S04E12: The Bus Pants Utilization

I was afraid while this week’s episode was taped.   I feared everyone on set would ask me how a theremin works.   And I had not done my homework.  In case this ever happens to you, read on, and I will spare you the embarrassment.

This week, Sheldon played his theremin, the eerie sounding electronic instrument favored by avant-guard musicians:  from the Beach Boys to Vladimir Illyich Lenin.   The theremin came to Lenin shortly after Soviet scientists developed a proximity sensor.

 

Just like Sheldon, Lenin enjoyed playing the theremin.

The key to a Theremin is a so-called “tank circuit”.   In a classical theremin you will find a coil of wire connected to two metal plates.  The coil of wire is sometimes called a “choke”. That’s because it does not allow  fast-changing signals (“high frequencies”) to pass through.    The two metal plates are called together a capacitor, because of their capacity to hold opposite electric charges on each plate.   Their reservoirs of charge allows fast signals to pass through, but are quickly depleted by slow-changing signals (“low frequencies”).  The parallel plates work in exactly the opposite sense as the coil.  One element blocks low frequencies, and the other blocks high frequencies.   Putting the two together allows only a narrow range of frequencies pass through.  Energy in the circuit sloshes around, between the charge on the capacitor and the current in the coil at a well calculable rate.

The specific frequency passed by the tank circuit depends sensitively on the values of the capacity of the parallel plates to hold charge (its “capacitance”) and the inability of the coil to change its current (somewhat opaquely called its “inductance”).   Every body and everybody has inductance and capacitance.  If we connect our tank circuit to an antenna you can change the resonant frequency by simply moving your hand near it, adding your own capacitance and inductance to the circuit and changing its tune.

A "coil" and two parallel plates (a "capacitor") form the heart of a theremin.

When you play a classical theremin, you don’t control the audio frequencies directly.  Our ears can only hear thousands of vibrations per second.   That’s fairly slow for electronics, and the size of the coils and parallel plates would have to be enormous.   It is much easier to build electronics working at higher frequencies.  So, theremin designers make use of a mathematical trick.   It turns out to be easy to find the differences between frequencies.  So by comparing two “tank circuits”, one you are modifying with your hand, and one without your intervention.  The frequency difference is sent to the theremin speaker.

Working off the difference is a common trick.  Your AM radio (if you still have one) has a tuner, but you are not tuning the tank circuit. Rather, you are tuning another circuit, close to the frequency you want to receive. Your radio uses the difference to find the signal.   Scrabble players take note;  this fancy trick is called superheterodyning.

The key here is the changing signals.   When physicists want to talk about the changes of values, rather than the values themselves, they need to work with differences, also called “differentials”.  The equations describing them are called “differential equations”.  Differential equations are key to understanding the flow of currents in the tank circuit of a theremin.   And the solving of differential equations was of course the main point of tonight’s story.

Unlike many other types of equations, there is no definite method to solve a differential equation.  Often physicists are led to try a few tricks, look them up in dusty old tomes, or ultimately to guess.  In modern times, we can enter the equation into a computer and hope it can find the answer.  Leonard had the brilliant idea this week to skip that step, and have the iPhone app recognize the handwritten equation and solve it directly.

Common differential equations have names.  The solution to the tank circuit is a “sine” function.   The “spherical Hankel function” mentioned tonight comes up when solving vibrations of spheres.   The laws of  population growth give a differential equation solved by “exponential functions” which is, unfortunately for us, the fastest growing of all the elementary functions.

I’m no iPhone designer, and the white boards were a salient part of the story this week.  Luckily we found a friend-of-a-friend of mine, Robert McNally who designs iPhone apps for a major online dating company.  Everything you see in this weeks show is 100% real, quality, iPhone development @%^#!.  Click on his name above, and you will learn a little of the inside story of the dueling app software.

Anyway, nobody liked my other iPhone app idea.  I want to make a Geiger counter with an iPhone.  I think it could work.  Just look for single bit errors in the iPhone memory due to ionizing radiation.  The error rate is proportional to the radiation.

So now they are out there.  Two good ideas for iPhone apps.  Elves, the shoemaker is waiting.

S04E11: The Justice League Recombination

Many of you may have laughed at Zack tonight because he confused a picture of the Solar System with a model of the atom.   But, building on that similarity a century ago won Niels Bohr a Nobel Prize.

Is that represent a planetary system or an atom?

A planet, left alone, would travel in a straight line, at a constant speed, forever.  That observation is so important, it became Newton’s First Law:  “Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force.”  Like the Pioneer Spacecrafts launched in 1972 and 73, at our current speed we’d leave the Solar System behind in just a few decades.   So if  Earth  is traveling in near circles around the Sun,  then a force must be acting on it.   What could be simpler?  But actually there are a number of subtleties that trip up and sometimes even amaze our first-year physics students:

Newton’s second law says that a force, such as the attraction of gravity between the Sun and the Earth, causes a directly proportional change of acceleration:  “Force equals mass times acceleration”.  Acceleration is just a definition: a change in velocity per time.  When you say your car goes from “zero to 60 mph” in 10 seconds, that’s a description of its acceleration.  But the Earth’s speed changes by less than 2% from its average over the course of a year and its average has barely ever changed in over 4 billion years.    If our orbit were perfectly circular, it would not even change at all.   What happened to all that acceleration that the force must produce?   The missing point is that velocity is not just speed, but also direction.    Every  six months, the Earth completely changes its direction as viewed from the Sun.  In such a circular orbit, the acceleration changes the direction of the motion not its rate…so velocity is still changing.

Newton’s second law also says the acceleration points along the same direction as the force.   A common misconception is that the acceleration of the planet in circular orbit points along the direction of motion.   But the force of gravity points along a line between the Earth and Sun.  So the acceleration cannot be pointing along the direction of such a planet’s motion.  The acceleration must somehow point along the same line between the Earth and Sun.   That is, it points at right angles to motion along the circular orbit.   So  the planet changes direction but not speed and is still accelerating.  A planet in circular motion can be acted on by a force forever, but its speed and thus energy never change.

