S03E18: The Pants Alternative

March 22, 2010

There’s more science than meets the eye on The Big Bang Theory. Literally.  Tonight’s viewers were undoubtedly puzzled by the presence of a little non-Euclidean geometry on the white boards.  Why was it there? What is it?

Non-Euclidean geometry on tonight's whiteboards...unobstructed by distracting characters and action. (from CBS promo clip.)

First let us recall that  Euclid himself developed his non-non-Euclidean geometry in 300 B.C.   He started by assuming as little as possible and left it to generations of junior high school students to prove all the rest, that triangles have 180 degrees and so forth.  As is typical in mathematics, the game is to use as few, most elegant, postulates as possible and leave the rest to clever derivation.

Every junior-high school student learns Euclid’s five postulates (briefly listed, with some legalities dropped):

1. Any two points can be joined by exactly one line segment.

2. A line segment can be extended to an infinite line.

3. For any line segment, a circle can be drawn.

4. All right angles are the same.

Now these four sound pretty elementary. It is hard to imagine ever being able to prove or disprove them and so they serve “obvious” as starting points.  But there is a pesky “fifth postulate” Euclid added:

5.  For a point outside a line,  there is exactly one line through the point that never meets the original line.

Now Euclid was a smart guy.  Why not just prove “the fifth postulate” from the first four?   He tried.   For 2000 years, mathematicians tried.  Even Karl Friedrich Gauss.   No dice.  It was not proved.  Modern mathematicians know it could never have been proved from the first four.

So mathematicians made lemons out of lemonade.   In 1826,  Nicolai Lobachevsky said, let me assume there are not one, but many, such parallel lines.  In the 1850’s Bernhard Riemann  said let’s assume there are none.  Chaos ensued.   Without the fifth postulate you cannot even prove all triangles have 180 degrees.   Crazier still, assuming Lobachevsky’s  version of the fifth postulate gives you less than  180 degrees in all triangles.  Riemann’s gives you more than 180. These are some strange triangles.

(As it happens,  it was all worked out decades earlier by Gauss and he stuck it in his desk without publishing.  Note to aspiring mathematicians…whatever you work on, there’s a good chance Gauss already tried it.)

A few decades later, at the turn of the 20th century, Albert Einstein and others realized there was more than abstraction to the fifth postulate, but that it relates to an actual uncertainty we have about our own Universe.  Being unable to prove Euclid’s fifth postulate is equivalent to not knowing if we live in curved space or a flat one.  We don’t really know if extremely large triangles in our Universe have exactly 180 degrees or a little more or a little less.    How can a triangle have more than 180 degrees?  Let’s take a trip:

It is possible, when walking around the globe, to make a triangle with three right angles. This triangle has 270 degrees, not 180.

Let’s walk (and dogsled, and  swim)  from the North Pole along the Greenwich meridian (0 deg. longitude) through England and down to the Equator.  Here make a right turn.  That’s a 90 degree angle.  Go until you hit San Salvador Island, west of Ecuador, located on the Equator at the 90th meridian (+90 degrees) .  Now take another right turn (another 90 degrees) and head back north through St. Louis, back to the North Pole.   So far we’ve taken two right turns, 90+90=180 degrees. But then we hit the North pole again, coming up through Canada.  We find we arrive having completed a triangle.  We took three turns.  But you are coming in at right angles to where we left.   The last angle has 90 degrees.  So we’ve made a triangle containing 90+90+90= 270 degrees, not 180.   Such is life on a curved surface.  Even if you can’t see the curvature while moving around, it is there.

You can do the same in a Lobachevsky space.  Imagine walking around on a Pringle’s potato chip.

Non-Euclidean geometry is the key to Pringles potato chips.

Often it is the case that a piece of mathematical abstraction has a direct bearing on our physical world.  In this case,  it just took over 2000 years to realize it.

In his fascinating 1965 sequel to Flatland, Dionys Burger’s Sphereland chronicle’s the life of the grandson of A. Square,  named A. Hexagon.   A surveyor in Flatland is distressed to find the angles of triangles do not add to 180 degrees.  A. Hexagon, being the progeny of the insightful hero of Flatand, awakens his surveyor friend to the fact that Flatlanders really inhabit a curved space.  Like our trip, triangles their angles do not have angles that add up to 180 degrees.

Now even our own, non-fictional, 3-dimensional space may be curved.  We just don’t know.   Astrophysicists measure the largest triangles they can find looking for small deviations.  They use the rays of the oldest light in the universe, the microwaves left over from just 380,000 years after the Big Bang.  So far, all triangles add up to 180 degrees, but with more precision we may at any time find we live in a curved space.  And that is not a problem.  Everywhere junior high school geometry books would just have to revise Euclid’s fifth postulate.  (That’s good news for the textbook publishers, who are always looking to come out with a new edition to sell.  Even if there is nothing new, I find for my own classes, they will just re-number the questions every 3 years and call it a new edition.)

Fun stuff, but what did this have to do with the show?  Why did we put it on the whiteboard?  Actually it directly references a speech Sheldon had in the script.  Had.  It was an earlier version script.

The scripts go through many revisions throughout the production week.  Every day the actors rehearse and the writers improve the script.   Comedy seems to work like an experimental science.  The writers sometimes find something better.  And for this week,  after I already sent in the equations and diagrams to the set dressers, the writers rewrote  Sheldon’s lines about retreating into a Riemannian space to relax.

So viewers never saw this little piece of science. The writers replaced it with something funnier:   Riemannian space was replaced by Sheldon’s favorite location in Sim City.  But maybe it still relates.  After all, how well has anyone measured the triangles of Sheldonopolis anyway?

S03E17: The Precious Fragmentation

March 8, 2010

Viewers tonight may have anticipated disappointment, that there was no physics to blog about in this evening’s episode.  But of course physics is everywhere.

Tonight our friends Leonard, Sheldon, Raj and Howard acquire a “Lord of the Rings” ring.   The “One Ring”, we’re told, to bind the Rings of Power of the land of Middle Earth.  At least they had a replica of it.   None of them ever tried the ring on, but had they done so — if it were the real ring — it would have rendered them invisible.  Invisibility is one of the principle powers of the ring.  Oh, and world domination, too.

Physicists today are working on creating invisibility.   Not having access to the Fires of Mordor or Elven blacksmiths, we instead have turned to Maxwell’s Equations.  These are the four elegant equations that describe all of electricity, magnetism, and light.  Because of James Clerk Maxwell and his four equations, we know that light is made from electric and magnetic fields.

The four equations that describe all of classical electricity, magnetism, and light -- Maxwell's Equations -- are simple enough to fit on a T-shirt

Maxwell’s Equations were developed over many decades of the 19th century by physicists studying electricity and magnetism, among them many great minds: Gauss, Ampère, Faraday.  But it was Maxwell who found the linchpin, the term that bound them all, and summarized the result in those four beautiful equations.  At my own university, UCLA, as at most others,  understanding Maxwell’s equations  is the pinnacle of the first-year course in physics.   Starting with balls rolling down an inclined plane and step-by-step understanding more and more physics, undergraduates are able to understand all of Maxwell’s equations after just one year of study, and thus understand perhaps one of the greatest intellectual achievements of all time.

