The Mad Scientist Diary

The two images above show the same hologram of a microscope viewed from two different angles. No matter how you look at a normal photograph, you always see the same image. However, with a hologram you can view an object in three dimensions simply by looking at the hologram from different angles, just as if it were a real object. With this particular hologram you can even "look into" the lens of the microscope to see the bug on the slide below!

Holograms achieve this remarkable feat by storing a lot more information about a scene then a regular photograph. Normal photographs only encode information about the intensity of the light that strikes the film. In a hologram, the phenomenon of diffraction is used to record information about both the intensity of the light and how far away it came from (encoded in the phase of the wave). 

Normally, when an object blocks a beam of light, it casts a completely dark shadow. However in some circumstances (like the shadow pictured above), this is not the case. 

In the experiment pictured above, a green laser pointer was pointed at a ball bearing suspended on a thread, casting a shadow on the opposite wall. Normally we would expect the resulting shadow to be a completely dark circle. But in this case, the shadow has a single point of light in its center! This point of light is called the Poisson spot. 

The spot appears (under the right circumstances) because of the wave nature of light. If light were just a stream of particles (imagine bullets fired from a gun), the shadow behind the ball bearing would be a perfect circle. In reality, though, light often acts like a wave. When a wave hits a barrier, it can diffract around it, interfering to create a new wave on the other side. This is why a ship anchored off the coast of a beach does not cast a "shadow" of calm water onto the shore. The observation of Poisson's spot in the experiment above shows that, at least in some circumstances, light behaves like a wave. 

When powdered hot chocolate is stirred into a cup of milk, the pitch produced by tapping on the mug changes drastically as the powder is stirred in. This phenomenon is often called the hot chocolate effect, but it can also be observed with other drinks such as instant coffee or cold beer. 

In every case, the change in pitch is caused by the presence of air bubbles in the liquid. These bubbles are stirred into the mixture along with the powder ( giving the hot chocolate a thicker, foamy texture). However, since the speed of sound is much higher in water (or milk) than in air, these air bubbles lower the effective speed of sound in the hot chocolate.  This in turn lowers the pitch at which the mug resonates when tapped. 

Quantum theory predicts that single photons can interfere with themselves, just like waves, when passing through a pair of slits. This may seem weird enough, but photons don't always act like waves! In fact, we can change whether a photon acts like a particle or a wave merely by looking at it.

The image on the left was captured while sending a beam of single photons through a pair of slits. As discussed in my last post the photons are acting like waves, producing an interference pattern. In this experiment we know nothing about the individual photons passing through the apparatus. Most importantly, we don't know which of the two slits an individual photon has passed through.

In the image on the right, I modified the experiment so that I could tell which slit each individual photon had passed through. Suddenly, the interference pattern disappears! By making the measurement I forced the photons to act like particles, which do not interfere. 

In my last post, I explained how Thomas Young's double slit experiment convinced the world in the 19th century that beams of light behaved like waves. A little over a century later, interference patterns like the one above shook up the world once again. This image was produced while allowing only a single photon pass through the slits at a time, confirming the quantum mechanical prediction that single particles of light behave like waves, and are able to interfere with themselves!

I took the picture above with a special camera that is sensitive to single photons. In order to create a beam of single photons, we start with a normal laser beam. We then pass the beam through a series of filters, each of which weakens the beam by a factor of one hundred. After two such filters, the beam is so weak that only a single photon is passing through the slits at a time. 

Quantum theory says that, until we observe it, a photon does not have a definite location but is instead spread out as a cloud of possible locations called the wave function. Since this probability distribution behaves like a wave, it interferes with itself as it passes through the slits, creating a probability distribution that looks like an interference pattern. When each photon is measured by the camera, its wave function collapses, causing it to "chose" a single pixel to trigger on the camera. However, over time the number of photons seen builds up according to this probability distribution, making visible the interference pattern pictured above. 

The image above shows what happens when you shine a laser through a pair of very small and very close together slits. This distribution of light is called an interference pattern, and is the quintessential example that light consists of waves. 

