S04E15: The Benefactor Factor

Pssst.   Do you want to buy a cryogenic centrifugal pump?     Tonight we find out that Leonard and the physics department want one.  And clearly it is big and expensive.

A cryogenic centrifugal pump. Although the one Leonard needs is even bigger.

It isn’t surprising that Leonard wants one. Modern physics experiments are often looking for extremely rare events.  Maybe just once per year a dark matter particle might bump into a cold, pure liquid detector.  Or perhaps once per year we might see an extremely rare radioactive decay that means something important to us.   The problem is that physicists need to look at a lot of material for an extremely long time without being fooled.

Physicists look for rare decays and events often by the small amount of light they emit.   To do the job, we use what is basically a television camera.  A small amount of light knocks an electron out of a metal called a “photocathode”.  A careful array of voltages are set up so that the electron gains energy and hits another metal producing several more electrons.  The process, called multiplication, is repeated until a detectable signal is present.  In order to not absorb the electron the entire structure is put into a vacuum tube.  The net result is called a “photomultiplier tube”.

A "photomultiplier tube" is the workhorse of physicists. It turns light into an electrical signal. It works better when cold.

The problem in looking for something rare, is that other processes don’t stop for you.  The sensitive light detectors are so sensitive that they often emit electrons without being struck by light.  These give false currents, even without any light, in a dark room.  The unwanted signal is  called a “dark current”.    Making the detectors cold greatly removes this effect.  But now you need to move a large amount, even tons, of cold liquids around.  That’s the job of a cryogenic centrifugal pump.

And while you are at it, you can remove the second source of noise: radioactivity.  A centrifugal pump can push noble elements, like xenon, through small holes but other molecules are larger and can’t fit.   But this is like the sieve in your kitchen lets the water through, but not the pasta.  The key here is also adsorption.   If a small molecule fits into one of the pores, then it is absorbed.  A trick is to find a material that catches what you don’t want.

The material in a molecular sieve blocks all but the smallest molecules and atoms.

Small versions of cryogenic centrifugal pumps are not terribly expensive.  But university budgets are tight. Physicists like Leonard still want to find rare events and are now dreaming of detectors with a ton or even ten tons of pure cold liquid, such as liquid xenon and argon.  For that they will need a large, expensive one.

Besides, my comedy friends tell me, words with the “hard C”  or “K” sound are funny.

S04E14: The Thespian Catalyst

Graphene is so yesterday.   This decade’s material-of-the-century are the tellurides.

At his official 2010 Nobel Prize acceptance lecture in Stockholm, Dr. Novoselov shows graphene, and Sheldon.

In his lecture, Sheldon told  his class (and about 15 million onlookers) about the strange behavior seen recently in certain compounds of bismuth, tellurium and tin. These strange new substances are insulators conductors insulators insulators and conductors simultaneously.  These tellurides and their cousins are part of a new class of recently discovered materials called, as Sheldon said,  topological insulators.

In materials such as typical plastics, electrons are pinned to the underlying structure and don’t move.    Because they can be used to keep conductors from shorting out, they are called insulators.  Relative to the best conductors, the electrical conductivity of the best insulators is 10²⁶ smaller, that’s a factor of 10,000,0000,000,000,000,000,000,000.   Few quantities in physics vary by so much.

On the whiteboards tonight, viewers saw bismuth telluride, cadmium telluride, and mercury telluride  making cameo appearances.    In these materials, the bulk volume is insulating–while the surfaces conduct.  At the same time.  How can that be?

Some clever wag may point out we could do this by just electroplating some plastic.  That was one of Richard Feynman’s first jobs and would be conductive on the outside but insulating in the middle.  But the difference here is that would be two materials.  Physicists never imagined this could be done with a single material at once.

The key difference from normal insulators is the reason they are called “topological”.  The description stems from the branch of mathematics called topology that characterizes the fundamental shapes of objects.   You can stretch a doughnut to form a coffee cup (one hole), but cannot make it into an object with two holes.   In the same way, the underlying structure of electron orbitals in an ordinary insulator can be represented by a simple loop.  A loop topologically distinct from the simplest possible knot:  a trefoil knot.

The structure of electron orbits in topological insulators are akin to the trefoil knot.

It turns out the interactions of the electrons’ spin with their orbital angular momentum creates a mathematical structure described by the trefoil knot.   For reasons beyond the ability of your science consultant to understand, the difference becomes apparent on the surface of the material: becoming metallic and conductive for the topological insulators but remaining non-conductive for normal insulators.  If you have a good explanation, please leave a comment.

Such effects have been seen before, but only with difficult-to-create flat structures.  But now, just like Hollywood, physicists have gone 3D with the advent  bismuth telluride.  Topological insulators can be created with standard semiconductor fabrication technology.  The simultaneous insulating and conducting nature of  the topological insulators is not an effect that can only be produced in expensive labs with high vacuums or extreme cooling.   These materials behave this way even at room temperature on the lab bench, or even held in your hand.