The received wisdom about popular science writing  is that with every equation I will lose half my readers.  So I will skip the “equations” and just describe Maxwell’s  four “rules” that have stood the tests of time by experiments:

#1. Electrons and protons create electric fields.

#2. There are no magnetic charges.

#3. Changing magnetic fields create loops of electric fields.

#4. Moving electric charges OR changing electric fields create loops of magnetic fields.

Now, what do these four rules mean for everyday living? A lot.

Rule #1  describes why you receive a shock in the winter after handling your fleeces.  When rubbing fabric, you build up an excess of electric charge in your body.  By this rule, an electric charge creates an electric field, which  means it creates two points in space with different voltages.   You are now resting at a higher voltage than, say your doorknob.  A voltage difference will drive currents and can do anything from toast bread to run your television.   When you touch the doorknob, current flows and … Zing!   By the way, “voltage” has no meaning on its own.  Only differences in voltages ever matter.  So when you see a sign that says “Danger:  Ten Thousand Volts”, it really should say  “Danger: Ten Thousand Volts Relative to YOU”.  If you touch something 10,000 Volts different than you, current will flow and for a few seconds you become the toaster.

Rule #2 was the subject of the boys’ Arctic expedition.

Rule #3: tells us how electric generators work.  Move a magnet through a metal loop and you will set up a voltage difference that will drive a current, making a generator.    If you reverse the situation, and drive a current in the loop then you can move a magnet and you’ve made a motor.   Every motor is a generator and every generator is a motor.   These basic building blocks of our technology were not invented by someone saying: “We need a way to make electricity” nor by saying “Is there a way I can use an electrical current to move things?”  Rather, they were the by-product of the basic research of the day, into the elemental nature of electricity and magnetism.  Curiosity, not necessity, is the mother of invention.

Rule #4 : The first part tells you how to make a magnet by running a current through a loop of wire.  Even a refrigerator magnet works because electrons in the magnet are moving in circles and making magnetic fields.

Now for the second part of Rule #4: “Changing electric fields make loops of magnetic field”.  Discovery of this last piece is Maxwell’s genius.  Maxwell wondered why, if a changing magnetic field could produce loops of electric field, why could not the converse be true as well?  He guessed that changing electric fields would produce loops of magnetic fields.

Indeed they do.  Very small, almost inperceptably, but they do.   So most remarkably, even in a perfectly empty space, changing electric fields will produce changing magnetic fields that will produce changing electric fields and so on, forever and ever.  Maxwell noticed by combining equations #3 and #4 he could make a wave, a wave that turned out to travel at precisely the speed of light.  The wave is created by changing electric and magnetic fields creating one another forever according to rules #3 and #4.     The fact that he could predict the wave traveled the speed of light led Maxwell to conclude that light is an electromagnetic wave.  (The conclusion was correct, but by accident.  We now know many things, not just light, that travel near or at the speed “of light”.  Had he known about all these other  he could not have concluded so quickly  that his waves were light waves.  Sometimes a little ignorance is bliss.)

Now, over 100 years later engineers are designing materials to interact with the electric and magnetic properties of light.  These materials can cause light to bend in ways that no naturally occuring material can, and are thus called meta-materials.  Light entering a meta-material can be made to bend completely around an object effectively making a cloaking device.

An example of a "metamaterial". Using Maxwell's equations, this new material can bend light around an object, rendering it invisible. (from Science Magazine)

The tricky part is that you must fabricate electrical components  smaller than the size of one wave oscillation.   Pieces less than an inch have been shown to effectively bend radio and microwaves (which are a type of light) around objects.  Visible light would require elements  100,000 times smaller. But techniques are getting closer all the time!

(Easter-egg alert:  Metamaterials featured prominently on the whiteboards of a previous episode: “The Creepy Candy Coating Corollary”, S0305.)

So our heroes don’t really need some  Dark Lord to make them a silly invisibility ring.  To the lab!!

S03E16: The Excelsior Acquisition

March 1, 2010

Tonight Sheldon wants to ask Stan Lee how the Silver Surfer uses his silver surfboard to accomplish interstellar flight.  As well he should!   Nobody, not even Sheldon, knows how we are going to travel between stars.

The Silver Surfer accomplishes interstellar travel on his silver surfboard. How will we?

Proxima Centauri is our best bet.  It is the closest star to our home orbiting around our own star, Sol.   Proxima Centauri is  an unremarkable red dwarf star named appropriately from the Latin proxima, which is “next to”, as in “proximate”.  It is not so-named because it is close to us, but rather because it is close to the star Alpha Centauri, a star in the constellation Centauri.   Alpha Centauri is the third brightest star in the night sky, but mostly just because it is so close.  We may want try to visit someday.  After all we are neighbors and have yet to bring them so much as a fruit basket.

“Close” is a funny word to use on interstellar distances.   Proxima and Alpha Centauri are so far away it takes light 4.2 years to arrive.  Nothing we know of can allow us to travel faster than light, our ultimate speed limit.  Even the television transmissions of the pilot episode of Big Bang Theory, which have been traveling at the speed of light since late 2007, are only halfway to whoever might inhabit the rocks orbiting those stars.  Not even Hulu.com  in Alpha Centauri has TBBT available yet.  (Life near Alpha Centauri has that in commonwith Earth.)

Alpha Centauri, being so bright, has probably been known to the earliest hominids who bothered to look up.  But Proxima Centauri being so dim was only discovered using powerful telescopes in 1915.  We may not be done yet.  Even dimmer stars known as brown dwarfs may be traveling the galaxy even closer to us than Proxima Centauri.  These stars are so cool, you have to look for them in infrared light.   Finding such nearby stars is one of the key missions of the newly launched WISE satellite.   When I told one of the BBT writers/exec producers we may soon find closer stars than Proxima Centauri he said “The Federation may be closer than we think”.

Proxima Centauri (red star, center) is the closest known star to Earth at 4.2 light years distance. (If you enjoy astronomy pictures such as this one, I highly recommend visiting NASA's "Astronomy Picture of the Day")

Right now our plate is full just with interplanetary travel within our own solar system.  A trip taking astronauts to Mars, as recently imagined by NASA, even at its closest approach will take over half a year.  Proxima Centauri is 750,000 times farther Mars’s closest approach to Earth.  At the same speed, that would take over a quarter million years to get there.  We must invent something faster.

Suppose our human engineers develop a technology that allows us to travel 1% the speed of light on average to Proxima Centari.  The astronauts only need now to spend 400 years on the spacecraft.   (I’m ignoring the tiny  benefit due to time dilation slowing the astronaut’s lifespan as we discussed earlier for the story of Paolo and Vincenzo.) The astronauts won’t survive to get there, but if they keep having children their 16th generation could make it.  I don’t think the intermediate generations will be particularly happy with their forbears for condemning them to a lonely flight through interstellar space.  If one generation rebels, and refuses to procreate the mission will be a failure.   Even if that 16th generation arrived successfully, they would hardly be Earthlings.