Richard Feynman put a fine point on it.  In the time of Kepler, many stated that the Earth moved because angels pulled the Earth along, flying ahead of the planet.   Newton showed us though that this model cannot be correct.   The angels must be pulling on us inward towards the Sun, thereby creating our (essentially) circular orbit.

Back in the early 1900′s, the existence of atoms, indivisible units of the known elements, was largely, and correctly, in favor.   What nobody knew, was the structure of an atom itself.  Theories abounded, that were all reasonable.    In the “plum pudding” model guessed by J.J. Thompson, the discoverer of the electron, there was an equal mix of positive and negative charges (protons and electrons) all mixed up uniformly in a kind of goo.  Not a bad guess but wrong.   Another model described atoms as cubes, with electrons at the corners.    A Japanese physicist, Hantaro Nagaoka, guessed a model with electrons surrounding a central positive charge arranged in a single disk, at a constant radius, much like a narrow ring of Saturn.

All these models were reasonable. In fact the plum pudding model turned out later not to be a bad explanation for the structure of the nucleus.   No amount of theoretical calculating would resolve the impasse.   It took an experiment to point the right way forward.  In Ernest Rutherford’s lab, evidence was seen that alpha particle (positively charged particles) scattered off of a densely packed solid nucleus.  So the  closest winner among the predictions above was the Saturn-like, or planetary model—which unfortunately predicted essentially nothing correctly.

Niels Bohr quickly refined that model to one with electrons orbiting a central nucleus at different distances.  He had the electrons orbit the central nucleus at a constant speed and distance, much like a planet, but with the force of gravity replaced by the force of static electricity between the (negatively charged) electron and (positively charged) nucleus.   He helped start quantum theory by assuming that, unlike planetary systems, electrons could only orbit the atom’s central nucleus at specific, fixed distances.

Experiment showed that Bohr’s model worked better than the Saturn model because it  explained the specific values of light frequencies emitted by atoms.   That left us with the picture of the atom so popular in popular culture, with little electrons zipping around a central nucleus just like planets around the Sun.

The planetary model of the atom is most familiar. It was the first to make good predictions. But it does not work completely.

Almost immediately physicists knew that Bohr’s planetary model of the atom could not be the final story.   It is a fact that accelerated electrons radiate power.   That is actually how a radio transmitter works, it accelerates the electrons in a metal antenna.   But since atoms can be stable forever, with their orbiting (accelerating) electrons, something was wrong.   Bohr finessed the issue by saying an electron could not move closer than a minimum radius.   But worse problems could not be solved.  An electron truly orbiting a central charge would do so in a particular direction, and therefore have angular momentum.  But experiments said otherwise, that it could even be zero.   No orbit around a central body can have zero angular momentum.

Ultimately the planetary model was killed by these disagreements with data.   Only the with advent of the full quantum mechanics, including the Shroedinger wave equation, could a picture be made consistent with all that was observed.   In this, better working, picture the lowest energy electrons exist in a kind of cloud around the nucleus, with nothing orbiting at all.  Unfortunately, when quantum mechanics becomes key, there is no familiar system, such as planets’ orbits, to compare it to.

In the modern picture of an atom, there are no orbits, just a cloud of probability of finding the electron.

Zack wouldn’t confuse a cloud of electron probability with a planetary system.   Since the planetary model of the atom is dead, one could even say his was a better guess than Leonard’s.

In a strange way Zack had a point when he said, “That’s what I love about science–there’s no one right answer.”    Science typically moves forward with multiple of guesses, such as the Saturn ring model of the atom.  Several explanations often  co-exist until experiments weigh in and pick some, one, or none.

No wonder Zack wants to “talk science with the science dudes.”

S04E10: The Alien Parasite Hypothesis

Tonight Amy prepared a brain sample for her two-photon microscope.  A two-photon microscope works on a principle that violates the basic statement of Einstein’s work that won him the Nobel Prize.

Amy Farrah Fowler prepares samples for her "two-photon microscope".

 

Einstein was busy in 1905,  often called his Annus Mirabilis (his “Miracle Year”).    He produced his work on special relativity– but he never won a Nobel Prize for that.   He produced the linchpin  for an elementary explanation for thermodynamics–but never won a Nobel Prize for that either.   Einstein’s Nobel-Prize winning work that year explained the most basic interaction of atoms with light, and forever changed our view of light.

Atoms are made of two charged particles, protons and electrons.  Through those electric charges they interact with light.  Modern physics has been studying these interactions for over 100 years and is the basis of everything from lasers to making pornographic pictures in airports backscatter X-ray scanners at airports.  Einstein’s Nobel Prize explained how only light above a certain energy will free an electron from atom:  Giving a small amount of energy to an electron in an atom may wiggle its orbit a bit, but won’t break it free.  Only with a large enough kick can an electron be separated from its atom.  But physicists found that visible light, no matter how bright, would not knock electrons free from a material, while even a weak ultraviolet light could.

Einstein proposed a solution.   He predicted that the energy of a beam of light was carried by individual particles of light, now called photons.  He  borrowed the idea from Max Planck, who had assumed such quantization  to explain the color and brightness of hot objects.    But now Einstein took the idea not just as a mathematical trick, but as a real description of the nature of a beam of light.  So light would collide with atoms like two billiard balls.  For most materials, visible light particles do not carry enough energy to knock electrons out of atoms.   Only ultra-violet light has enough energyto knock out electrons.  No matter how intense you make a the visible light, the story goes, you will never knock out electrons because the individual photons do not have enough energy. Because this represents one of the most basic interactions of light (the photons) with electrons is called the photoelectric effect.

During my own undergraduate days we demonstrated this effect in our student laboratory.   We shone light onto a metal and looked for a charge buildup due to escaping electrons, just as it would if it were exposed to static electricity.    But no matter how intense the visible light, no charge was built up.  But a small ultraviolet lamp, such as you might use in a tanning bed, quickly charged the metal.   Only ultraviolet photons have enough energy to knock out electrons, so there is a minimum for anything to happen.   This is the same reason that rays damage your skin so easily, but visible light does not.

