabilities of what we'll actually observe. One could imagine that what we see as free will is the branching of the wave function at each moment of decision: when we decide "Should I flip this switch or not?", both histories "happen" and both have some chance of being observed. It's not entirely comforting, but it better than clockwork.

Shifting gears, I've also at times contemplated how time travel would fit into physics if it were actually possible. The framework for thinking about questions of time is general relativity, since the ability to loop back to an earlier time would imply specific things about the structure of space-time. Relativity is a classical (i.e. pre-quantum) theory, and in it one should view all of space-time as a single four dimensional object. If "loops" in time are possible, those must be built in to the structure of space-time from the start. In practice, that means that time travel paradoxes from sci-fi simply aren't possible: "If something happened, it happened", as Sean Carroll puts it. In other words, history will automatically and by definition be self-consistent. You can't specify a single space-time object that includes a person murdering their own grandfather as a child, so that can't happen. But again, that's a classical theory, so we wouldn't necessarily expect to have free will in that context. What happens when we bring quantum mechanics back into the mix?

Sadly, that still doesn't save the day. The "quantum histories" that we're summing over in this case must be self-consistent space-times! Yes, we still have a chance of seeing any possible history actually occur, but if the switch you're considering flipping would kill Grandpa, you simply don't have that option no matter how easy the action itself might be. So the comforting notion that free will is hidden within quantum mechanics doesn't hold up in a world with time travel: quantum histories have to be defined globally, not locally.

In fact, even if time travel isn't possible, I suspect that conclusion holds: the idea that every moment and every decision spawns a branching tree of quantum histories doesn't quite capture all of physics. There are global effects that give important contributions to quantum calculations, quite apart from time travel (I study some of those in my research). So if there is free will out there, we probably shouldn't look to quantum histories to provide it. I'm not sure that we're left with much wiggle room, though: perhaps traditional notions of what free will really means just aren't right.
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"Polish hand magic", and satisfying answers

steuard: (physics)
Monday, June 21st, 2010 08:16 pm

A recent SMBC comic featured "Polish hand magic", a rather remarkable mathematical trick for multiplying on your fingers. I want to talk a bit about the trick, and maybe a little bit about the broader philosophical idea involved. So go read the comic, and then I'll babble a little.

( Read it? Okay then... )

The broader issue that this touches on is our scientific desire for a satisfying explanation of the workings of the universe. I've always hoped that once we really understand the foundations of physics, we'll know the reasons behind all of the seemingly random patterns in particle physics and astronomy and cosmology. ("Why are there four fundamental forces? Why are some of them so much stronger than others? Why are there three copies of the fundamental particle multiplet, with such different masses?" And so on.) It would seem almost cruel if there weren't some deeply satisfying structure beneath it all, and one big hope for string theory has been that it will provide those answers.

Or at least, it was. These days, people have come to realize that no matter how unique the basic structure of string theory may be, the connection between those immutable laws and the particle physics we actually observe depends on many details of how the universe happens to be shaped here where we live. I didn't want to accept that at first, but it wouldn't be the first time science turned out that way. Kepler's early attempts to explain the orbits of the planets in terms of nested Platonic solids seem almost laughable now that we know the true history of the solar system: at this point, asking for a fundamental reason why we have the planets we do doesn't even make sense. So while there's still some hope that string theory will pick out our particular universe as uniquely preferred, it doesn't have to be that way.

So there's the question: When is it reasonable to hope for a deeply satisfying answer, and when should we expect that much of even a beautiful pattern is just due to random chance? Is there any way to guess in advance?

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arXiv vs. snarXiv

steuard: (strings)
Saturday, June 5th, 2010 03:28 pm
Entertainment of the week: arXiv vs. snarXiv. How well can you distinguish actual high-energy physics paper titles from computer generated fakes?

As every theoretical physicist knows, the arXiv.org preprint server is the go-to place for current research. (That "X" is supposed to be the Greek letter chi.) Essentially every string theory paper is posted there long before it's published, so active researchers check the new submission list daily.

The newly released snarXiv is "a ran­dom high-energy the­ory paper gen­er­a­tor incor­po­rat­ing all the lat­est trends, entropic rea­son­ing, and excit­ing mod­uli spaces." It generates titles, author lists, and abstracts (for now). Its creator goes on to explain that "The arXiv is sim­i­lar, but occa­sion­ally less ran­dom." His blog post (linked here) even goes on to suggest good uses for the snarXiv at each stage of your career. This is all absolutely hilarious to those of us who follow the arXiv for a living. For everyone else, it's a chance to laugh at us.