I think we can prove that we humans will never attempt interstellar transit until we know how to travel at least 25% the speed of light.  (The mission to Mars discussed above is only 0.001% the speed of light.)   Suppose a mission really was undertaken to travel to Proxima Centauri with a fantastic new technology that would take us there at 1% the speed of light.  It will take 400 years.  Now suppose anytime in the next 200 years, a new technology is developed to increase that average speed to 2% per year.  Given the rate of technological progress that is not a bad bet.  So the spacecraft that launches later would beat the earlier craft.   So not until a technology reaches some reasonable fraction of the maximum speed limit, the speed of light, would anyone bother to take an early flight.   The speed would have to be as large as 25% the speed of light to nearly guarantee this would not be a problem.  At least then the same generation will arrive as left the Earth.  It may not ever be possible, but the argument shows it is unlikely any such mission would be mounted until that is possible.

These are the stars in your neighborhood. Each white ring is about 1.7 light-years appart.

(If some smarty-pants wants to suggest worm-holes or other space-bending technology, keep in mind that these ideas don’t even work on paper.)

This says nothing of the many other technological hurdles must be met.  Traveling even at 1% the speed of light, the spacecraft would suffer terrible damage from interstellar gas and dust.   The rate of cosmic rays, charged particles flying throughout interstellar space, would likely give fatal cancer to anyone who tried this mission and they would arrive long dead.

So it pays to go back and understand what is special about the Silver Surfer’s surfboard that allows interstellar transport.  Often science fiction writers will come up with an idea before engineers and scientists.   Perhaps with the Silver Surfer there is an idea we’ve missed.  A good place to start with any such questions is James Kakalios’s terrific book “The Physics of Superheroes“.  Yet no explanation of Silver Surfer can be found — maybe it is just because Silver Surfer started out as a super-villain, not super-hero.  Fortunately someone actually asked the Silver Surfer’s creator, Jack Kirby, why he uses a surfboard.  To which he explains:

“Because I’m tired of drawing spaceships.”  -Jack Kirby



S03E15: The Large Hadron Collision

February 8, 2010

In tonight’s episode, Leonard finds he is invited to Large Hadron Collider, “the LHC”.   In case this ever happens to you,  I have a handy phrasebook at the end of the post.  (Or take it with  you if  take a  free CERN tour open to the public.)  But first, even though the LHC has had about a billion dollars of news coverage over the past two years, there may be viewers that have not have heard that the LHC is the largest “atom smasher” ever built.

“Atom smasher” is a quaint 1950’s term for a “particle accelerator”.  Particle accelerators  produce “high energy” collisions for people like me, “high energy physicists”.   As a side benefit, they  also produce the brightest visible light and X-ray sources available for study of new materials and biological systems.

How high is “high energy”?    The LHC is designed to produce collisions of protons that have been accelerated by 7 trillion volts.  That sounds like a lot.  How much?  When two of these protons collide they have  the energy you would get out of eating 0.00013 micrograms of a candy bar.

That is not much energy for a machine touted as recreating the Big Bang.   There are much higher energy collisions on a Manhattan sidewalk than this.   The key point is  that high-energy physicists care about the energy per particle.    Collisions on the highway, or even a baseball with a bat, are collisions with objects with over 1027 (1 followed by 27 zeros!) particles in them.   So any one proton in the collision of two cars has very little energy compared to the LHC.

A ball and bat make a much higher energy collision that the LHC. What matters though is the energy per particle.

Even the “Big Bang machine” as an analogy is a bit off the mark.  The collisions do not make a high temperature replica of the Big Bang.  Having only two particles collide is barely enough to think about as having any temperature at all.    (Some reactions that would occur in a high temperature fluid, cannot happen at the LHC with its only two colliding particles, even though they are high enough energy…to get around this, some physicists will someday use the machine to collide large nuclei, but the high-energy frontier is the collisions of single protons.)

Perhaps a more apt, albeit less sensational, description is an old one:  High energy accelerators are giant microscopes.  A deep law of physics is that the higher the momentum of a particle, the smaller size it can resolve.   High energy means high momentum and going down this path for a few centuries brings us to the Large Hadron collider.

Optical Microscopes:  The artisan lens-makers of Flanders over 400 years ago inspired Galileo to combine lenses to make a telescope to study the heavens.    A slight rearrangement of the optics, produced a microscope, producing images of biological structures too small for the human eye, on the scale of a millionth of a meter or “micron”.   The minimum size structure visible is dictated by the “size” of visible light, about half a micron.   But a “micron” is enormous on the biological and even atomic scale.   Barely any of the structures in the nucleus of a living cell can be seen.

Electron Microscopes:   In the early 20th century, a polio epidemic spanned the world.  In 1% of its infections, polio would leave children paralyzed for life.  Optical microscopes were not up to the task of imaging the poliomyelitis virus.  So German engineers pressed into service the physics rule that high momentum means access to small sizes..  By bombarding a sample with high energy electrons, the polio virus could be seen.  (Images of structures are  in black and white.  It is meaningless to even ask the color of something so small that not even light can resolve it.  But like Ted Turner, physicists often colorize their images. )   Over the years, the technology has improved to the point where even the locations of individual atoms can be measured to 0.000000000050 meters.

Accelerated electrons allow imaging the poliomyelitis virus which causes polio (false color). This is far too small to see under a regular, optical, microscope.

The Large Hadron Collider:  and other recent accelerators are sensitive enough to offer the possibility of looking inside even a proton.   Structures the size of 0.000000000000000001 meters (that’s a billionth of a billionth of a meter) are routinely studied by high energy physics like Leonard.

Founded soon after the Second World War, CERN used physics as a proving ground for European unity in peaceful pursuits.  I spent a few years working at CERN, the home of the Large Hadron Collider.  English is lingua franca at CERN, but having been around for nearly 40 years, English spoken in this island surrounded by the French-speaking countryside of France and Switzerland has developed into a dialect of its own.   In case you, like Leonard, are ever invited to CERN here are a few helpful phrases instructing you how to speak in the CERN dialect:

How does this look like?“:  When giving a presentation on scientific work, I often find myself asking rhetorically about the data, choosing between either “How does this look?” or “What does this look like?”.  In the CERN dialect, this hybrid phrase means you never have to choose.

Profit: In French, the verb profiter means  to take advantage of. This allows a much more efficient construction, as in “Let us profit from the sunshine and eat out of doors”.

British English: For some reason, English taught in European schools appears still to be British English, not American.  So use “autumn” for “fall”,  never use “how come?” for “why?” and so forth.

Avoid   ‘s :  Face it, the “apostrophe -s” is hard to hear, and the rules are often even screwed up by a native English speaker.   This is also not a construction that has a counterpart in many other languages.  A phrase, “Let’s go to John’s lab and look for Mike’s screwdriver” is not something you are likely to hear in the CERN dialect.  Rather say “Let us go to the lab of John and look for the screwdriver of Mike” if you want to be sure to be understood.

Replace specific English words with French ones: Occasionally the French word is substituted directly for an English one.   Being located on the French-Swiss border, working at CERN you will be crossing the border–several times a day.   “Customs Officer” is a word you’ll need, but klunky.  Replace with douanier.

For what concerns… :  Phrases do not always get shorter.  If you are concerned about your particle tracker, don’t say “Concerning the tracker”, say “For what concerns the tracker….”