“Wait!” you might be thinking.  What if the atom could absorb two particles of light, “two-photons”, at once?  Couldn’t the combined energy of two low-energy, even infrared photons, be enough to kick out an electron?   And you’d be both right and eighty years too late.  The effect was predicted by Maria Goeppert-Mayer in her 1931 Ph.D thesis.   She later went on to win a Nobel Prize of her own for completely different work, explaining the structure of the atomic nucleus.

In her 1931 Ph.D. thesis, Maria Goeppert-Mayer discovered an effect Einstein missed: two-photon absorption. This became the basis of the two-photon microscope.

The effect is very small, since two photons must combine with the atom at the same time.   Most collisions of light with atoms are so small they are characterized by a small area.   In my undergraduate lab we did not have anywhere close to the intensity for this effect to even begin.  The effect predicted by Maria Goeppert-Mayer was so small that a new unit of measure, using the square of the small area,  had to be invented.  To this day, the unit is called the “GM” in her honor.

The effect would have remained just theory, without a light source intense enough to produce it experimentally.   Charles Townes, the inventor of the laser, had such a device.  His student, Isaac Abella (later one of my professors) was one of the first to demonstrate two-photon absorption experimentally, using infrared laser light to produce absorption at a factor of two less energy than Einstein’s model.

The two-photon technique has revolutionized the ability of scientists (and if I were  Sheldon I might add  “…and biologists”) to study thick biological and even living tissue.  A two-photon microscope uses precisely this effect predicted by Goeppert-Mayer.     Hence the discussion:  Sheldon complained to Amy she was cutting the samples to thin.  You can’t slice tissue too thin for an electron microscope, but thick samples is where a two-photon microscope comes into its own.   Lucky for us, Newport Corporation lent us a two-photon microscope, the one you see on the show.

In a two-photon microscope, not enough energy is delivered to liberate the electron, but does excite the molecules of a flourescent dye with two photons.  The resultant single photon fluorescence is a single photon of nearly twice the frequency of the incident red or infrared light, typically green and can be separated from intense incident light to form an image.

An image taken with a two-photon microscope of a neuron from the brain of a mouse. (Journal of Neuroscience)

Another advantage is that the rate of exication now depends on the square of the illumination, since the technique needs two photons to be absorbed.  By carefully focusing the incident light, only one small selected region of the sample glows, allowing a detailed picture without the extraneous light from everywhere else, as you would have in a conventional microscope.

And so we finally see scientists wearing lab coats on The Big Bang Theory.  That’s what happens when you let in the biologists.

S0409: The Boyfriend Complexity

Lucky Raj.  This week he gets time on the biggest optical telescope in the world, the Keck Observatory.  (Well now second biggest, see comments.)  “The Keck” has two telescopes each 10 meters (33 feet) in diameter.

The Keck Telescopes are the largest optical telescopes in the world. Operated by University of California (my own university) and Caltech, they sit atop Mauna Kea in Hawaii at 13,800 feet above sea level

A large telescope helps you twice.  First of all, a larger area means a bigger bucket with which to catch light from distant objects.  The more light you can collect, the fainter objects you can see.  Second, it is an inescapable law of optics that  the finer detail (resolution) you want see, the bigger the lens (or in this case, curved mirror) diameter must be.    That’s the main reason you might use binoculars at a baseball game or opera.  There’s plenty of light.  But instead of your own quarter-inch pupils you can see more detail using the 1-2 inch lenses of binoculars to create an image you can see in finer detail.

What about the Hubble Space Telescope, surely the best telescope in the world?  Actually the Keck telescope is better than Hubble in all but one aspect.   It is on the ground.  Ground-based telescopes have to look through the air between them and space. Most of us are  familiar with when looking a great distance, either down from a mountain or across a large body of water, objects on the other side are seen moving around as if they are under water.   That distortion is due to rapid changes in the air, called turbulence, which mess up the image you are trying to see.  Hubble’s strength is that it is above all the atmospheric turbulence.

Still Keck’s astronomers are up to a challenge.  They monitor what should be point-like stars and they deform their telescopes’ mirrors within thousandths of a second to undo the atmospheric distortion.  They call it “adaptive optics”.  Under the right conditions, Keck can use adaptive optics to observe objects better than even the Hubble Space Telescope.

The best ground-based telescopes are located on tops of mountains to be above as much of the atmosphere as possible, or at least in locations with very stable atmosphere.  Astronomers say such locations have “good seeing”.   The Keck telescopes are located atop Mauna Kea, the highest point in Hawaii, at almost 14,000 feet elevation.  So lucky Raj, not only does he get time on the biggest optical telescope in the world, he gets to go to Hawaii, right?

Not so fast.  He only went down the hall. Professional operators point the telescopes.   Modern astronomers don’t look through an eye-piece anyway, they record images with digital cameras.  They receive images over the internet.   So Raj just went down the hall, to a dingy little conference room with a bunch of computers.  (Did anybody notice what email client Raj still uses?)    If you are interested in becoming an astronomer don’t despair.  Students and faculty still sometimes do go to Hawaii, or even Chile, to observe.

Modern astronomers don't look through eye pieces. They record images with digital cameras.

Raj had something exciting to do tonight, looking for planets in a stellar system outside our own.  Also called extrasolar planets or exoplanets, astronomers’ instruments are actually sensitive enough to find planets orbiting other stars.  But generally not by direct imaging.  The nearby star is too bright and the planet is almost always too dim.   In Raj’s case he was looking for a star passing in front of the star Epsilon Eridani, a star from Sheldon’s song.

Imagine you were an extra-terrestrial watching our own Earth go around the Sun from another stellar system.   Our Earth has a diameter about 1/100-th the size of the Sun.  So a distant observer around another star could hardly see the little bit of light reflected by the Earth from the Sun compared to the enormously bright Sun itself.  But if you, the alien observer, are in just the right place, sometimes the Earth will pass between us and the S It makes a kind of tiny eclipse called a “transit”. Because area goes as the square un. of the diameter, our Earth would block out 1/10,000-th of the Sun’s brightness.   A sensitive enough measurement would see its transit in principle.    Observers in our stellar neighborhood would see this dimming for at most a few hours, but regularly every year.     Jupiter would be much easier, it would block a full 1% of the Sun’s intensity, although only once every twelve years, the time it takes Jupiter to orbit the Sun.