When I tried the arXiv vs. snarXiv quiz, I got to 10/10 and then stopped for fear of embarrassing myself if I eventually got one wrong.
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About that icon

steuard: (strings)
Thursday, April 22nd, 2010 10:34 am
Apparently, [livejournal.com profile] ukelele's daughter just pointed to my string/physics icon and asked, "What's that?". [Edit: Since I've changed physics icons, you'll need to look at the enlarged version below to see what she was asking about.] It strikes me that she may not be the only one who's wondered that. So here's a stab at a broadly understandable explanation. I'll try to keep it fairly short, but I'll stick it behind a cut anyway (since I'll embed a picture or two). Mind you, this won't make any sense to a 3-year-old, but I already took a stab at that in my reply to the original comment.

( No, it's not a severed aorta... )
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Quantum histories

steuard: (physics)
Thursday, April 22nd, 2010 12:12 am
I've been thinking lately about the many things we usually leave out of intro physics. It's hard to strike the right balance between practical and inspirational, between strong foundations and broad horizons. But I'd like to see that change, at least a little: you won't entice students to love the subject without a glimpse of what makes it beautiful.

Just for fun, let me share an example: the quantum idea that reality is a sum over all possible histories. It goes something like this. When I throw a ball and you catch it, common sense and classical physics agree that the ball follows a specific path through the air.

But quantum mechanics tells a remarkably different story. In this picture, the ball takes every possible path from me to you at once: a straight line, or a high arc, or a zig-zag, or three quick loops around my head before diving between your legs and then up over your head and back down into your hand, or anything else you can imagine. Moreover (and further straining credulity), every single possibility is equally likely! Of course, with so many options, the odds of any given path are basically nil: what we really have to compare are "neighborhoods" of almost-identical paths (those similar enough that we couldn't tell them apart anyway).

Very roughly speaking, quantum mechanics says that every possible path gets to cast an equal vote in favor of its neighborhood. But there's a catch: each path gets a specific "direction" assigned to its vote (think of this like the spinner from a game of Twister). In most neighborhoods those directions go every which way, so when you add up all the votes they pretty much cancel out (just as many lefts as rights, etc.). But there's usually one special neighborhood that votes as a block, with all its vote directions more or less the same. That overwhelmingly probable neighborhood is what we see as the classical path. Common sense emerges from chaos in a truly remarkable way.


[The deeper beauty of this story is that the math of these "vote directions" immediately explains the reason behind the equations of classical physics. The vote direction of a path is precisely its "action" (interpreted as an angle). We learn in calculus that near the minimum of any function its value is nearly constant, so the neighborhood of the path with minimum action will have nearly constant vote direction. And indeed, the "principle of least action" was the basis of the Lagrangian formulation of mechanics long before quantum mechanics was ever imagined, but nobody knew why. Good stuff!]
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Musings on the infinite

steuard: (physics)
Friday, April 2nd, 2010 11:21 am

A few weeks ago, my friend and former colleague Sean Carroll was a guest on the Colbert Report to promote his book about the nature of time. Toward the end of the interview, they discussed the idea of the "multiverse", which Sean uses to refer to the (possibly) infinite number of "universe-sized" regions within the vast web of space and time where we live. The notion is that if we could somehow travel far enough (faster than light) to regions many times more distant than our telescopes can see, we could find countless independent "universes" that can never talk to each other at all. Some of them would be much like our own but others could be very different, maybe even with different laws of physics. Steven Colbert seemed quite interested:

Colbert: Am I in these other universes?

Carroll: There will be people very much like you.

Colbert: In these other universes, is it possible that my show's on at 11 and John Stewart is at 11:30?

Carroll: Maybe more often!

It's a cute exchange, and it's a variant on the old idea that "in an infinitely big universe, everything that could possibly happen must happen somewhere."

Trouble is, I don't know that I buy that argument, for rather subtle reasons. However we define them, the number of "independent universe-sized regions" of space and time is countably infinite: we could in principle come up with some way of labeling each one by an integer. But many sets (like the real numbers) are uncountably infinite: no matter how you try to label each real number by an integer, you'll miss the vast majority of them. The real numbers are just a much bigger infinity than the integers are. Going on, the set of all possible curves in space is a yet larger infinity. (Assuming space and time are continuous! If they turn out to be discrete, then the set of curves has the same infinite size as the real numbers.)

The thing is, the set of "everything that could possibly happen" is a lot more like the set of all curves than like the set of integers: if anything, it's a still larger infinity. So no matter how large our multiverse may be, it's mathematically impossible for every possible history to occur somewhere. Does that mean that our Steven Colbert (on at 11:30) is the only one? Quite possibly so. I'm not convinced that the multiverse idea opens up as many possibilities as people sometimes think.

