Here is my second draft of an article on slowing light which I wrote for the magazine of Fantasy and Science Fiction. The second draft usually contains the most science.
Slowing Light
Recently Lene Hau of the Rowland Institute managed to slow light down to a speed of 17 meters per second, slightly faster than Paul can bicycle on the level. The speed of light has always been the standard metaphor for high speed so the concept of slow light seems like the ultimate oxymoron . Her achievement inspired Paul to look up Bob Shaw's Nebula winning short story "Light of Other Days." Pat read it too and exclaimed,"that's a damn good story." Indeed it is. In the story a troubled couple from the city drive up into the lochs of Scotland, the land of slow glass. They come upon panes of glass dotting a scenic countryside. The glass drinks in the light coming from the landscape. The light that enters the glass now, exits the other side of a 6 millimeter-thick slab ten years later, thus the name slow glass(Bob Shaw of course used a quarter inch as a measure of thickness). The "scenedows" store the scenes of the lochs and release them over a ten year period, the city dwellers planed to install the scendows and replace their views of a dingy city with the view of the loch, a view that was always changing. Let's take a look at the speed of light, we'll start fast chasing light across the vacuum of space, then slow down a bit in ordinary glass, We'll drop our speed by seven orders of magnitude in Dr. Hau's sodium Bose-Einstein condensates and finally return to slow glass.
In a vacuum
Paul was recently asked what is the essence of light? He replied that in the 1870 view based on Maxwell's equations light is an electromagnetic wave. (In the next paragraph we'll do an experiment to explore electromagnetic waves.) In particular, light is a wave that can exert a sinusoidal force on electric charges. (Visible light accelerates electrons back and forth in the chemicals of the rods and cones of the human retina causing chemical changes that lead to electrical signals interpreted by the brain as light.) Electric charge is the essential ingredient here. Light is created when an electric charge accelerates, and when light hits a particle with electric charge it causes that charge to accelerate. (Light does not influence things without electric charge, and since light iself does not possess charge, one beam of light can pass right through another beam of light, both beams will be unchanged by the encounter.)
An experiment
To get a feel for what light is, let's do an experiment. Take two pieces of scotch magic tape about as long as your fist is wide, about 10 cm, stick one tape on top of the other, so that the sticky side of one tape is stuck to the smooth side of the other. Pull the two tapes apart with a quick snap of your wrists. The tapes will attract each other and also attract you too, in fact you may have trouble at first as they are attracted to and stick to your hand. Shake them free and bring them toward each other. The two pieces of tape will attract each other. This force-at-a-distance is due to the electric charges produced on each tape by pulling them apart. In Maxwell's view, the charges on one tape create an electric field which exert forces on the charges on the other tape. Wiggle one tape and changes propagate along the field, these changes in the electric field include electromagnetic waves. Electromagnetic waves, including light, are transverse waves in the electromagnetic field. There is a time delay between when you move one tape and the changing electric field causes the other tape to move, a time delay because the changes propagate at the speed of light. Here is one place where english units are useful, the speed of light is one foot per nanosecond, so if you hold the tapes a foot apart and wiggle one the other will move after a nanosecond delay, a billionth of a second. (Using electronic timing these delays can be measured.)
The tapes get a net electric charge when you pull them apart. Such charge is called triboelectric since it is the product of contact forces.
The two tapes originally have no net charge even though each piece of tape contains over 1022 positive charges in the nuclei of atoms making the tape it also contains an equally huge number of negative electrons. The equal and opposite charges give the tape no net charge. Stick the tapes together and pull the tapes apart and you transfer charge from one tape to the other. So that the tape with its glue side touching the other tape gets an excess of plus charge and the tape with the smooth side gets an excess of minus charge.
(Pat this is probably unneeded excess, but interesting unneeded excess....The names plus and minus were bestowed by Benjamin Franklin , the names serve to remind us that when equal numbers of plus and minus charges are combined they produce no net charge just as plus and minus numbers would. Ben didn't know what electric charge was, he just knew it was produced by rubbing two materials together. He arbitrarily named the charge obtained by amber when rubbed by cat fur minus. we still use this standard today. By Ben's definition, the tape that has the smooth side up against the sticky side of the other tape becomes negatively charged.