Toilet: A word we avoid in polite English conversation, toilet, corresponds in French to the very clean faire la toilette.  At CERN, don’t “go to the bathroom”. There is no bathtub in there anyway.  When nature calls you can very politely “go to the toilet”.

For more information see this nice page from Francois Briard a CERN employee who is heavily involved with their public outreach.  He also sent me a link to some fun movies.

Of course any of the guys would have friends at the university that could get them into the LHC lab, including many places not open to the public on the tours.   But plane tickets to Europe, a place to stay, and especially European gasoline for getting around do not come cheaply.   So their excitement is duly warranted.

Time for a “toilet” break.

P.S.  For over a decade, in my high-energy physics class I’ve always asked the students the following question:   “Every time a new accelerator turns on, some clowns appear and say it will destroy the Earth and/or Universe.  Explain whether this is likely or unlikely.”   Sure enough, the same thing happened with the LHC turn-on.  A key point I want my students to realize  is that Nature has much higher energy particles making much higher energy collisions all around us.   Basically these guys are fear mongering with an attention-grabbing stunt.  Now just because it is fear-mongering and an  attention-grabbing stunt does not mean it is wrong.    There are always loopholes.  So it is logically incorrect to say a disaster is absolutely impossible, as some of my colleagues have said. (Or at least what the media says they said.)  In fact it is logically possible at any moment something you do in your kitchen could even create ice-9.  So I think physicists should be careful and not say “absolutely impossible” when they really mean to say “is ridiculously stupid”.

P.P.S.  That said, I have an “I survived the Large Hadron Collider 9/10/2008 T-shirt”

S03E14: The Einstein Approximation

February 1, 2010

The hottest material in physics can be made with a pencil and Scotch tape.   That’s “hottest” in popularity, not temperature.  When a new, interesting, material is discovered, teams of physicists will race against each other to figure it out.   This decade’s material-of-the-century is graphene.

Graphene is merely chicken wire made with carbon atoms…chicken wire that is no thicker than a single atom.

Atomic chickenwire: A image of an actual sheet of graphene. Each little black dot is an empty space surrounded by six carbon atoms, forming a hexagon. (The width of the entire image is about one thouand times smaller than the width of a human hair.)

Carbon atoms love to form chains, as in alcohol, or even rings, as in chemicals found in gasoline.   Even more tangled-up connections of carbon create popular substances like diamonds and soot.  Physicists knew for decades that the existence of a single sheet of interconnected carbon atoms was possible, in principle.  But they also knew that such a structure could hardly be grown as a crystal since the structure tends to roll up and form three-dimensional bonds.

But only six years ago, in cutting-edge experiments (using Scotch tape and pencils), physicists succeeded in creating small quantities of graphene, smaller than a speck of dust.  Pencil lead, despite its name, has no “lead” in it.  Rather it is many layers of carbon sheets, like a deck of cards, stuck together called graphite (from the Greek “to write“).  The experimental heroes just stuck a little of the humble pencil graphite in a folded over piece of tape…and pulled, separating hundreds of atomic layers in two smaller stacks.   A student can repeat the process as many times as needed, until a single layer is  created.

The students transfer the single-sheet candidates from the tape to a silicon wafer for further study.  One of the researchers’  breakthroughs was to discover a quick way of identifying single layers from less interesting multiple layers.   Like oil floating on a puddle reflecting sunlight after the rain, the film thickness determines its color.   The thin, elegant, highly-sought single sheets of graphene appear pale pink, while their fatter cousins are blue.

The process produced perfect crystals, with no apparent defects.  Graphene would prove to be harder than diamond, yet flexible.  Graphene is not a metal, yet highly conductive.  Success having many mothers, after the discovery, claims of priority going back several decades have been staked.

Pity the poor condensed-matter theorists.  For over a century they have pushed pencils across their pads in search of new materials to propose.  Yet there graphene was, literally right under their noses, the entire time.

A few episodes ago, Sheldon took us in his mind to the fictional country of Flatland, where only two dimensions of motion are allowed.   Not at all fictional, graphene is a carbon Flatland with electrons fixed to move only in its two-dimensional world.  Lacking that one extra dimension turns most of the rules of materials on its head.  Graphene has captured the imagination of physicists with its potential applications.

High speed transistors:  The heart of computers and most other electronics are the fast switches called transistors.  The electrons in graphene are extremely mobile, able to cross thousands of carbon atoms without a single scatter.  So the idea, at least, has been put forward that graphene could be the basis of a new generation of higher speed, smaller integrated circuits.

Super-batteries:   Because its mass per area is as low as any imaginable material, graphene could revolutionize energy storage in batteries and the adoption of renewable energy.  Capacitors too, one of the basic building blocks of all electronics (they hold charge in circuits), could be replaced by far smaller graphene components.

Displays: Having the seemingly contradictory properties of transparency and conductivity at once, perhaps one day graphene sheets will produce large area touch-screens.  Now scientists only need discover what the iPad is good for.

Gas sensors:  Graphene’s low noise and high surface area could perhaps make it sensitive enough to detect even a single gas molecule adsorbed onto its surface causing a detectable step-like change in its electrical resistance.

Graphene could revolutionize electronics.

But what attracted Sheldon’s attention tonight is the theoretical description of electron motion in graphene.  By a mathematical coincidence, the equation that describes electron motion in graphene is almost the same as the fundamental equation of free electrons in relativistic quantum mechanics:  the famous Dirac Equation.   Because of the electrons’ interactions with the carbon nuclei, the electrons move as if they are massless.   So graphene can serve as a kind of laboratory for particle physics theorists, like Sheldon, to test their understanding of the mathematics they use every day under more abstract and less controllable conditions.

Graphene.  It’s the greatest thing since sliced pencil lead.

S03E13: The Bozeman Reaction

January 18, 2010

My favorite word in physics is Zitterbewegung.  Coming in at close seconds are Bremsstrahlung and Ansatz.  These technical terms, at least for physicists,  mean “rapid oscillation”,  “braking radiation” and “starting point” in German.  (I chose not to even mention Eigenvectorbecause I didn’t want to have to explain it.) However, viewers of tonight’s show saw  Sheldon use the most famous of all German physics words, Gedankenexperiment.    Thanks to Kai of the German BBT fansite “Big Bang Forum” for the audio files.

Like modern physicists, Sid Caesar employed German words.

Today’s modern physics is peppered with German words, a relic of the founding of modern physics in Germany, Austria and Switzerland about 100 years ago.   The German-speaking  heritage of  the giants of late 19th and early 20th century physics is not hard to discern from their names:   Ludwig Boltzmann,  Max Planck,  Albert Einstein, Erwin Shroedinger, Lise Meitner, Otto Stern, Werner Heisenberg, Wolfgang Pauli, James Franck, Max von Laue, …

These masters gave us the concept of a Gedankenexperiment, or a “thought experiment”.   Physics is at its deepest core an experimental science.  Questions that cannot be subject to experimental testing, at least in principle, are outside the realm of physics and are left, at best, to the philosophy department.  Now some experiments are too hard to do as a matter of practice, or  too unsavory.  But even if in principle an experiment could be conducted, the question of its outcome remains squarely in physics.  An experiment you can think about doing, but don’t need to actually perform, is a Gedankenexperiment.  Physicists use Gedankenexperiments for several purposes.   First, they allow teachers to isolate  physical effect perfectly in an explanation for students.  They allow presentation of possible paradoxes and their resolution for pedagogical purposes.   Second, they allow us to see if a set of physical rules are impossible.  If the result of a Gedankenexperiment contradicts the known laws of physics, then at least one of the principles upon which the Gedankenexperiment rests must be flawed.