Like waves on the ocean, light waves have both crests and valleys. When a crest meets a crest, they reinforce one another to form a still larger crest. However, when a crest meets a valley, they completely cancel out. This process is called interference. In the double slit experiment described above, each slit acts as a source of light waves. As the two waves cross they interfere, creating dark spots where crests meet valleys. These dark spots then become the dark bands of the interference pattern. 

As a fun side project this summer, I fixed this old water bottle rocket launcher that was used in an old physics class. The physics department's PREP program (a summer camp for high school girls) then built rockets for the launcher, which we fired off on the university's main quad. 

Unlike the simple water rocket launchers I built as a kid, this launcher is capable of shooting rockets up to several hundred feet into the air. The rockets (made out of soda bottles) are placed on the pipe at the top of the launcher. They are pressed down against an o-ring to create an airtight seal, then wedged in place with a metal clip. The soda bottle can then be pressurized (through the pipe) to up to 100 psi. When the clip holding the rocket down is finally pulled away the pressure is released, propelling the rocket upwards on a column of water. This rapid decompression of the bottle vaporizes some of the water inside, forming a miniature cloud inside the bottle! 

We had mixed results with our first round of rockets, but the whole process was so much fun that I plan on building some of my own this semester. 

The picture above is the culmination of my last two summers of work: a trapped cloud of extremely cold rubidium atoms!

These atoms were cooled in a magneto-optical trap or MOT (described in a previous post here) that uses lasers to create an "optical molasses" that slows the atoms down. The resulting cloud is less than a millimeter in diameter (the bright spot in the center of the hazy purple cloud in the second image) but contains many thousands of rubidium atoms.

While I have not yet measured the temperature of these atoms, typical temperatures in a MOT are measured in hundreds of micro Kelvin above absolute zero. Put in perspective, that makes these atoms several thousand times colder than outer space. 

The video above shows the traces of individual subatomic particles in a cloud chamber here at the University of Rochester.

A cloud chamber is a sealed container containing a fine mist of very cold alcohol vapor. The vapor forms a thin cloud that is on the verge of crystallizing to form snow. Just as clouds in the atmosphere are triggered to precipitate by small particles of dust, the alcohol vapor in the cloud chamber will form snow when a charged subatomic particle passes through. The snow formed by an individual particles forms a white streak in the chamber as seen in the video above.  

The majority of the particle tracks seen in the video are emerging from the rod in the center of the screen which contains the radioactive element thorium. Each time a thorium atom decays, a fragment consisting of two protons and two neutrons (an alpha particle) is emitted. These particles form the traces seem emanating from the rod: each trace indicates that another atom has just split. 

The beautiful crystal shown above is a polarizing beam splitter cube (PBSC) that will be part of the magneto-optical trap that I am building. The purpose of the cube is to split a beam of light into two beams with different polarizations. 

The polarization of light can be visualized by thinking about waves travelling along a string. If the end of the string is moved up and down, a vertical wave will travel along the string. This wave is said to be vertically polarized. Similarly, waving the string from left to right would produce horizontally polarized waves. Light waves behave much these waves on a string and can also be vertically or horizontally polarized. 

Here's another successful test of our hybrid rocket motor! This test shows off one of the coolest properties of a hybrid rocket: variable thrust.

The thrust is controlled by the flow of oxygen and can thus be set by simply adjusting the pressure of oxygen coming from the regulator into the back of the motor. The motor can even be turned off and then back on again over short periods of time, as shown in the video. 

The first test of our hybrid rocket motor was a success! 

Today I made the first nozzle for our test rocket engine. Unlike the rest of the assembly, which is made out of aluminum,  the nozzle is made out of steel to make it more temperature resistant. This first nozzle has a simple straight 1/4'' bore down the center and will be used for testing the engine assembly to make sure it works and to provide a baseline thrust measurement  Later nozzles will be made with more complex geometries. 

I've nearly finished machining the end plates for the rocket nozzle test engine I am building with my younger brother. 

