S03E17: The Precious Fragmentation

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!!

20 Responses to “S03E17: The Precious Fragmentation”

  1. Tony Says:

    We all know that epic time-wasting is often a part of being a postdoc, but – dang! this episode was just embarrassingly silly and crude. How the heck do they manage to retain their funding at their labs? It’s like a Homer Simpson job at the Springfield Nuclear Power Plant: getting your work done is entirely optional, AND somehow you remain employed throughout the series!

  2. Tyler Says:

    Tony, have you ever seen The Office? “getting your work done is entirely optional, AND somehow you remain employed throughout the series!” is the entire premise of the show.

    Anyway, nice job putting Maxwell’s Equations into words, instead of equations. I’m curious about this, however:

    “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.”

    The way I’ve seen that “linchpin” term described is as a solution to the inconsistency in the original Ampere’s Law, as described here: http://en.wikipedia.org/wiki/Ampere%27s_law#Shortcomings_of_the_original_formulation_of_Amp.C3.A8re.27s_circuital_law

    Basically, if you draw a loop around a wire near a capacitor, the “enclosed current” is different depending on how you define the surface bounded by that loop, so there *must* be another term. I guess this is perhaps a better way to present the material to a typical undergraduate class (“the equation we’ve been using is inconsistent” is probably more compelling to most students than “wouldn’t it be cool if there were more symmetry in these equations?”), but it leaves students with the impression that Maxwell’s thought process was different than what you describe here.

    I wish we had a History of Science course that science majors and others could take as an elective…

    • David Saltzberg Says:

      Indeed, when I teach it I start with that inconsistency. Often a few students find it on their own in advance. For example if you consider just a line segment with charge flowing, you get a different answer for the magnetic field from Ampere’s law (without the Maxwell term) than the good old Biot-Savart Law because charge builds up at the ends, which create a changing electric field.

      I don’t know historically which idea Maxwell had first. At some point though he must have had both. If someone knows for sure I can edit what is there.

      • feldfrei Says:

        What makes it difficult to understand Maxwell’s original thoughts from our modern viewpoint is the use of mechanical analogues throughout his work. He was mainly concerned with constructing a model for the medium (known as the ether) and at his time the modern concept of fields as a property of the vacuum (without any mechanics and no ether at all) was not yet developed.

        Paper “On Physical Lines of Force” (1861)

        Click to access On_Physical_Lines_of_Force.pdf

        Paper “A Dynamical Theory of the Electromagnetic Field” (1864)

        Click to access A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf

        The most remarkable feature of Maxwell’s equations is their transformation property: invariance under Lorentz transformation. If one looks back in history this means that special relativity was already implicitly contained in Maxwell’s theory of electromagnetism but it took about 40 years until Einstein came up with the modern interpretation of the transformation: principle of the constancy of the speed of light, no ether, no absolute time.

        Thus, Maxwell’s theory was way ahead of its time (EM waves were discovered experimentally by Heinrich Hertz in 1887). In contrast, quantum theory came much later than the experimental observations which had to wait decades to find a theory explaining them as e. g. the emission spectra of the elements. The latter have been used extensively since Kirchhoff and Bunsen introduced the spectrum analysis and new elements have been discovered like cesium, rubidium or helium – at a time when nobody yet knew about energy levels in atoms.

        The history of science is quite interesting …

  3. shellorz Says:

    IMHO, Sauron’s one ring is better than the metamaterial you’re talkign about, even though we could make it work beyond the infrared frequency. Indeed. such a “cloacking device” would have a considerable drawback : when cloaked , you couldn’t be able to see what’s outside, for you need light to come in to be able to see 🙂
    Being able to see and to be invisible at the same time somwewhat is against physics laws, isn’t it ?

    • David Saltzberg Says:

      What you say must be true for the invisibility ring as well. Any photon absorbed by your retina, no matter how you are cloaked, is a photon another observer will not see. However that is a very small change in intensity. Perhaps what the person in the metamaterial can do is look in uncloaked infrared with infrared glasses on. Then they would be detectable with an infrared camera, but how many people carry those around anyway.