Sheldon was using Gedankenexperiments for their third purpose, to see if a physics theory has any meaning at all.   If Sheldon has a physics theory, but there is not a single observation that would be different with versus without it, then his theory might as well not even exist.   Physicists are currently grappling with Gedankenexperiments to see if various interpretations of what it means to make a measurement in quantum mechanics (what Sheldon called “the quantum measurement problem”) have any meaning at all.

“I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.” –Richard Feynman

Gedankenexperiments could someday illustrate if the quantum measurement problem really exists as a physics problem.  In tonight’s episode, Sheldon tells us he had “four out of the five Gedankenexperiments” that he thought would be necessary already written out on his laptop.  Was he close?  After what happened to his laptop, the world may never know.

Several famous Gedankenexperiments of this sort remain:

Shroedinger’s Cat was discussed at the end of Season 1.     In quantum mechanics, particles can exist in multiple observable states at once, in what is called a “superposition”.  To examine the implications further, Schroedinger put a Gedanken-cat (“thought cat”)  in a box and based on whether a certain radioactive atom decayed (or not), a bottle of poison would be opened (or not) and kill the cat (or not).   An experimentalist who has not yet looked in the box would have the treat the cat as a superposition of an alive and dead cat.  Schroedinger originally devised this Gedankenexperiment as a reductio ad absurdem argument.  He intended to show the concept to be ridiculous because, he argued, nothing as large as a cat could exist in a superposition of states.   However, the tables turned on Schroedinger since nothing has ever been done to show that such a state of a cat is impossible.  Instead, this Gedankenexperiment can now be used as an example of how quantum mechanics works.  Even the kitty litter would be both soiled and clean at once.

Einstein’s twin “paradox” was, like the Schroedinger’s cat Gedankenexperiment, developed to show a dramatic consequence of Einstein’s theory of relativity, but is only mislabeled as a paradox.  In his wonderful TV series Cosmos, Carl Sagan illustrates this Gedankenexperiment with  the story of two Italian boys (story starts at 21:50, ends 24:55), Paulo and little brother Vincenzo.  The boys and their friends are passing a nice day in a small Italian town.  Paulo decides to break off and spend some time riding through the Italian countryside at near the speed of light, all the more impressive considering he is riding a Vespa.   Einstein’s theory of relativity predicts that Paulo ages more slowly than his brother whom he left behind.  So when Paulo returns, all Paulo’s friends have grown old and died. Only Vincenzo, now a very old man, is left patiently waiting for Paolo in the piazza. Paulo, however, has experienced only a few minutes of time passing and remains a teenager.

A common misconception is that the “paradox” of this story lies in their ages because, the wrong argument goes,  a younger brother can never be older than the first-born brother.  Actually there’s not problem with that.  The real “paradox” raised was to say that since motion is relative, we cannot specify which brother is “really” moving and who was “really” at rest.  Each brother would see the other moving.  So in that case how could one brother age faster than the other since we can reverse the roles and say Paulo is on a stationary Vespa while Vincenzo was on a moving piazza.  The resolution of the paradox is that at some point Paulo had to turn his Vespa around.  Paulo accelerated but not Vincenzo.   The brothers can say who accelerated and the paradox is resolved, i.e. no paradox.   Sagan himself identifies the wrong paradox in this clip.  I am sure Sagan knew better–but we wouldn’t make that mistake on The Big Bang Theory.

After only a few minutes riding at near light-speed on his Vespa, young Paulo finds his little brother Vincenzo is 90 years old. (starts at 21:50 ends 24:55)

Maxwell’s Demon: is a famous Gedankenexperiment posed for the theory of heat.  In a hot gas, molecules are moving faster on average than in a cool gas.   The theory of heat (a.k.a. “thermodynamics”)  says that if you have two bottles of gas at equal temperature and connect them with a pipe, heat will not flow from one to the other.  However each gas has molecules with a variety of speeds around the average.  Imagine a gatekeeper, Maxwell’s Demon, who could preferentially allow fast molecules into one bottle and the slow ones into the other. One gas would heat up while the other cools without the work required by the theory of heat.  The resolution of this paradox is less obvious than Einstein’s twin paradox and physicists still can argue about it.

Wigner’s Friend is a  Gedankenexperiment proposed by the great physicist Eugene Wigner to explore the roles of consciousness in the quantum measurement problem.  It can be discussed as an added layer to the Schroedinger’s cat experiment.  Suppose Wigner leaves the room with the cat of unknown status  in the box while his friend looks in the box.  Typical theorist, he exits the room leaving the dirty work of cleaning up dead cats to an experimentalist friend.  He asks to be told about the experimental results later.   If it is Wigner’s friend’s consciousness that forces the cat to be 100% alive or 100% dead, then even for Wigner, who is out of the room and does not know the result, suddenly lives in a world where the outcome is 100% determined.  Alas, there is no more problem with Wigner living in a world with a superposition of dead/alive cats and corresponding sad/happy friends than there was with the original cat experiment.  I don’t know of anything fruitful that has been gleaned from this Gedankenexperiment.   In fact, I suspect Schroedinger chose a cat in the first place  to have a complex conscious being in the box. Wigner was no slouch, however, so perhaps I am missing something.  One thing is sure.  The next step will be for the theorist to report on the experimentalist’s hard-won findings to the newspapers.

At the same time as the German-speaking scientists of 100 years ago were developing modern physics, their Yiddish-speaking neighbors were writing comedic theater.   Just as physicists worldwide find funny old German words in our technical lexicon, viewers worldwide hear Yiddish words in the situation comedies of today.   Similarities between comedy and physics abound.


S03 Ep12: The Psychic Vortex

January 11, 2010

Hey Kids!  “Math Doesn’t Suck.”  That’s what we learned in tonight’s episode.

First, Sheldon takes us on a visit in his mind to Flatland.  Flatland is a small book written over 100 years ago about a people living in a world with only two space dimensions. Its inhabitants call their two directions  North/South and East/West.  They are unconcerned with our own three-dimensional world that includes a third direction; Up/Down.  Its a book that nearly every one of my physics friends, as well as those in math, engineering and computer science read as a teenager.   Except me…Flatland was the Moby Dick to my Zelig.

So the episode shamed me into finally reading Flatland.  I figured that by now it wouldn’t have anything new about dimensionality I hadn’t picked up somewhere else.   But I was wrong.  Something I had never considered is that being from a world that is one dimension larger allows you to peer inside everything in a world one dimension smaller.  For example, here is a picture of a Flatlander’s house:

A typical house in Flatland.