One end plate has an O-ring seal and will later have an adapter to connect it to an oxygen line. The other end plate has a recess to hold the replaceable nozzles that I will begin building next. The acrylic rod in between the two end plates has a 1/2'' hole bored through the center, which will be the surface that burns when the engine is ignited. 

Over the past few months I've been working with my younger brother on a cool new project. Inspired by a video on YouTube here, we have been designing a hybrid rocket motor that he plans to use to test different nozzle geometries. 

The image above is a rendering he made of our final design. Pure oxygen gas will enter the engine on the left side through the hose barb into a PMMA (acrylic) tube. The oxygen allows the PMMA to burn. The resulting hot gases exit the motor on the right hand side through the nozzle, which is replaceable so that we can easily test different nozzle designs. 

The animation above shows the path traced out by the tip of the bicycle wheel's axle as it rotates around the string in slow motion. In my previous post, I explained why the wheel rotates around the string. Now we can address the really interesting question of the gyroscope's levitating act: why does the top of the axle curve back up every time it starts falling? 

In order to see where this "force" comes from, we need to trace the paths followed by an individual point on the rim of the wheel. This is pretty tricky to do in your head, but is made much easier by computer animations:

This animation traces the paths of two points on the rim of the wheel. The blue point starts on the top of the wheel, while the red point starts on the bottom. 

When the animation starts, the two points are in the same plane: the blue dot is right above the red dot. However, by the time the red dot is up on top, the red dot has moved to the inside and the blue dot has moved to the outside! This may be easier to see from a top view: 

Whenever a point gets to the top of the wheel, it veers out (away from the string at the origin), while the point at the bottom veers in. These are only two points, but the same holds for all  the points on the wheel! Thus the wheel feels a constant "force" pushing the bottom out and pulling the top in. We can visualize that force as vectors on a force diagram:

The effect of these "forces" is to twist the wheel back to its original horizontal position! However, the forces themselves are a result of the rotation of the wheel around the string, which only starts when the wheel begins to fall. Thus we see the oscillating motion shown in the first animation of this post: the wheel begins to fall, picks itself up, then begins to fall again in a continuous cycle. This is how the bicycle wheel holds itself up against the force of gravity.

I hope these animations have shed some light on precession and helped reveal the beautiful physics that causes it. This series of posts was adapted from a paper I wrote on this topic, so if you'd like to read a more technical (undergraduate level) explanation of precession, feel free to message me for a copy. 

For more information, check out this blog post: http://arundquist.wordpress.com/2012/05/26/gyroscopic-precession/

It turns out that the secret of the bicycle wheel's gravity-defying feat lies in the way it spins around the whole wheel spins around the string. Thus, in order to understand why the wheel stays up, we must first explain why the wheel rotates this way.

Just as an object that is moving in a straight line wants to continue to move along that line, an object that is spinning wants to continue spinning. We call the amount of resistance the spinning object has to slowing down its angular momentum. A heavy wheel spinning at the same speed as a lighter wheel has more angular momentum, and a faster spinning wheel has more angular momentum than an identical slower spinning wheel. We represent angular momentum as a vector (an arrow) pointing along the axis about which the object is rotating, 

Once it is set spinning, the bicycle wheel has a constant angular momentum. Since the wheel is rotating about its axle, this angular momentum is represented by an arrow along the axle of the wheel (a): 

When the wheel is let go, it begins to fall (b). The axle of the wheel is now pointing down at an angle. Since the wheel is still spinning around its axle, the new angular momentum of the spinning wheel must now also be pointed down at the same angle (the solid blue line in b). However, the total angular momentum of the wheel must remained unchanged (the blue dashed arrow). In order for this to happen, there must be a THIRD vector: the red arrow in (b) so that the two vectors add up to the original angular momentum vector. 

Since the rotation described by an angular momentum vector is around the vector, the wheel must be rotating around the string...which is exactly the motion we observed! The bicycle wheel is forced to rotate around the string in order to conserve angular momentum.