      • shellorz Says:

        I hear you. But the one ring is a fictional magic ring. Which means it can’t exist or if it can, it uses techniques beyond our knowledge, like cloaking you in another dimension or something 😉

  4. shellorz Says:

    PS : that shirt is awesome. Did you make it (photoshop) yourself or is it sold somewhere online ?
    A more cypherered version would be the 4 equations with a “FIAT LUX” legend.

    • David Saltzberg Says:

      For one:

      Or do a google image search on “maxwell’s equations t shirt and then there was light” and you will find many places that sell it.

      FIAT LUX … it is the UCLA Latin motto!

      • shellorz Says:

        thx, I’ll look into getting one I guess.
        Didn’t know about UCLA’s motto. Hopefuly, it’s not undeservefuly used (For instance Goethe’s last words were “mehr Licht, mehr Licht(more light more light)” and people reused this expression as a motto for “more enlightenment, more science” when many think he actually said that because he wanted more light in the room). Err, that was off topic.

      • Arne Says:

        @shellorz: Some citizens of Frankfurt, the town where Goethe was born, actually have yet another theory on his famous last words. Goethe, beeing born in Hesse and spending his youth there, was about to say “Mer liecht hier so schlecht”, which is hessian dialect and means “One is lying here very uncomfortably”. Unfortunately, the first two words of his hessian complaint sound quite the same as the High German “Mehr Licht”, thus the confusion. 😉 How’s that for going off topic, ahem…

    • Vanessa Says:

      Dunno if you’ve found your shirt, but you can find it on cafepress.com. Quite on interesting site selling t-shirts and hoodies and the like. Spent the whole of last night browsing through designs that would make any geek drool. 😀 Here’s the link: http://www.cafepress.com/+god_said_maxwells_equations_dark_tshirt,96599631

  5. thonoir Says:

    Fascinating and entertaining, as always.

  6. vivow Says:

    Even though it was kind of silly, i like this episode. Mostly tho because i have a golden “the one ring”. Still dont know if it was worth all the money 😉

  7. Uncle Al Says:

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

    If they want grant funding (with academic overhead covered) they’ll need convince more than one Dark Lord to cooperate. If they do it on their own tab at home, Homeland Severity (the Eye of Sauron) will bust their chops (confiscate their shoes, and rip away their underwear). They’ll awaken in Dreamland surrounded by armed Oompa-Loompas.

    Every ccd camera is an NIR camera after you pop out the IR cutoff filter and add a daylight blind filter. Cotton is white by lightscattering, varying as (lambda)^(-4). BWA HA HA!

  8. feldfrei Says:

    Just another short comment on Maxwell’s equations: the electromagnetic properties of the vacuum are described by the constants ε0 and µ0. However, quantum field theory tells us that the vacuum is not empty but rather filled with virtual short-lived particles. If the field strength is sufficiently large, the vacuum can be polarized and magnetized and shows a nonlinear response. Recently, a nice example was studied theoretically – a matterless double-slit in form of two focused super-intense laser beams. Inside the foci the refraction index of the vacuum is modified resulting in scattering of a weak probe laser beam:

  9. feldfrei Says:

    The periodic table shower curtain is awesome – but what about the chart of nuclides? http://upload.wikimedia.org/wikipedia/commons/thumb/7/79/NuclideMap_stitched_small_preview.png/800px-NuclideMap_stitched_small_preview.png
    That would make a nice staircase wall decoration 🙂

  10. shellorz Says:

    you can get the curtain from thinkgeek for 30 bucks if I recall correctly


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    […] último episódio que passou nos EUA (S03E17 – “The Precious Fragmentation”), o professor diz que há “física em todo lugar” e fala sobre invisibilidade, o poder do Um Anel do Senhor dos […]

  12. Mir Muhammad Lodro Says:

    What a Maxwell’s Equations are! These equations have captivated me and I’ve become over-obsessed with them. I’m also so surprised why Maxwell is much celebrated than other big names in Physics, although his contribution was the displace current in Ampere law. it was Heaviside who simplified his twenty equations to four equations.

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