Since the Flatlanders (not to be confused with The Flatlanders) have no concept of  covering the “top” and “bottom” of their houses, we can see right inside their rooms and even their cabinets.    More abstractly put, we can see the inside of circles, which they cannot.  Similarly a four-dimensional being could see right inside one of our spheres. Four-dimensional people could see right inside every part of our bodies, organs and even cells as if they were all laid out on paper.

But one page in Flatland really blew me away.   Gravity cannot point “down” for them because they have no concept of down.  It points South in Flatland.   It is never explained, but this could be achieved by tilting Flatland relative to the Earth.  Flatland would be tilted in a dimension they cannot even comprehend.  Also gravity is much stronger in some regions of Flatland than others.   So it seems that Flatland is not so flat at all…it must  not only be tilted, but curved space  like so:

Flatland is really tilted and curved. Flatlanders just don't know it.

The increased “steepness” on one end means gravity has a stronger effect there.  Because Flatlanders have no idea of Up/Down, they have no concept of “steepness” either.  Therefore they have no explanation for the variation of gravity in their land.   In the language of modern mathematics we can say that Flatland is a two dimensional world, but it is “embedded” in a three dimensional one.  It would be decades after this book was published that  Albert Einstein described the possibility of gravity in our own world being related to curvature of space.   Like many science fiction writers,  Flatland’s author, Edwin Abbot, was a step ahead of the physicists.

Little books like this can give a pre-teenager or teenager a taste for mathematics that lasts a lifetime.   Which brings us the the second bit of mathematics in the episode:

I am sure the viewers noticed a bit of mathematics “stunt casting”.   At a university mixer, Raj meets Abby who is played by Danica McKellar.  Yes, she is the McKellar of the Chayes-McKellar-Winn Theorem   (“Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Z²”).   She wrote this paper while still an undergraduate math major (at my university, U.C.LA.)    Basically her theorem tells you how magnets must behave if you put them in a particular configuration.

Danica McKellar proceeded to write a wonderful set of books for pre-teen and teenage girls about mathematics, Math Doesn’t Suck followed by Kiss my Math about algebra and pre-calculus respectively.  A third book is on the way.

Mathematician Danica McKellar guest-starred as Abby in tonight's episode. Her books are terrific for middle school girls.

I bought them to take a look, and will be sending to my niece.  These are terrific books with real-world examples that connect directly to mathematics curricula.  They are fun and quirky.   But make no mistake…The content is serious math.  For example, she explains prime factorization,  in terms of a middle-school crush.  She gives little tricks to conquer the dreaded “word problems”.   She warns against common mistakes: 33 is not 9.  She includes testimonials from her friends,  women who used math to succeed, such as  a petroleum engineer and the finance director of a style magazine.   Other times she just gives friendly advice about growing up such as explaining why young women should not try to dumb themselves down to be popular.  The  first book leads up to and includes algebra. The second gives the reader all she needs for pre-calculus.  Somehow it still all looks fun.  I will see if my niece agrees.

The examples are intended  to resonate with young women.  I was having dinner with two female friends last month who remembered math from middle school.  They pointed out to me that many of the examples in middle-school math books use examples like football, that would  more likely interest boys than girls.  No one would accuse Danica McKellar of doing that in these books.

As we saw from Sheldon’s childhood love of Flatland, a small book can make a big impact on the  life of a pre-teen future mathematician, physicist or engineer.  So consider picking up Danica McKellar’s books for the tweenager you know.  Even if you don’t know any young women, you can click here and Danica McKellar  will send books to the library or school of your choice and send you an autograph.

S03E11: The Maternal Congruence

December 14, 2009

Tonight we learned that Leonard’s mother, Beverly Hofstadter (played by Christine Baranski),  and Sheldon have been collaborating on Quantum Brain Dynamics theory. This theory attempts to explain the origin of consciousness.  If Quantum Brain Dynamics theory is correct,  our brains are not mere  calculating machines, just complex enough to hear, see, taste and feel.  Rather they would rely on the non-deterministic nature of quantum mechanics to generate human consciousness.   If this is truly required for our brains to be conscious, the theory goes, then no conventional computer would ever emulate our human insights and experience.

Will computers someday have human consciousness?

Such a theory of the brain can be attractive for a couple of reasons.   First, suppose we think of our brains as just a fancy computer with a slightly better operating system than Windows.  (In my case, Windows-67, which fortunately still works better than Vista.)   It begs a disturbing question.  Will our laptops soon become sophisticated enough to become conscious?  And if so, will our own human consciousness start rolling off assembly lines?

Second, in the standard textbook treatment of quantum mechanics, observers play a special role.   Schrodinger’s cat may be simultaneously alive and dead until a observer takes a look and “collapses” the cat’s status into either 100% alive or 100% dead.  In quantum mechanics, the probabilities to find the cat alive or dead are precisely calculable, but on a case-by-case basis which you kind of cat you will find is impossible to predict.    But what is an observation?  If an atom bumps into another particle,  it does not seem to make sense to say the atom “observes” the particle; it  makes more sense to just say the atom and particle  just are parts of  a now larger system.   But when do interactions become complex enough to cause the “collapse” into a definite condition: dead or alive.   The Quantum Brain Dynamicists claim that the consciousness of the observer plays the key role in measurement and that consciousness itself is a quantum mechanical process.

So Quantum Brain Dynamicists have gone forward to even propose a few quantum mechanical processes might be occurring in a live human’s brain.   In modern laboratories, if extreme care is taken and samples are placed at very low temperatures you may be able to see quantum effects.  Careful laboratory techniques can coax atoms into a new state of matter called a “Bose Einstein condensate”, where many atoms lie in exactly the same quantum state and exhibit quantum behavior on a large scale.   It took 70 years between the time such a state was predicted and when it was finally produced in a laboratory.  It took the researchers’ ability to produce temperatures less than one-millionth of  a degree above absolute zero to accomplish.   Many tried and failed.  Finally the eventual success was recognized by the Nobel Committee as such a great feat that the few who accomplished it were awarded the 2001 Nobel Prize in physics.     Quantum Brain Dynamicists entertain the idea that the same kind of condensate might exist in a living human brain, at normal body temperature.

Does that sound pretty unlikely?  It did to me.  So I poked around a bit.  The amount of published material in refereed scientific journals turns out to be small.  Most of what I found about it was published on webpages and small publishers which is a red flag.  But not so fast.   Roger Penrose, a highly respected mathematical physicist, the inventor of quasi-crystals and other important ideas, is an advocate of the theory.  Penrose suggested in his book The Emperor’s New Mind that the “collapse” due to observations is not based on any algorithm and therefore distinct from what any mechanical computer could ever perform.   Because no step-by-step method describes the “collapse” fundamental mathematical difficulties conveniently disappear.  There are a few papers  on these ideas published by Springer, a serious publisher of scientific work.   Usually ideas about how the world works  separate nicely into mainstream (even if speculative) versus crackpot.  Here we find the distinction is not so clear.

The writers had put Quantum Brain Dynamics into the script, which made me nervous.   Would millions of viewers balk?   Would they send millions of emails complaining that the show had confused pseudoscience with science?  Would they boycott the sponsors?  But as we’ve seen, the idea, while extreme, could not be fairly rejected out of hand.   The writers figured a way out.  Listen carefully to tonight’s dialogue.  The show’s writers don’t have Sheldon and Beverly merely working together on Quantum Brain Dynamics theory, but disproving Quantum Brain Dynamics theory.  Problem solved.