During a "transit", an extra-solar planet passes in front of a star, dimming it ever-so-slightly ever-so-briefly.

Astronomers have other techniques, too.   Just as stars’ gravity pulls on planets to make them go around their orbits, the planets pull on stars.   Newton’s third law requires it.  For every force (in this case gravitational pull of a star on a planet) there must be an equal and opposite force (in these case the pull of the planet on the star).   The only difference is the stars are much more massive and don’t change their velocity anywhere near as much as the planets do in response to the same force.   Thus the stars move in tiny circles with the period of the planets orbiting them.   For the same reason when you jump off a table, not only does the Earth pull you down, but you pull the Earth  up towards you with exactly the same force.  Astronomers can measure this tiny dance of the stars by measuring their motion towards and away from us.  A star that is heading towards us will emit radiation just a little bluer than one heading away from us which is just a little redder, due to a shift called the Doppler effect (remember the Halloween episode?):

The "Doppler Effect" precisely measures the motion of stars, which changes as their own planets pull on them.

Want to find more exoplanets?  There’s an app for that.  The  iPhone has a (free) exoplanet app.  It beeps every time a new extra-solar planet has been discovered.  (And besides, the app has really cool animations.)   So far, it is easiest to find the largest, Jupiter-sized, planets,  which are closest to their host star.  But as the technique improves astronomers will find smaller and smaller planets.  We have not yet found a planet at the right size and distance to host water on an Earth-like surface.  But it may come soon.  The Kepler satellite uses the same technique as Raj, but using a space telescope so it is even more sensitive.   I would not be surprised if they announce an Earth-like neighbor within the next year or so.

Astronomers know of over 500 exo-solar planets to date.    Since the technique only finds really large ones so far, they are safe from Drs. Tyson and Brown.

S04E08: The 21 Second Excitation

We preempt tonight’s science to bring to you breaking news about last week’s science.  Astronomers just announced Eris may be smaller than Pluto.

 

Pluto and Eris are dwarf planets that orbit the Sun in the Kuiper Belt.

Eris is a dwarf planet discovered only within the last ten years.  Along with Pluto, it orbits the Sun in the Kuiper Belt, at over 30 times the Earth’s distance to the Sun.    But Eris’s discovery was a day of reckoning.  Eris was larger than Pluto.  How embarrassing.  How could Pluto be a planet, so the public argument went, if an even larger body was not?   It was a simple and persuasive argument.  Certainly easier to explain than the full reason for demoting Pluto: that some planet-like objects like Pluto are different than the eight solar planets since they don’t clear their orbits.  Eris was larger than Pluto–what could be more direct.

Up until now, the size of Eris was estimated by a number of techniques.  One way was from its mass.  Its mass is measured from the time it takes for its moon, Dysnomia, to complete its orbit. The larger the mass of the central body, the faster its moons will orbit it.  (Mathematically, the duration of the orbit of a small body around a large, central one goes inversely with the square root of the mass of the central body.)   For example,  if  Earth were four times as massive, our own moon, Luna, would orbit us in just 14 days.  That is, the gravitational  force on the Moon from the Earth would be four times as strong and the only way the Moon could travel in a circle around us at its current distance  would be to increase its speed by a factor of two.  We’d have 24 months to remember.   Then, assuming we counted months properly, it would be Christmas in Vigintiquattuorber.

 

Eris is orbited by its moon Dysnomia. The period of orbit tells us Eris's mass, but not its size.

So anyone can compare the mass of Pluto to the mass of Eris and determine which is physically larger right?  Wrong.  That’s only if you know the two objects have the same density.

To measure the physical size of an object you need to do something geometrical.  A few techniques: extracting the cross section from its brightness and even direct imaging gave some results, but up until now with significant experimental uncertainty.  The experimental uncertainties were always such that Eris could have been smaller than Pluto, but it just looked like that would be unlikely.

A special astronomical event changed all this.  One of the most useful moments in astronomy is when an object passes in front of  a star.  This event is known as a occultation, and can be thought of as a kind of eclipse.   Occultation and eclipse are not exactly the same thing.  In an “occultation” the nearer body completely covers the farther one–in this case Eris passing in front of a star in the constellation Cetus.  Distant stars appear point-like to us.   An “eclipse” can be an occultation but also when a body passes into the shadow of another is a completely different kind of event also called “eclipse”.  Sometimes the nearer body does not completely obscure the body behind it, in what is called a “transit”.  Too many things to remember?  Just tell your friends it is a “syzygy”.

Watch the occultation of a star by an asteroid (0:56)

Stars occupy such a small angle on the sky that predicting these events are hard, but astronomers are up to the task.  Eris is so small that its shadow is much smaller than the size of the Earth.  Astronomers had to predict which spots on Earth had the best chance and a few found it. When Eris passed in front of a dim star in the constellation  Cetus, astronomers measured exactly how long the star was blotted out.   The larger Eris is, the longer the star disappears from the sky.  A telescope in Chile found it dim for 76 seconds.   A few other measurements at other telescopes yielded Eris’s diameter.  And to everyone’s surprise, Eris was smaller than its mass suggested.  (Actually this was within the range of experimental uncertainties of the previous measurements.)   It is a physically smaller, more compact object than Pluto.

For a wonderful account of this observation made by one of the discoverers of Eris, see Mike Brown’s blog about the event, which is where I found most of my information.

Dr. Tyson should come back.  And he should bring Dr. Brown with him.  I suspect Sheldon needs to have a word with them.

S04E07: The Apology Insufficiency

Tonight’s show had a special guest star, Dr. Neil deGrasse Tyson, Director of the Hayden Planetarium in New York City.   As we learned from Sheldon,  Dr. Tyson was instrumental in defining a new class of solar system object, the “dwarf planet” — and then demoting Pluto into it.