Normal matter becomes charged when one material is rubbed against a different material. Contact between two different materials transfers electrical charge from one to the other.
The details of the charge transfer are unknown, even today. You might have read, or been told, that it is the negative charges&emdash;named electrons&emdash;which move between two objects when they are rubbed together. As of 1995 scientists do not know the details of which electric charges actually move when two tapes are pulled apart. Recent scanning tunneling microscope experiments suggest that entire atomic or molecular clusters are transfered from one material to the other. These clusters can transfer either positive or negative charge.
An editorial aside. This is a good example of how you should always ask the question "How do you know that?" Keep asking until someone can point you to an experiment that convinces you of the truth of their statement. )
Move one tape back and forth, the other moves too. The force between the two tapes will cross a vacuum, (Hm! I wonder if we can get NASA astronauts to perform this experiment for us?) Most of my students are unsurprised that electric forces can cross a vacuum. However they are surprised that light can propagate across a vacuum, even though light is just a wave in the electric field. When you were moving one tape back and forth you were sending out electromagnetic waves, extremely low frequency electromagnetic waves, but electromagnetic waves nonetheless. Those waves were traveling away from you at the speed of light.
Maxwell noticed that he could combine his equations for electric and magnetic fields to produce a wave equation. When he looked at this equation he could see it contained the speed of the waves of electricity and magnetism, he calculated the speed and found it was the speed of light! This lead him to announce that light was an electromagnetic wave. He was lucky, since gravity waves also propagate at the speed of light, and, gravity waves are not light. Just because the wave travelled at the speed of light that did not make it light.
The speed of light in a vacuum is fast, it was measured by Ole Roemer in 1676 by timing eclipses of the moons of Jupiter, the light from the eclipses (Interesting isn't it to talk about light from an eclipse it seems like we should talk about the speed of dark!) He noted that when the earth was on the side of its orbit nearest Jupiter the eclipses were seen 8 minutes earlier than average while when the earth was on the far side of its orbit they were 8 minutes later than average. this could be explained by assuming that it took light 16 minutes to cross the diameter of the earth's orbit. Knowing the diameter of the earth's orbit then gave the speed of light. That speed is fast, 300 million meters per second. (Or as it says on our friend Ron Hipschman's T-shirt "the speed of light: 186,000 miles per second, not just a good idea its the law!")
But the universe is large, so large that the universe itself acts as a giant pane of slow glass. Look at the moon, you see it where it was a second and a half ago. Look at the sun, (for safety only do this briefly at sunrise and sunset), you see the sun as it was 8.3 minutes ago. Look at stars in the sky, you see them as they were years ago. (A close star is alpha centauri a mere 4.3 light years away . While distant Deneb is over 1800 light years away.) Look at the Andromeda nebula, or galaxy, you see it as it was and where it was 2.5 million years ago. This is as far as you can see with your unaided eye. Telescopes allow us to see further back in time, almost all the way back to the big bang, the record for the most distant object is being pushed back all the time. Now it is over10 billion light years. With microwave receivers we can pick up the fading signal from the big bang itself coming to us across 13,7 billion light years.
Bob Shaw's slow glass farmers specify the thickness of slow glass in years. "This is a 10 year thick piece of glass." A 10 year thickness of the universe would be 10 light years thick, representing the same path length as 10 x 10 16 m of vacuum or in modern metric terms 100 petameters.
In Glass
We now know that light travels slower in window glass. About 2/3 as fast as it does in a vacuum. In Newton's time they did not know the speed of light in glass. They did know that light bent when it went from air into glass. (Experiment here?)
To successfully spear a fish you have to know that if you stab the spear at the place where you see the fish, you may not hit the fish!
the fish is not where it seems to be.
If you shine a beam of light like that from a laser pointer into a tank of water you can see the beam bend. This bending is called refraction and is the result of the change in speed of the light as it goes from air to water. The light always bends so that it goes into the water closer to perpendicular to the surface than it enters from air. If you place the laser pointer in a waterproof bag and put it underwater then you will see one of the most important rules of optics, light follows the same path out of the water that it follows in to the water. This is the law of reversibility of light paths.