I don’t watch  first-hand  the writers at work, but they sometimes talk to me during their process.   One of the things I’ve learned is that a good part of comedy writing appears to be problem solving.  For example, how do you get two people who are fighting the last time they saw each other to be talking again so you can finish the story?   Likewise, physicists too are often led through their work by a big idea, inevitably finding obstacles to telling a consistent story.  Finding clever solutions seems to be a common part of the work of theoreticians and comedy writers alike.  In an example from physics, one of the biggest problems in theoretical particle physics today is that many models predict that protons decay in less than a second—thereby the Sun, Earth and Human Beings would never exist. Something had to be done. The particle theorists finally solved the problem by inventing (i.e., “making up”) something called “R-parity” that could not change, in order to put the brakes on proton decay.  The quantity now appears in many, if not most, theoretical models in particle physics.   And much like the solutions of comedy writers, “R-parity” may well turn out to be a joke.

S03E10: The Gorilla Experiment

December 7, 2009

Tonight we took a 2600 year journey with Penny and Sheldon “from the ancient Greeks through Isaac Newton to Niels Bohr to Erwin Schrödinger to the Dutch researchers that Leonard is currently ripping off.”

From the Ancient Greeks: Ancient societies,  including the Greeks, watched the skies carefully.  Since they didn’t have Google Calendar, it was only by watching the positions of the stars each night could they mark the passing of the days and seasons and know the best time to plant crops.   (It must have been a nice time to be an astronomer.  If you didn’t treat your astrophysicist nicely, you might not have enough food next year.)  Most of the points of light in the sky, the stars,  appeared to stay in the same place with respect to each other, year after year for as long as anyone could remember.  But a precious few, just five, moved relative to these fixed stars.   We know them as Mercury, Venus, Mars, Jupiter and Saturn.  As Sheldon explains, our Greeks forbears called them “wanderers”, or as we have derived from their language  “planets”.

Your science consultant stands up to a UCLA astronomy professor who voted out Pluto.

When you look out the side window of your car, you can see objects fixed to the ground, bushes, trees, poles etc.  Those near the side of the road zip by.  Objects in the distance seem to barely move at all.   Although you have the same speed relative to all the fixed objects outside your car, close objects have a high angular speed and you have to turn your head fast to watch them. The far objects have a low angular speed which don’t require much tracking of your eyes.  This allows us to understand the motions in the sky of  stars versus the planets.  The change in position in the sky is determined by their angular speed.    Even though stars are moving extremely fast relative to the solar system, most faster than even the outer planets, they are so far away that changes in their position on the sky (their angular position) can only be detected with careful observation, if at all.    For example, compare the farthest planet, Neptune  (thanks, Pluto-haters) to the closest known star Proxima-Centauri, a  little red dwarf star.   Neptune is about 4,500,000,000  kilometers from Earth and moving a modest 5 kilometers per second relative to the Sun.  If you watch Neptune over the course of  a lifetime it will move halfway around the sky relative to the stars since it completes an orbit around the Sun every 164 years.    By comparison, Proxima Centauri moves even faster than Neptune relative to the Sun but its position relative to other stars barely moves; its angular speed is tiny.  The key difference is that Proxima Centauri is 40,000,000,000,000 kilometers away.  Only precise astronomical measurements can see its motions, only hundredths of a degree over a lifetime.

At the other extreme, one of the fastest lights you will see move across the night sky is likely an airplane.  They are moving at only 0.2 kilometers per second.  But since they are close, say 100 kilometers away, they move faster on the sky than planets or stars.  Galileo and Newton realized this, except for the part about airplanes. They knew that if the Earth orbited the Sun, the lack of apparent motion of the “fixed” stars meant they were extremely distant.  The Universe was much larger than imagined.  That story of the learning the Universe is larger than we thought is repeated many times throughout  the history of astronomy.  First by realizing the nearby stars are really so far away.  Then by measuring the extent of the galaxy.  When other galaxies were discovered our idea of the size of the Universe grew larger still.   Today we do not know how large the Universe is, we only know that the speed of light is not fast enough to let us see all of it.

Through Isaac Newton: Newton explained why the planets orbit the Sun much like how a child might swing a cat by its tail over his head.  If the child lets go, the cat flies off in whatever direction it was heading.  In the absence of the Sun, the planets would fly off in straight lines at constant speed in one direction.  Instead, the Sun pulls on the planets using gravity.   The inward pull causes the planets to move in orbits around the Sun rather than straight lines. The same force of gravity that pulls objects to the ground on the surface of the Earth is what causes the planets to orbit the Sun, the Moon to orbit the Earth and what causes the Earth and Moon together to orbit the Sun together, just like the planets.

But what Sheldon was trying to get Penny to say?

Notice that the Moon and Earth go around the Sun together, even though they have wildly different masses.   Objects of different masses fall at the same rate in a vacuum.  Their masses don’t matter.  The Sun causes objects at the same distance to move the same way.  So the Earth and the Moon move around the Sun at the same rate.  The Moon’s extra motion around the Earth is just a small variation in its journey around the Sun. Even the tiny International Space Station orbiting the Earth, really has its path dominated by the Sun.   Its motion around the Earth is just a tiny little wiggle in its path around the Sun.

To Niels Bohr: Theorists had tried many models to explain the architecture of the atom.  But it was only once the experimentalist Ernest Rutherford scattered charged particles from gold foils that it became clear that a  central positive charge, an atomic nucleus,  was surrounded by distant electrons with negative charge.   The motion of the planets around the massive central Sun served as a convenient model.  First the Japanese physicist Hantaro Nagoka (1904) proposed the electrons formed rings much like the dust surrounding Saturn.   Rutherford himself proposed a planetary model (1911), just as planets orbit the Sun under the force of gravity, Rutherford proposed electrical forces kept the electrons in orbit around an atomic nucleus.  Yet even at the time, physicists knew this could not work, since electrons moving in a circle mut radiate light, lose energy, and fall inward, crashing into the nucleus.  The Danish physicist Niels Bohr (1913) took the planetary model, but proposed that only certain distances from the nucleus were allowed, i.e. that the energy levels were quantized. Such quantization had previously served Planck and Einstein to describe the behavior of  light.  Now, Bohr gave birth to a quantum mechanical view of matter, the branch of physics necessary to explain atomic and molecular structure and upon which much of modern technology is based.

The planetary model for the atom, with which Niels Bohr started quantum mechanics, is a view of the atom still held by much of the public.

To Erwin Schrödinger: Bohr’s model was inspirational, but still didn’t work so well.  For example, all electrons in this planetary picture would carry angular momentum around the nucleus, but many do not.   The predicted intensity of radiation from atoms did not match the data.   In 1926,  Erwin Schrödinger developed a more rigorous description of quantum mechanics and the atom.  Rather than thinking of electrons like planets, it is because of Schrödinger we think of the electrons being distributed in regions around the atom.  Electrons are more or less likely to be found in any one place given by a mathematical function resembling a wave.  Schrödinger therefore called it the “wave-function” and in quantum mechanics every particle has one.