Dr. Neil deGrasse Tyson, astrophysicist, guest starred on tonight's show as Dr. Neil deGrasse Tyson.

Several objects nearly the same size as Pluto share approximately the same orbit, one even larger.   If Pluto is a planet, then so must be the other five or so large round blobs orbiting our Sun (that aren’t moons).   Up until a few years ago you could recall their names in order with a simple mnemonic:   “My Very Elegant Mother Just Served us Nine Pizzas”  (for Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto).

Eris is bigger than Pluto and orbits the Sun at nearly the same distance. But it was never called a planet.

 

But as Dr. Tyson points out at the Hayden, let us not simply count planets.  More important,  the planets seem to fall into different classes. The first four are small and rocky with iron cores, typically called the terrestrial planets.  The next four are the gas giants.  Having two different types  of planets is not accidental.  As the solar system formed out of a blob of gas about 5 billion years ago, the innermost material was much hotter due to the proximity of the Sun.  So small dusty and metallic grains could form and coalesce, but nothing that would be gaseous.  Only out around the distance of Jupiter and beyond was it cool enough that methane and water would crystallize into ice and coalesce into the gas-giant planets.

At least so goes the theory.  We can’t watch our own solar system being formed.  But over the last two decades we started taking actual data, because we have the ability to observe planets around other stars. We are now on the verge of being able to measure the actual distribution of terrestrial and gas-giant planets around many different stars.  We’ll see what the data tell us.

We would probably have a fifth rocky planet but the constant gravitational influence of Jupiter as it orbits the Sun keeps the material beyond Mars from coming together and instead we find the Asteroid Belt.  Some are still large enough to forms spheres under the influence of their own gravity, such as the asteroid Ceres.   Ultimately the definition of a planet included the new criterion that it  have mostly cleared its orbit of other material.  Ceres and  Eris fail.  And so too went Pluto.

Would we have called Ceres a planet too? (windows2universe.org) Do definitions really matter?

Beyond Neptune we find a different kind of objects.  Out near Pluto are thousands of objects composed of rock and ice.  Their composition is similar to that of comets.  And it is no surprise. That is where many of the short period comets  (say 50-200 year orbits) originate from.  These objects form a third type of object, beyond the terrestrial planets and the gas-giant planets and form what is called the Kuiper Belt, a large collection of objects that also orbit the Sun in roughly the same plane as all the planets.  These are some of the objects of Raj’s research in previous seasons,  “Trans-Neptunian Objects”.

I think having the public ruckus over Pluto was good for science.  After all, we showed our benefactors that our ideas are not written in stone.  We demonstrated  a hallmark of science, that when a better idea comes along we are willing  to change our definitions and theories.

What really amuses me though is that this happened with astronomers, who otherwise cling onto old nomenclature more than any other field I know:

Let’s start with “planetary nebulae”.  A nebula is the word that astronomers give to any cloud-like object that astronomers find. So far so good.  Astronomers long ago found some of them around of stars.  At the time, astronomers thought that this was the gas and debris that lay in a planetary disk,  hence the name.  Astronomers now know, that these nebula are actually formed by stars in their death throes.  Gas is thrown off as the star ends its life.  It has nothing to do with forming planets. As long as astronomers are keen to fix up the definition of planet, why not fix up “planetary nebula” to something else as well?

The "helix nebula" is a cloud of gas puffed out by a star 700 light years away and is an example of a "planetary nebula". If you look carefully you can find it on the wall in Leonard & Sheldon's apartment.

Another pain left over from 2000-year old astronomy is the classification of the intensity of the stars in our sky, called apparent magnitude.   Now you might think that a larger magnitude is brighter, but you’d be wrong.  That’s backwards.  Fine, we can live with a minus sign.   The dimmest star you can see with your naked eye is 6.   The star Vega was chosen as the calibration point, 0.  Well actually Vega is magnitude -0.03.  But why change the scale?   Ever?     Once per 2000 years?  No.  Was Vega chosen because it was the brightest star in the sky?  That would be sensible.  Well close. It is fifth brightest.  It was the first star to be photographed, however, and that set the scale forever after.

To make matters worse, take a look at magnitude quantitatively.  Out here in California, we are used to talking about Richter scale for magnitudes of earthquakes.  And it is pretty simple.  A “magnitude 6″ earthquake  is about 10 times the shaking as a magnitude 5 quake.   A quake with magnitude 7 is 100 times more shaking than 5.  That’s a good way to measure when the distributions vary so widely.  It is called a logarithmic scale, or ratio scale.   So is a magnitude=5 star 10 times as dim as a magnitude=4?   No.  What is it then?   A factor of 2.5119.   Why?   Because that’s the fifth root of 100.   Ask a silly question, you’ll get a silly answer.     This scale is left to us from the Ancient Greeks.   There’s nothing wrong with it, but it does make teaching it to non-science majors needlessly difficult.

Stars can classified by their surface temperature.   From hottest to coolest they are tagged with letters.  By now, you are not expecting A,B,C,D,….  Right.  It is O,B,A,F,G,K,M.   It is a relic of a previous attempt to classify stars based on the strength of the absorption of light by hydrogen.   It is easy to remember though: “Oh, Be a Fine Girl (Guy), Kiss Me!”.

At least the reclassification of Pluto is progress.  Astronomy will be around at least another 2000 years to slowly fix the others.   From now on we only need concern ourselves with “My Very Elegant Mother Just Served Us Nachos”.

S04E06: The Irish Pub Formulation

The first force discovered by the first physicists was gravity.    Over four hundred years ago our understanding that gravity was a force at work throughout the Universe, was explained by Sir Isaac Newton.  Nearly 100 years ago we modernized our understanding with Albert Einstein’s General Theory of Relativity.   And despite all this homework, gravity is still the force least understood by physics.

Physicists understand gravity well enough to get us to the Moon. So why is Sheldon still working on gravity?

Over the centuries three other basic classes of forces were discovered:

Electromagnetism is familiar to us and pushes currents into our houses and electrons through our electronic devices.  Lucky for us, it holds atoms and molecules together.