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"Simple enough for a beginner" indeed

steuard: (physics)
Saturday, March 27th, 2010 11:48 pm

Browsing a local bookstore, I spotted Supersymmetry DeMYSTiFied. The "DeMYSTiFied" series seems to have a style similar to the "For Dummies" books but with more of a "study guide" flavor (they all include "end-of-chapter quizzes and a final exam [to] help reinforce learning"). I guessed the book must be intended for a broad audience excited about cutting edge physics.

So when I randomly flipped it open, I was surprised to find myself in a chapter called "A Crash Course in Weyl Spinors" on a page full of equations. Flipping around some more, the book seems at least as equation-heavy as the average textbook, but presented in that "For Dummies" style. The same cognitive dissonance appears in the ad copy:

It's a no-brainer! You'll get:

  • An explanation of the Wess-Zumino model
  • Tips on how to build supersymmetric lagrangians
  • [etc.]

I'm really wondering about the intended audience for this book. It clearly assumes that the reader is comfortable doing sophisticated calculations in quantum field theory (often a 2nd year graduate course), and it's teaching techniques that you'd only need if you're going to read (and write) primary literature in particle physics. But the "golly gee let's make this fun and simple" style seems like the last thing that would inspire confidence in an ambitious physics grad student, particularly when it's competing with well-regarded textbooks written by masters in the field.

A final bizarre note: At the moment, Amazon ranks this book #36 in the category "Science for Kids". Hey, folks with kids: order this and let me know how it works out for ya!

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Conference tidbits

steuard: (strings)
Friday, March 19th, 2010 06:59 pm
I really enjoyed Strings 2010 this week, for the physics and for the people. But there were also a number of random fun bits to share. For example:

* I got to ride a Segway for the first time. (Very briefly.) Takes a little getting used to, but I can see that it could pretty quickly feel quite natural. It's quite remarkable that it works.

* Less surprising: keeping up with a technical talk is difficult if the audiovisual staff are on the phone two rows back trying to fix the camera. More surprising: it's also difficult when someone's snoring halfway across the lecture hall.

* A few choice quotes by the speakers (I won't pretend they're verbatim, and profuse apologies if I've misquoted anyone): (I'm happy to explain the context in the comments if necessary.)

( I'll hide most of these behind a cut. )

Liam McAllister: "Since I'm in Texas I can feel safe using the phrase, 'You can't get lard unless you boil the hog.'"
Eva Silverstein: "Aren't you a vegetarian?"
Liam: "Yes, so perhaps I've missed the point. I was given to understand that getting lard is something good."

( One more. )
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Conference: Great idea

steuard: (strings)
Tuesday, March 16th, 2010 08:28 pm
Unbeknownst to me, at some point in the last few years I leveled up my Conference Socialization skill. I'm not sure how: actually getting my PhD might have helped, or having a "real" physics job, or just having lived for a few years interacting with people as a professor rather than as a student. It also helps that the people I knew in grad school (and elsewhere) have scattered off to other institutions, so that's helped me bridge a bit to other social circles. In any case, I've been having a great time, not just in (most of ) the talks but also the socialization during breaks.


Fun moment of the day: during the introduction of one talk, someone used my pretty D-brane figure to illustrate one step in a chain of reasoning. (Just the picture at right, not the whole slide). It made me grin to see that people in the actual field are aware of it. (They didn't credit me for it, sadly, though doing so without disrupting the point of the slide would have been tricky. I asked the speaker a question in the next break and mentioned the picture, and he said, "Oh, I probably should have credited you...," so at least he sounded a bit apologetic. I'm not too troubled by it.)
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Highly relevant icon

steuard: (strings)
Tuesday, March 16th, 2010 12:52 am
I've just arrived in College Station, Texas for Strings 2010 at Texas A&M. I've been to this conference once before (Strings 2002, in Cambridge, England), and it's a fantastic chance to get a broad overview of what's going on in the field. That's particularly useful to me at the moment since I've been a bit out of touch for the past two or three years (apart from attending a few weekly seminars at Caltech). Given that the conference was in the US for once I figured this was a good chance to attend.