To the Dutch researchers that Leonard is currently ripping off: Wave-functions behave counter-intuitively.  Perhaps because our intuition was developed more while running across the African  Savannah than while orbiting an atomic nucleus.  One particularly counter-intuitive behavior of the wave-function is the Aharohnov-Bohm effect featured so prominently in this episode.   The effect describes what happens to the wave-function near a magnetic field.   It isn’t surprising, perhaps, that if your particle, described by its wave-function, crosses a region with a magnetic field that something about it might change.  What Yakir Aharonov and David Bohm predicted using Schrödinger’s wave-function description is that you could have an effect by just going around, but never sampling directly, a magnetic field.   Specifically, if electrons follow two different paths around a region of magnetic field and come together, they will have changed in different ways:  While one wave-function might be at the crest of its wave, another might be at its trough.   Putting the electrons together after their separate journeys, makes the “interference pattern” that Bernadette so rightly admired because they can be beautiful.   The effect was predicted and subsequently observed with magnetic fields decades ago.

The Dutch researchers Leonard was ripping off  have seen the effect now with electric, not just magnetic fields.   The Dutch researchers accomplished it using electrons naturally moving around their sample, through a process called diffusion.    Leonard was trying it even more directly by passing a beam of electrons through a sample.  You may have noticed they added a vacuum pipe carrying an electron beam into Leonard’s lab.  (The end of the pipe is covered in aluminum foil, to keep the flange clean while being built.)  The small nan0-fabricated rings would keep all their electric field inside and he would steer his electrons around either side and create an beautiful interference pattern.

An electron interference pattern. Electrons can behave like waves on the ocean, forming crests and troughs in their intensity.

I leared something new hearing Penny describe the whole thing to Leonard.   Before she said it to the live audience, I never realized the Aharonov-Bohm effect was so funny.   I bet we could have had them rolling in the aisles if we mentioned the Stern-Gerlach effect.

P.S. Easter Egg alert.  You can see your science consultant in tonight’s episode sitting across from an actual UCLA graduate student in theoretical physics, our very own Sheldon. (He is even working on one of the same problems: N=8 Supergravity.)   A gold star to the first person who identifies which scene it is. Scenes are rehearsed several times and then run through several times in front of the camera to get it right. Luckily the props department gave us an interesting little book on quadrupole moments of nuclei from the 1960s to read. Most of the books you see around the apartment and on the sets are real physics books, some very interesting, so there is always something good for us to read between takes.

S03E09: The Vengeance Formulation

November 23, 2009

In tonight’s episode, Sheldon is angry. Or maybe it is just me.  Some European researchers  appeared to beat Sheldon to the discovery of magnetic monopoles.  In real life.  And they are not even particle physicists. Now Sheldon could be upset, but he can’t cry foul if he were scooped by a team that “got there first” with a technique that was better, or at least faster.  There is only one problem.

At the end of last season,  Sheldon led the gang on a months-long expedition to the Arctic to find the magnetic monopoles predicted by string theory.  The team returned in the season premiere, after a long ordeal, but like all such experiments before them, without catching any magnetic monopoles.    Then things took a strange turn for all of us.

In between the season premier’s taping date (August 11, 2009) and its air date (September 21, 2009)  an article  appeared on September 3  in the prestigious journal Science claiming discovery of magnetic monopoles. The equally prestigious journal Nature immediately ran a news summary,  “Overwhelming evidence for monopoles: Multiple experiments reveal materials with single points of north and south“.

Worse still, the researchers interviewed for the Nature article were taunting Sheldon in public:

People have been looking for monopoles in cosmic rays and particle accelerators — even Moon rocks,” says Jonathan Morris, a researcher at the Helmholtz Centre for Materials and Energy in Berlin.

Instead, these researchers claimed, they found monopoles in small magnetic crystals “the size of an ear plug”.  Boy, Sheldon and everyone else searching for monopoles in cosmic rays and at accelerators must have been pretty stupid to be looking in all those wrong places.

But here’s the “only one problem”.    For every  North magnetic pole the researchers created in their small crystal samples, another magnetic pole, the South pole could always be found.   As Sheldon describes to Ira Flatow on National Public Radio’s Science Friday, “mono-” means one in Greek (“di-” being two.)  These samples  always had two.     Sure, to have called them “monopoles” is only off by one,  so maybe the editors of Nature will claim they were close enough.  But one versus two makes all the difference, between revolutionary “monopoles” and mundane “dipoles”.   They experiment reported simply did not discover magnetic monopoles.

Long tubes of magnetic field in spin ices produce effective monopoles at both ends. The two monopoles (North and South) are really a dipole.

The experiment reported in Science was a tour de force.   The experimenters did a beautiful job of separating the “North” and “South” poles by an enormous distance (nanometers, or billionths of a meter, which only a physicist could call “enormous”) in the materials, called spin ices.   So-called because the arrangments of spins is similar to that of hydrogen atoms in frozen water.  The experimenters created long tubes of magnetic fields, like spaghetti, whose ends behaved just like magnetic monopoles.  However, spaghetti has two ends.  They had created two objects like monopoles with opposite charge….in other words, a dipole.  Now each of these quasi-monopoles is still interesting.  It creates an anomaly in the crystal called a singularity.  The researchers measured and quantified much about the behavior of these singularities by scattering neutrons off of their samples.  Condensed matter theorists had developed interesting models about how such singularities would behave, and this experiment provides much needed data on the topic.

My only beef, and probably Sheldon’s too, is that overselling results by the media has consequences.  The public naturally comes away thinking a discovery of a completely different magnitude has been made.  What happens if one day Sheldon or someone else discovers a real magnetic monopole?  Physicists would have cried wolf too many times.

Now perhaps the media went farther than the researchers claimed.   For example, when my Ph.D. experiment, the CDF detector at Fermilab, announced evidence for the top quark in 1994, the New York Times said the final element of matter had been discovered (NYT 4/26/94).    Well every single one of us knew full-well that at least the tau-neutrino and probably many other particles had yet to be discovered.  Sad to say, this happens often, and consumers of the science media should take reports of major discoveries with a healthy dose of skepticism.   (Extrapolating, it makes me wonder how much we should believe of what reporters say about politics or world events.)

Thankfully there are exceptions.  Sometimes after an interview reporters come back to me with their near-final draft and ask for comments.  Those reporters get it right.  I heard from someone that went to journalism school that they discourage reporters from going back to the interviewees for a final check,  to promote impartiality.  But what’s the point of of impartiality on a news item that is not even correct?

So perhaps the same happened to the authors here.  I checked the original article and right in the first paragraph they are careful to state that they have created objects “resembling” monopoles.   They say that they “look like” magnetic monopoles.  While they never explicitly stated that these were not real monopoles, I think the researchers have done an honest job in the original article.   It is in the news summaries, such as the one linked above, and its echoes throughout the news world, where things got carried away.

Perhaps after listening to Sheldon’s interview on NPR’s  Science Friday, the journalists who wrote the news summaries confusing this experimental observation with true monopoles will post a clarification.  Sheldon is waiting.

Will you keep Sheldon waiting?

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