The “strong” force holds nuclei together.  The atomic nucleus is made of neutrons (no electric charge) and protons (positive electric charge).   Since same-sign charges repel, the atomic nuclei should all blow apart.  They are trying to, but another force, the strong force, holds them together.  The strong force is stronger than the electromagnetic force in the nucleus.  But only at short distances.  That’s why we don’t experience the strong force on our human scale.  Its range determines the size of the biggest nuclei we can make.    We have never made a nucleus larger than about 300 protons and neutrons.   Since they are packed in a sphere and protons and neutrons are about the same size, you can calculate the radius using simple geometry:  Volume =4/3πr³.  

So the radius of the largest nucleus is about 4 protons and neutrons in radius (8 in diameter).  That’s about the range of the strong force, about 4 protons’ width.   That is 0.000000000000004 meters.   (We’ve since learned that this “strong” force is generated by a more elementary force at work inside the protons and neutrons themselves, called “quantum chromodynamics”, but that’s a story for another day.)

The final force on our list  is the so-called “weak” force.  The weak force is so weak it doesn’t hold anything together (that I know of).  But it still operates at the subatomic level.   Its strength would be comparable to the electromagnetic force but its range is even smaller than the strong nuclear force.  It’s range is almost 1000 times shorter.  It’s important though because it is the only force that can change protons into neutrons and other transitions. Without it, the Sun could not fuse 4 hydrogen atoms (4 proton) into helium (2 protons and 2 neutrons) and would not have an energy source.

But these last three, while discovered later, are the best understood.   These three play nicely with the over-arching framework of quantum mechanics.   You may often hear that quantum mechanics is the domain of processes that are very small.  That isn’t really the right story.   Quantum mechanical effects have been seen to operate over distances the size of the Earth as one type of neutrino morphs into another.   And that’s not the limit.   I once co-authored a paper about a possible quantum mechanical effect that takes place over a distance of 1 billion light years.

So it is an over-simplification to say quantum mechanics is the physics of very small distances.   It misses a key feature.  Quantum mechanics actually uncovers a special relationship between distance and momentum.  So it is really when the product of the characteristic distances and momenta are small that quantum mechanics is important.

Just as quantum mechanics reveals a special relationship between distance and momentum, the theory of relativity, which describes gravity tells us about a special relationship about time and space.  And that’s not all.  Quantum mechanics also describes a special relationship between energy and time.   Meanwhile relativity is concerned with how momentum and energy are related.  To summarize…

Relativity and Quantum Mechanics tie together different physics quantities at a deep level.

The two theories are about different relationships. It is when we try to deal with all these relationships at once, that gravity gets into trouble.

One of the biggest dramas in physics of the last 50 years of physics has been to reconcile the relationships of quantum mechanics with the theory of relativity.  And three out of four times we were ultimately successful.  There are good working theories of the quantum mechanical behavior of the electromagnetic, strong and weak forces.  They are tested every day in the laboratory to high precision.

But gravity has not yielded.  Much of the theoretical work in physics works on forming a consistent formulation of quantum mechanics and gravity.  These are the goals of string theory and loop quantum gravity that Leonard and Leslie once argued about.    Other attempts are underway.  So far though, none has passed an experimental test, most don’t even make a distinguishing experimental prediction.

And that, finally, brings us to the science in today’s show.  Sheldon’s seminar is not just about “thermodynamic fluctuations”, an elementary part of our theories of heat and energy.    Rather, it is how gravity might emerge from a process that looks a lot like them.  A new theory arguing this point came out recently from a respected theorist in the Netherlands, Erik Verlinde.   The relevant equations were on tonight’s apartment whiteboards.

(Meanwhile, the whiteboards in Leonard’s lab were about something different…the search for hypothetical particles called axions.   I promise that had nothing to do with Sheldon’s editorializing with what he wrote on the board above it.)

So it is a great embarrassment of physics, that the first force we discovered, gravity, is still the least understood.   But I have hope.  After all, Sheldon is on the job.

S04E05: The Desperation Emanation

Bob on Sesame Street taught us to know the people in our neighborhood.

(Song starts at 0:50)

But Sheldon in The Big Bang Theory taught us to know the stars in our neighborhood, too.

Our stellar neighborhood is a bit larger than your own neighborhood.  As we discussed before, the nearest star to our own solar system is Proxima Centauri.   Suppose you lived in a typical suburban house with a 50 foot driveway.  If your driveway were like the distance from the Earth to the Sun, then Proxima Centauri would be about 2500 miles away.   Even survivalists can’t get this far from their neighbors.

When the writers asked me to find the names of the stars, in order of proximity to us, I figured that would be easy.  But it was a case where the internet fails.  Nearly all the lists on the web are in disagreement with each other.   And the writers needed an answer…fast.

Luckily one of my friends at  UCLA, a professor over on the Astronomy floor bailed me out.  He told me about RECONS, the Research Consortium on Nearby Stars.   They maintain a definitive list on the stars in our neighborhood.   (And for the record, Wikipedia had it right.)

These are the stars in your neighborhood. In your neighborhood. In your neighborhood.

So we heard the list from Sheldon. Special thanks to none other than “The Bad Astronomer” for helping out with the pronunciation of the star names.

(Of course the closest star to Sheldon is not Proxima Centauri at all.  It is Sol, our own Sun.   If you were thinking that during Sheldon’s song, good for you!  You may stay after class and clean the erasers.)

What about those crazy names?  These stars were discovered over thousands of years.  Some are visible to the naked eye.  “Sirius”, the brightest of the stars, was named by the Ancient Greeks after their word for scorcher.  Others are named for the constellation they are in.  “Alpha Centari A” is the brightest of the stars making up the constellation Centaurus.   “Epsilon Eridani”, named after the constellation Eridanus and the fifth greek letter, is the fifth brightest star in that constellation.  But closest need not mean the brightest.  Many of these nearby stars were not discovered until modern times and are named after their discoverers: Jérôme Lalande discovered “Lalande 21185″ in 1801 and “Ross 154″ was only found in 1925.