Work has heated up over the last five years and  many other compounds have been found to display not only the dual properties of topological insulators, crystals made of bismuth, selenium and copper have been made superconducting,moving electrons with no dissipation at all.

Topological insulators hold promise for new types of computing and materials whose applications we have not even thought of yet.  Their behavior is interesting in and of itself to physicists.  Sad to say, some popular articles have fallen prey yet again to the monopole falacy. This is the same annoying error that Sheldon complained about to Ira Flatow on NPR’s Science Friday.   Now in this latest article (and others) it says one of the interesting features of topological insulators is to make quasi-particle versions of axions, analogues of what are being sought in elementary particle physics.  However, just as with the magnetic monopole claims, that article misses the point completely:   Particle physicists don’t look for new particles  just to see their mathematical behavior.  We look for them because their existence  means something about the Universe.  In the case of the axion, it would validate certain explanations about why deep symmetries exist in nature. Axions could even be the dark matter in the galaxy.  But an axion-like-thing observed in a condensed matter system is not an axion.  It has none of that meaning.    Materials are topological insulators are still interesting in their own right. Such popular articles mislead readers at a deep level and do a disservice to these new materials by compromising the description of why they actually are interesting.

In fact topological insulators are so promising, we can only hope Sheldon’s boards will some day make a second appearance in Stockholm.  (And if, like Sheldon’s students, you want to tweet how boring this post is…hit the button below.)

S04E13: The Love Car Displacement

You say tomato, I say tomahto. You say lanthanide, I say lanthanoid. Did anyone think Amy made a mistake tonight when she said lanthanoid, not lanthanide? If so, then stay after school to clean the erasers because Amy was right. The IUPAC, the International Union of Pure and Applied Chemistry,  won’t stand for  it. Despite 90% of scientific literature using lanthanide the ever-vigilant folks at the IUPAC want us to use lanthanoid. And The Big Bang Theory does its part to educate the public.

Puh-lease! The word is "Lanthanoid".

The lanthanoid series of elements is that special part of the periodic table that doesn’t fit horizontally so is usually put at the bottom.  The defining characteristic of an element is the number of protons in its atomic nucleus.  If you are an atom with 57-71 protons, then congratulations, you are a lanthanoid.  From lanthanum to lutetium these elements have room for up to 14  electrons to fill an oddly shaped shell around the atomic nucleus (called the “f-shell”).  The strange shape of their orbits make the lanthanoids the under-appreciated miracle workers of modern technology.

Lanthanoids make The Big Bang Theory television show possible.  Theatrical lighting needs to be bright and just the right color.  Lanthanum (57 protons) and cerium (58 protons) rods in arc lamps are extremely popular on Hollywood sets. Praseodymium (59 protons) in aircraft engines strengthens the metals and bring special guest stars to Burbank Airport. Neodymium (60 protons) and samarium (62 protons) make the highest strength permanent magnets.  Such magnets are likely found in your TV speakers or headphones.   OK, I doubt we use promethium (61 protons) on set, which is always radioactive.  If not for europium (63 protons), we’d  still be watching Big Bang Theory in black & white, missing a key element in the red phosphors that made color TV first possible in the 1960s.    And without gadolinium (64 protons) and terbium (65 protons) there would have been no green.     The show could not be edited if all its high-definition data could not be stored on a hard drive using, you guessed it, the easy magnetization properties of dysprosium (66 protons).   However without holmium (67 protons), the show could go on.   If you watch The Big Bang Theory online, chances are it comes to you on a fiber optic loaded with erbium (68 protons), an optical amplifier.  I confess that the next thulium (69 protons) embargo might not be a show-stopper.    Ytterbium (70 protons) changes its electrical properties under strain and is a key element for monitoring earthquakes;  living in Southern California, we like our ytterbium.   And finally lutetium (71 protons), well, its f-shell is full, so one could argue it shouldn’t be a lanthanoid at all.

The lanthanoids are not popular just because of their good looks.

Why are their names so unfamiliar?  The fact that the lanthanoids  sometimes go by the name rare earths might give you a clue.  It might, but it doesn’t.  The lanthanoids are not particularly rare in the Earth’s crust.   And the word earth originally meant that their oxides were highly alkali and water-insoluble.  Except they are not. You’d think IUPAC would be happy that we at least we’ve mostly stopped calling them rare earths.

The lanthanoids, often called "rare earths", are actually not so rare at all. They are 1000 times more abundant than gold.

But the members of IUPAC are not an easily placated lot.  In English, the suffix -ide, is already reserved in chemistry for an element that has taken up an electron from another atom thereby forming a negative ion.   That’s the -ide in sodium chloride, which is common table salt.  Lanthanoids are lanthanoids no matter what element they are or are not bonded to.

And the periodic table being periodic, the story repeats itself with the actinoids.    If you listened carefully tonight you knew Amy already ruled those out, because they are all radioactive.

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.