I've got to admit that a part of me is a bit self-conscious about not having been particularly active in the field for the past few years. "What are you working on?" is a standard question, and while I do have an answer (I swear it's going to be done soon!), I've allowed the day after day grind of teaching to make my research progress frustratingly slow. That just compounds my natural shyness in large groups of people. So I'm not sure how much luck I'll have with the networking side of things while I'm here. Still, getting up to speed on the physics (and building some internal excitement and momentum) is my main goal, and I think it'll be hard to go wrong on that. I'm looking forward to it! (And honestly, I'm perfectly willing to tell people that I'm here to get back in the swing of things: maybe my concerns about meekness are overblown.)
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Angular "units": a nice perspective

steuard: (physics)
Tuesday, December 1st, 2009 04:19 pm
I had a neat realization during a conversation with my colleague Cameron today, so I thought I'd share. Feel free to tune this out if you're not a math/physics type.

Cameron was pondering the various "units" for angles: the common ones are degrees, radians, and rotations (a.k.a. revolutions). Physics students learn that many common equations (such as v = r ω) only work when angles are in radians: they given wrong answers if you use degrees or rotations. It's a standard story: radians are defined in terms of a ratio of lengths (arc length/radius) so they are automatically dimensionless (since a ratio like "meters/meters" cancels out).

But in what sense is "rotations" not dimensionless? After all, you're just counting things, so what you end up with ought to be a pure number (which has no units by, definition). For that matter, "degrees" is just counting things too (albeit more finely spaced things). Given that multiplying by a pure number can't possibly change the units of your answer, it's hard to understand on a conceptual level why angles measured in degrees or rotations shouldn't work in the equations. (The equations themselves are entirely clear about what works and what doesn't, mind you! It's just understanding them that's subtle.)

The resolution that I've come to is that "degrees" and "rotations" are not units in the sense that "seconds" or "meters" are units. They can't be, as noted. Instead, "degrees" and "rotations" have the same status as SI prefixes like "kilo" and "micro". After all, "kilo" effectively translates as "times 1000", a pure number, but you wouldn't expect your equation to give the right result if you removed a "kilo" that was supposed to be there! So I would assert that one can think of "degrees" as an SI "prefix" meaning "times 2π/360" and "rotations" as an SI prefix meaning "times 2&pi". Explicitly plugging in these definitions then just gives your result in terms of the base unit, the most natural one: radians.

It may not actually be all that helpful in practice (my advice is still "just use radians"), but I think this gives a cute new perspective on what these angular "units" actually mean.

Update: Another useful note: The choice of "base unit" occurs when we define the angle in radians: θ = s/r. That choice then carries through the rest of the equations that we use for angular motion. If we had instead defined the angle as θ = s/(2πr), the "base unit" would have been rotations, and that factor of 2π would show up in every other rotational equation. Radians are clearly the simplest choice, but there isn't anything privileged about it. (Just imagine the ugliness of equations throughout rotational motion if we decided to choose our fundamental definition of angle to be θ = 360s/(2πr)!)
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PV=nRT

steuard: (Default)
Saturday, July 18th, 2009 03:26 pm
A few minutes ago, Kim and I heard a pop and then a brief but loud hissing sound coming from... somewhere. We looked around the apartment, but we couldn't figure out what it had been. I finally thought to look outside, and sure enough the back tire on my bike is now completely flat.

All I can figure is that it's 100 degrees today and the sun has been beating down on the black bike tires since early afternoon. Between the increased pressure of the hot air inside and the heat acting on the rubber itself, I guess a patch must have failed. I'm just glad I wasn't riding at the time!

(And now I want to know "Which patch?" and "How could I have avoided this?", but we're too busy getting ready to move for me to figure it out right now.)
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Pretty funny if you've taken upper division quantum

steuard: (physics)
Thursday, June 11th, 2009 11:11 pm
Via Bad Astronomy, here's an in-depth discussion of A Unified Quantum Theory of the Sexual Interaction. I'll warn you that the target audience is a bit specialized: much of the humor is targeted at people who would read "a superposition of kets with different energy eigenvalues leads to a time dependent relative phase" and think, "Well, duh." I should also warn you that, to paraphrase the Bad Astronomer, the discussion combines high physics with low humor. The following is fairly typical:
Self- interactions involving a solitary phase are generally difficult to observe, although examples have been documented that involve short-lived but highly-excited states accompanied by various forms of stimulated emission, although the resulting fluxes are generally not well measured. This form of interaction also appears to be the current preoccupation of string theorists.
I'm not sure what I think of that last bit.
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High energy physics photo titles

steuard: (physics)
Tuesday, January 13th, 2009 11:35 pm
Via [livejournal.com profile] nasu_dengaku, I've discovered a photographer on Flickr who posts photos from his trip home from work (apparently in Milan, Italy) with titles usually taken from the theoretical high energy physics preprint listings on arXiv.org (often with a few words changed). In the handful of examples I've checked, the titles were taken from papers that were posted to the hep-th archive on or very near the day that the photo was posted, so I halfway suspect that the photographer might be a physicist himself (either that, or he's just taken to reading the arXiv daily looking for fitting titles).