And to this day, astronomers still are finding nearby stars.  Teegarden’s star was missed until 2003.  It is so close that it moves across our sky faster than almost any other star.   Surveys find nearby stars because over the years their position on  the sky can change slightly, just thousandths of a degree per year.  But Teegarden’s star, a modest little red dwarf,  moved so fast across the sky, it was always overlooked.   It is humbling to think that the 23rd closest star closest to our own solar system was missed until this very decade.   And there may be more…

Some of the stars are close together:  Proxima Centauri and Alpha Centauri are a pair, forming a binary star system.  So are Sirius A and B.   About half the stars closest to us are pair-bonded.   Our star appears to be alone.  Or is it?  Some people have proposed we have a distant and dim partner, called Nemesis.  So-named because when its orbit brings it back close to Earth, its gravity would disrupt the comets and asteroids causing them to rain down on us.  It has been proposed to explain a possible periodicity, about 27 million years, of mass extinctions found by paleontologists.  The periodicity of these extinctions is not universally accepted.  And the explanation of periodic extinctions being induced by a companion star even less so.  Nevertheless, I named the first electronics board I build as a graduate student “Nemesis”.

If there is such a “Nemesis” star orbiting our own, a new survey will find it.  The WISE satellite, the Wide-Field Infrared Survey Explorer (led by my same friend at UCLA) is looking.  Infrared light is redder than the reddest light you can see.  Really hot objects, thousands of degrees, glow in the visible light such as a lightbulb filament or the Sun.  The reason you can see your friends’ faces it that visible light reflects off of their faces to your eyes.  But if you had infrared eyes, your friends, cooler than the Sun but still hot, would glow but in the infrared.   (Compared to absolute zero, all your friends are “hot”.  Compared to the Sun, they are “cool”.  Feel free to compliment them on this.)   So infrared is the go-to color for astronomers to find small, cool, faint stars, that might have been missed by all astronomers until now.

The human body glows with the infrared light due to the heat it generates. Astronomers look for dim, cool stars with infrared telescopes.

Such dim stars could have their own planets orbiting them, and if close enough, could sustain life, maybe even intelligent life.   There may even be one closer than Proxima Centauri.  When I mentioned that to one of the co-creators and writers of the Big Bang Theory- when he was visiting UCLA to give the Physics and Astronomy Department commencement address — he told me, “The Federation may be sooner than we think.”

Update:  Since the time this espisode aired, the measurements of the distances to the Procyon stellar system and 61 Cygni system have changed slightly, so their order according to RECONS is now different than the order in the song.   Thanks to eagle-eared viewer Åingeal S. for asking me why they were “wrong” which allowed me to locate the difference using the internet archive of the RECONS webpage.

S04E04: The Hot Troll Deviation

Sometimes you need a secret decoder ring.  We had a few shout-outs to the world of physics and chemistry tonight.

Starting with the very first line of the episode:

KOOTHRAPPALI:   (TO SHELDON) I’m telling you, if xenon emits ultraviolet light, then those dark matter discoveries must be wrong.

And now you are in on the most controversial discussions in physics today.    We’ve discussed here before that about two-thirds of the matter in the galaxy is a dark, unknown substance: the aptly named “dark matter”.   Meanwhile teams of physicists are working hard to be the first to prove dark matter exists, by capturing one of its interactions in a particle detector.  For whoever detects it first, there is no end to the fame.

 

Sensitive detectors look for dark matter. A dark matter particle may kick a nucleus in the detector leaving behind detectable energy, such as ultraviolet light.

 

The race is on.   Many detectors are running.    Each is gambling on different techniques.  But what almost all have in common is they are looking for extraordinarily weak and rare events.   So physicists build their detectors from materials with extremely low radioactivity and place them deep under ground to keep them as quiet as possible.   Two of the running experiments have a signal the authors have claimed is consistent with dark matter.  The first is called  “Dama-Libra” (the Italian group who Leonard talked about to his mother in season two) and the other is called CoGeNT (some physicists need their shift key taken away from them.)

But a new type of detector started working recently.  Xenon is a gas in every breath you take, but being a noble gas just goes along for the ride, never interacting in your lungs.  But xenon can be refrigerated to below -162 degrees F where it becomes a liquid.   When a dark matter particle passes through it, it occasionally will give a single xenon atom a small kick.   That small kick causes the xenon’s atomic nucleus to move a short distance through the liquid—producing free electrons, heat, and light.   The highest frequency light your eyes can see is violet.  But energy deposited in xenon produces light with a  color a little bluer than violet, called ultra-violet light.  You can’t see it but particle detectors can.   The xenon detectors is enormous, 100 kilograms, hence its name XENON-100.  But XENON-100 doesn’t see the tell-tale ultra-violet light from dark matter collisions.   Is it because the others’ dark matter discoveries were wrong?  Or is there just not enough ultra-violet light being produced in the liquid xenon?  That’s what Sheldon and Koothrappali are arguing about.  And so. are. the physicists.

But the whiteboards today had nothing to do with this science.  Today’s whiteboards honored a special guest.  Once while talking to a Big Bang Theory writer, he recommended I watch the film Real Genius (1985).   I didn’t know what to expect but put it in my Netflix queue nevertheless.   When I saw it I was blown away….not necessarily by the story or the characters (which were fine), but by the important part: the scientific sets and dialogue.    It turns out that Real Genius had a scientific consultant,  Martin Gundersen, a professor of physics from across town, the University of Southern California (USC).    Now that I know how much goes into getting sets and stories right, I was in awe of what a great job they had done, from the sets to weaving physics right into the plot line.   So I sent Prof. Gundersen a fan letter.   He  responded and eventually was able to visit the set of The Big Bang Theory during the taping of this episode.

 

Prof. Martin Gundersen, the science consultant for Real Genius (1985). He recognized the whiteboard in Leonard and Sheldon's apartment during the taping of this episode.

 

So those of you that are whiteboard fans AND have a good memory know what was on the whiteboards.  It was identical to one of the boards used in Real Genius 25 years ago….