This means that when you go spear fishing you should use a laser spear. Then you can point right at the image of the fish. When your laser beam hits the water it will bend and hit the actual fish at exactly the point you are aiming at!
Isaac Newton thought that light was made of particles. To explain refraction he made the model that the particles of light sped up as they entered glass. Picture light approaching a slab of glass at an angle. In Newton's model the light particles behave as if they are pulled toward the slab, accelerating toward it, and so bending into the glass. It's as if they were sucked in to the glass by a gravity-like force. In Newton's model the speed of light in the glass is greater than the speed of light in air.
Christian Huygens produced a wave model for light at the same time as Newton. To explain refraction the wave model requires that light slow down as it enters the glass. (In these wave models the light slowed down parallel to the surface as well as perpendicular to the surface.)
It wasn't until 1862 that Jean Foucault measured the speed of light in glass and found out that it was slower than in vacuum. (But by then Thomas Young had already used diffraction to show that light was a wave.)
The speed of light waves in glass determines the bending of the light as it enters the glass, the slower the waves, the greater the bending. The equation for the bending uses the index of refraction. It is not surprising then that there is a relationship between the index of refraction and the speed of light. The index of refraction has no dimensions, for ordinary glass it is 1.5. It is simply the ratio of the speed of light in a vacuum to the speed of light in the material. So vacuum has an index of refraction of 1.0 by definition, water is 1.33, glass is 1.5 which means that light travels 2/3 as fast in glass as in a vacuum, and in diamond it is 2.4, so that light travels less than half as fast in diamond as it does in a vacuum. ( By the way air has an index of refraction of 1.0003)
A model of how light slows down in glass
Here is a model of how light slows in a material. Step back to 1900 when Maxwell's equations were the last word on what light was, and when we knew that atoms contained electrons. Maxwell pictured light as a wave but unlike Thomas Young, Maxwell knew what light was a wave in, it was a wave in the electric field (It is also a wave in the magnetic field but we can ignore that here.) Electric fields exert forces on electric charges. So when an electric field wave passed by an atom it exerted forces on the electrons in each atom. Now these electrons were bound to their atoms and yet they accelerated up and down under the electric forces from the passing light. Because they were bound to the atoms the electrons lagged a bit behind the electric field wave's ups and downs. The electrons removed some energy from the light. The oscillating electrons then re-emitted the light! But the re-emission was slightly delayed. Each atom has its own characteristic delay time. After the light had gone far enough into the material, almost all of the energy of the original light had been absorbed and re-emitted many times. The net effect of these continuous delays was the slowing down of the light wave as it moved through the material. The slowing down that is the origin of the index of refraction.
(Pat notes that the light between the atoms travels at the speed of light in a vacuum, Paul notes that even for relatively short wavelength visible light, one light wave has a wavelength that spans 5000 atoms so it's hard to separate out the speed of a light wave between atoms, but that indeed, Pat's model is right.)
Here's a model of the slowing down of light using water waves. Picture an array of fishing bobbers on the surface of a lake. These bobbers have weights suspended under them. If you push one down it bobs up and down with its own resonant frequency. Watch as a series of water waves moves through the field of bobbers. If the wave hits only one bobber that bobber moves up and down re-emitting waves with a slight delay. That is, the crest of the re-emitted wave comes out with a delay after the bobber has been hit by the incoming wave. An entire field of bobbers will slowly draw all the energy out of the initial waves and create a new set of waves traveling slower than the originals. (Although the frequency will remain the same.) If the waves are tuned to the resonant up and down frequency of the bobbers then the energy goes away very quickly and the wave is slowed greatly. For most clear things like air or water or glass, the resonant frequency of the electron clouds shaking around the atoms is in the ultraviolet, so visible light is slowed down some.
(In the modern quantum mechanical view, light is created and destroyed as a particle but propagates as a wave in probability amplitude. This probability amplitude is delayed by interactions with electrons in much the same way as the electric field wave of Maxwell.)