At any rate, the photos are often pretty neat and the physics-inspired titles definitely make me look at a lot of them in a new and different way. A few examples:I wonder if I could get a grant to study that last topic?
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(Not) Appropriate for class

steuard: (Default)
Tuesday, December 9th, 2008 09:31 am
I'm twiddling my thumbs waiting for my flight back to LA after a job interview in Michigan, and I just took a look at the most recent xkcd comic. I'm torn: we just covered special relativity last week in my intro physics class, and I emphasized the fact that observers who move relative to one another may disagree on whether events are simultaneous or not. So this comic is remarkably timely and applicable: ideal to share with my class! (We talked about the twin paradox, too, so the mouse-over text is relevant as well.) Nevertheless, I think perhaps I'll opt against.

(If you're interested, you can take a look at the space-time diagrams handout that I wrote for the class. It's a bit terse, especially for me, but I think it covers the essentials. It's not really meant to stand on its own without lecture and class discussion, but it ought to be comprehensible at least to people who have encountered the subject before.)
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Life after physics

steuard: (physics)
Saturday, September 13th, 2008 01:32 am
All the talk of LHC doomsday scenarios can get you thinking (even though it may be more likely that the LHC will produce dragons than Earth-swallowing black holes or strange matter), and the HTML source of hasthelhcdestroyedtheearth.com has reminded me of an incredible paragraph from a paper by Sidney Coleman and Frank De Luccia ("Gravitational effects on and of vacuum decay". Physical Review D21 (1980) p. 3305).

In the paper, Coleman and De Luccia studied implications of "vacuum decay", the suggestion that the laws of nature that we know have not settled into their final form. Instead, the idea goes, perhaps the laws of physics got "stuck" as the universe cooled down from the Big Bang much a rock falling down a cliff might get caught on a ledge partway down. The rock is likely to be knocked loose in the next big storm or sooner, perhaps with no apparent cause at all. The same thing could happen to physics if we really are stuck in a "false vacuum": whether caused by a specific event or just bad quantum luck, our seemingly eternal laws of physics could come loose ("decay") and fall into a totally different state. Coleman and De Luccia analyzed what might be left after such an event happened, and had this to say about their results:
This is disheartening. The possibility that we are living in a false vacuum has never been a cheering one to contemplate. Vacuum decay is the ultimate ecological catastrophe; in the new vacuum there are new constants of nature; after vacuum decay, not only is life as we know it impossible, so is chemistry as we know it. However, one could always draw stoic comfort from the possibility that perhaps in the course of time the new vacuum would sustain, if not life as we know it, at least some structures capable of knowing joy. This possibility has now been eliminated.

With that quote in mind, it may be disquieting to realize that a fair number of physicists have come to believe that string theory predicts that the universe has something like 10500 different choices of "vacuum" and that we might be living in any of them. I don't think we know anywhere near enough to say how likely they are to decay.
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LHC Fun

steuard: (physics)
Saturday, September 13th, 2008 12:47 am
I'm sorry that I didn't post anything about the Large Hadron Collider starting up on Wednesday. This is an exciting time for high energy physics, even for those of us without direct ties to the experiment. I'm sure lots of you have been following the whole story (Brian Greene's NYT article is a good start), from the cool science the LHC may illuminate to the crackpots filing lawsuits because they're afraid the machine will create black holes that will engulf the Earth.

On the off chance that you haven't seen them, here are a handful of LHC-related tidbits that I've enjoyed recently:
Good stuff, good stuff. (And really, those webcams are worth checking out.)
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Yeah, I get that all the time

steuard: (Default)
Tuesday, August 19th, 2008 08:32 pm
Kim recently reminded me of the "Overheard in New York" quote blog (probably the best of the various "Overheard in..." cousins). One entry that showed up today caught my attention:

Good looking brunette: Yeah, then we talked about physics.
Intrigued girl pal: Oh, really? Why?
Good looking brunette: Not sure, but I remember it turned me on.
Intrigued girl pal: Oh...
(awkward silence)
Hot guy pal: (nods head)
Good looking brunette: What? I really like physics! Its the math... I really like math.


Meanwhile, today's SMBC comic had a physics theme as well (I've wondered the same thing at times).

And while I'm posting physics-related stuff, here's a discussion of Olympic decathlon scoring by my former colleague Sean Carroll. Did you know that the insanely complicated decathlon scoring system can give a score with an imaginary component?
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