 

 

Chris Knight (Val Kilmer) steps out of the way so we can see the original whiteboard in Real Genius (1985).

 

I don’t want to spoil the plot of Real Genius by explaining how excimer lasers work.  It’s only been 25 years and not everybody has had a chance to see it yet.

Finally, we saw Sheldon make a smell of hydrogen sulfide and ammonia gas.  Hydrogen sulfide smells like putrefying eggs.  And ammonia smells like ammonia.   We were careful not to tell how hydrogen sulfide could really be made since it’s been in the news that people have been hurting themselves and others when making it with household chemicals.   We at The Big Bang Theory are nothing if not socially conscious.  So instead I imagined Sheldon made it with something only available around the lab,  an aqueous solution of hydrogen sulfide.   That immediately produces:

(NH₄)₂S →H₂S + 2 NH₃

By now I expect you are running out of the room.

S04E03: The Zazzy Substitution

In tonight’s episode we heard the names of many physicists who took part in the Manhattan Project, the U.S. program that built the first nuclear bombs.  We were  introduced first to the name of one of the most famous physicists of the twentieth century, the chief physicist in charge of building the so-called “gadgets”, Dr. J. Robert Oppenheimer.

 

J. Robert Oppenheimer, theoretical physicist and leader of the Manhattan Project

Unlike Sheldon (and many others),  I prefer to say “nuclear” not “atomic”.   “Atomic” tells us nothing special.  All chemical reactions use atoms, and you’d be justified in calling even T.N.T. an atomic bomb.  What is special about nuclear power is that it uses the forces in the nucleus, which are about a million times stronger than the forces holding the rest of the atom together.  It is specifically nuclear reactions, not chemical reactions, that are responsible for the extraordinary power of a nuclear bomb.

Oppenheimer was a theoretical physicist, who was reported to be extraordinary clumsy around laboratory equipment. “Oppie”, as he was called, was a fan of languages and even taught himself Sanskrit.    Those who knew him described him as somewhere between aloof and pretentious.   Either way, he had trouble dealing with people.   His brother Frank, also a physicist, reports him having said:

“I need physics more than friends.”  – J. Robert Oppenheimer

At this point I wonder, does he sounds similar to any of the fictional physicists we know?

But at the same time, Oppenheimer and our fictional hero could not be more different.  Oppenheimer had a driving ambition to be close to the political powers in Washington.  So much so, Oppenheimer even lied and falsely implicated his friend, Haakon Chevalier, as being linked to Communist espionage, ultimately causing  grave damage to his friend’s career, while furthering his own.   Like a Greek tragedy, this misstep ultimately led to Oppenheimer’s own fall from political grace, ultimately even having his security clearance revoked — a stunning blow to the man who had been the scientific leader of what was  perhaps the largest secret military project ever undertaken.

Oppenheimer also had a strong affinity toward Eastern religion, specifically Hinduism.  When the first test atomic bomb was dropped at the Trinity Site on July 16, 1945, he famously recalled pondering several phrases from the Bhagavad-Gita:

If the radiance of a thousand suns were to burst at once into the sky, that would be like the splendor of the mighty one.

and

Now I am become death, the destroyer of worlds.

I never understood the strange grammar of that second quote, since he was speaking in translation.   Perhaps a Sanskrit-reading reader of this blog could explain below if a similar construction exists in the original.  (Updated: see comments.)

As it happens, I visited the Trinity Site last weekend.   I had given a seminar last Friday nearby, at the National Radio Astronomy Observatory, home of the Very Large Array in Socorro, New Mexico.  (That’s the same array of telescopes Jodie Foster used in the movie Contact.  And yes, she really went there; they still have pictures of her visit on the walls.)  Twice per year, the Trinity is open to the public.  You can combine that with a trip to the VLA.

 

Your science consultant at the Trinity Site.

After a short drive through the White Sands Missile Range we arrived at the site.  You might worry about the the wisdom of  walking around unprotected where a 20 kiloton nuclear weapon was detonated.  What about the radioactivity?  After the atomic bomb test, the heat of the blast melted the sand and plutonium fallout into a glass, forming a unique  mineral called trinitite.    Small bits of the green glass are underfoot nearly everywhere you walk.

 

During the nuclear explosion at the Trinity Site, desert sand fused with nuclear fallout to produce a new mineral, trinitite.

For the hour I walked around,  I was exposed to radiation dose of 0.5 “millirem”.   A millirem is one thousandth of a “Roentgen Equivalent Man”, an outdated but well-known unit for measuring radiation exposure.

That may sound scary but 0.5 millirem is very small compared the natural sources of radiation which are everywhere.   The average person in the U.S. receives over a 350 millirem dose every year, mostly from radon.  Even if you try to escape radon,  the potassium-40 in your bones are constantly undergoing radioactive decay.   For my trip to the Trinity site, I received by far most of my dose from the two-hour airplane flight each way from Los Angeles to Albuquerque.  In a commercial jet you are above much of the atmosphere that normally protects you from radiation due to cosmic rays, particles from space striking the earth.   (Extra for experts:  it is not just the dose, but the duration of the dose that matters.  Doses received slowly, over the course of a year, give your DNA more chance to repair itself before possibly forming tumors than if you receive it all at once.)   It takes a 100,000 millirem dose before it starts to have measurable effects on   your blood.  At twice that, you start feeling radiation sickness.

In many other cases radiation is  outright helpful.  X-rays help doctors diagnose broken bones and the positrons emitted in PET scans allow doctors to find cancer.   Gamma-ray and other beams are often used to destroy tumors once they are found.  Biologists use radioactive markers to understand all sorts of processes important to life.   Smoke detectors rely on the decays of americium  to light a phosphor.    Nuclear power reactors provide an enormous supply of electricity while producing essentially no greenhouse gases.

Now disregarding my earlier complaint about “atomic” versus “nuclear”, let us now in all seriousness consult the Doomsday Clock of the Bulletin of the Atomic Scientists:

 

The Doomsday Clock of the Bulletin of the Atomic Scientists

It is six minutes to midnight, folks.