At the ultraviolet resonance, the electron motions actually absorb the light and convert it into excitation of the atom, the electrons change energy levels. The light is then delayed for huge times, (like one hundred millionth of a second.) but in general the light is re-emitted with a random direction and phase so we don't say it is slowed down, we say it is absorbed and re-emitted. Any images it was carrying are scrambled in this process.
Slow Sodium
Drive around almost any big city at night and you will see yellow street lights. These lights electrically excite sodium metal vapor to emit light in the yellow part of the spectrum. The sodium atoms have a resonant frequency in the yellow part of the spectrum. This means that these sodium atoms have a strong interaction for a narrow range of yellow light frequencies. Dr. Hau knew this, unfortunately, she couldn't use this strong interaction to slow down yellow light because the sodium atoms absorbed the light instead. She shone a yellow laser light at the sodium atoms and they absorbed that wavelength almost as well as a block of lead would have. However then Dr. Hau shone another wavelength of laser light onto the sodium, this second laser beam made it so that the sodium could not absorb the original beam of yellow light, via a process known as laser induced transparency. (Pat do you want details? The second beam made an interference between quantum states in the sodium atoms, similar to the interference produced by Young's two slit experiment.) However the sodium atoms still interacted strongly with the yellow light slowing it down without actually absorbing it! (In her experiment about 1/3 of the yellow photons made it through the sodium cloud.)
Dr. Hau then proceeded to cool the sodium atoms down to one of the coldest temperatures ever achieved in a laboratory anywhere, to 50 nanokelvins, just 50 billionths of a degree above absolute zero! As the atoms cooled they slowed down. All atoms obey Heisenberg's uncertainty principle, as the atoms slowed their momentum became closer and closer to zero with less and less uncertainty. Heisenberg assures us that this means that their location then must become uncertain. The location became so uncertain that the sodium atoms began to overlap. All of the sodium atoms began to behave like one quantum mechanically coupled object, they would all have to change their quantum state together. This quantum coupled system is known as a Bose-Einstein Condensate, or BEC, after Bose and Einstein who predicted it in 192?. The first BEC was created at the NIST laboratories in Boulder CO in 1996?.
It was in this BEC of sodium atoms that Lene Hau managed to slow light. She fired in a pulse of light and timed how long it took to cross the cigar shaped region of the BEC. Using the first equation I ever learned in fourth grade, velocity equals distance divided by time, she calculated the speed of light through the condensate and found it to be slowed to 17 m/s.
Slow Glass
After reading Bob Shaw's short story, Paul immediately wanted to "do the numbers" and rounding off to show that he is indeed a physicist not a mathematician, Paul finds that the light in the slow glass travelled about 1/2 a millimeter a year, recalling the good trick for remembering the number of seconds per year, about pi times 107, means that the light travels about 5 x10-4 m in 3 x 107 s or about 2x10-11 m/s. That's about an atomic diameter in 5 seconds.
One difference between Bob Shaw's slow glass and Lene Hau's sodium BEC is that Bob Shaw's works across the entire visible spectrum and so recreates scenes in full color. While Dr. Hau's works only at one precise frequency, the frequency of one of the 2 sodium D lines. Other wavelengths or frequencies of light speed through the sodium at nearly the speed of light in a vacuum.
Dr. Hau hopes to be able to improve her result soon slowing light even more to a few centimeters per second. But she still has a long way to go to catch up to the vision of Bob Shaw.
another possible extensions
Later Bob Shaw included this Nebula award wining short story in a longer Novel about slow glass titled Other Days, Other Eyes.
In the novel he gives more details about how slow glass works. At the surface of slow glass the light is converted into a slowly propagating wave of stress through the glass then re-converted into light at the far side. (In Paul's life as a scientist he worked on acoustic delay lines known as SAW or surface acoustic wave devices where an electromagnetic signal in the radar portion of the spectrum was converted into an acoustic signal as a surface wave on a piece of quartz. The signal then propagated at the speed of surface waves, even slower than a sound wave, in quartz. At the far end of the quartz the signal was converted back into an electromagnetic signal once again. Paul's work occurred in 1971 just about the time that Bob Shaw was writing his novel.)
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Scientific Explorations with Paul Doherty |
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30 June 2006 |