March 10, 2006
I just created an "Other" page on the website. This will be the home of the quotations and physics-related ideas that will purely and concisely define my world view and future ambitions.
January 24, 2006
I've posted a summary of my SL research in the Fall 2005 semester on my
Hopefully progress won't be impeded as much this semester, by the inconsistency in producing SBSL.
September 27, 2005
I just returned from my
E=mc^2 Day event. Fred Goldhaber, Robert Crease, David Cassidy, and Massimo
gave wonderful and insightful talks.
Some interesting results with the SL experiment. I added 5 ml of
glycerin to the water to make bubble trapping and stabilization easier
to do. Indeed this was the case, except that producing SBSL was
impossible! I even tried pumping on the water to remove any excess
gas, but this did not help. It is very confusing since Ken Lee
reported in his journal that 5 ml of glycerin significantly stabilized
the SL bubble. I also replaced the glycerin doped water with fresh
degassed water, but was still unable to produce SBSL, even at a
driving voltage of 7 volts, which is quite excessive. This is
frustrating since I have recently screwed down a CCTV camera into my
lab table and connected it to a TV monitor which magnifies the image
of the bubbles in the flask by a large but unknown factor. I want to
use this camera to observe the SL bubble in greater detail. This means
first getting SBSL again, which will simply require persistence and
patience, and is guaranteed.
September 20, 2005
I'm back finally, to writing in my journal. The first few weeks of
school have been a pain in my ass. Having my dorm room assignment
screwed up for the semester and deciding what classes to take have
made it difficult for me to continue with the experiments, until
now. Anyway, the most recent experiments with SBSL have led to the
The degassing conditions necessary for SBSL to occur this time are
strangely different. Degassing the water (that is, pumping it down by
vacuum, until there are virtually no more observable air bubbles in
the water, makes it impossible to sustain or even form a trapped air
bubble. When a bubble is injected, it migrates towards the center of
the flask, but then instantly dissolves. When air is partially
dissolved back into the water (over the course of 6 hours of exposure
to STP) the trapped bubble dissolves within several seconds
instead. The following degassing procedure appears to be most
effective in producing the necessary amount of gas content in the
1. Pump on the water in the flask until the pressure reading from the gauge meter is down to 20 Torr.
2. Once at 20 Torr, immediately close off the vacuum pump valve and test to seee if you can trap a stable bubble for a longer duration.
3. Repeat above procedure if initial pumping is not enough to form a stable bubble.
The next steps will be to try using water chilled to 10 Celsius, along with glycerin, and that Vitamin water I mentioned before.
August 18, 2005
On Friday of August 12th, we the students spent our last day together in the Laser Teaching Center. Of course we made sure it would be a memorable one. We first created a nice and mellow lab ambiance, with some of the lights turned off and and the optics displays turned on. We then created our own laser light show, where we took an old speaker and covered it with a latex glove to form a membrane which we epoxyed a mirror to. We then shone three lasers (the red HeNe, the green diode, and the violet) at the mirror, which reflected towards the ceiling. The idea was that when the speaker (which was also connected to an old radio that was connected to Dr. Noe's boom box), pulsates with each musical note, the laser beams would form random patterns that correspond to each note. The effect was quite fascinating and worked very well with the classical music we played such as Shostakovich Violin Concerto, Ave Maria, Vivaldi: Four Seasons, etc. People from the electronics center, the machine shop, and Dr. Metcalf's research group all came to see it. We then decided to enhance the show by pouring liquid nitrogen vapors around the mirror, so that one could see all the colorful laser beams converging and diverging. The oscillations of the looping laser patterns also reminded me of string theory since every note corresponded to a particular pattern of oscillations of a laser beam, in the same way that every mode of vibration of a string in string theory corresponds to a particular fundamental particle in the Standard Model. Indeed string theorists frequently use this analogy to describe what string theory says about our universe - it is a symphony of vibrating strings.
After the laser light show, Moon, Amol, and I went with Greg to his
dorm to pick up his speakers which we used to watch "Death to
Smoochy", while also eating pizza. The eggplant pizza was quite
excellent-too bad we didn't try it earlier. Moon was the first to
leave, even before the movie ended. Lindsey followed suit shortly
thereafter. Matt and Amol then went to give their Simons talks. Nilus,
Greg, and I stayed behind and cleaned the lab up a bit. I then went
back to my dorm and finished packing my stuff to move out of my
suite. Greg was gracious enough to help by using this cart he has to
take my belongings downstairs and load them into my mother's car. I
came back to the lab after packing and heard from Dr. Noe that a
Simons student was using collapsing microbubbles to drive a small
motor! Apparently John brought him back to the lab when I wasn't there
and showed him my workbench and even trapped a bubble for him to
see. Too bad I wasn't there to show him SBSL. Anyway, I spent the rest
of the evening making up journal entries from August 7-11. Afterwards,
I shut everything off at my workbench and left for home.
The fact that this was the last day at the LTC wasn't as depressing as
I thought it would be, since all the other students, except for maybe
Greg, will be returning throughout the year to continue on with their
projects. Thus, I prefer to look at this last day not as the beginning
of the end, but the end of the beginning. This was indeed a memorable
summer. For me, I developed the skills and confidence to make things
happen not just in my mind, but also with my hands, and further
strengthened my interest in SBSL and the long term goal of working up
to a replication of the sonofusion experiments. The other students in
the lab here, created a research environment that I couldn't have been
happier with. The chemistry we had as a group was important, I think,
to each of our successes in our projects. I'm also going to miss all
the intense discussions about physics, philosophy, politics, and
religion. It's not everyday that you meet people who are comfortable
enough with these subjects to discuss them casually. But this is what
an intellectual environment is supposed to be - a haven for
free-thought and freedom of inquiry. Finally, I sincerely hope that I
contributed something concrete to the other students by my presence in
the lab. This research experience would not have been what it is if I
was singularly focused on Sonoluminescence, though I am happy to say
that I achieved what I initially planned to do. I hope to see you all
again soon; but in the mean time, good luck to everyone with
everything that awaits you all this year, and thank you for helping to
make this a productive, memorable summer experience.
August 7-11, 2005
Much has happened since I last wrote. All the REU students
are official gone, except for Greg and me. I finally managed to repair
all the PZT transducers. The microphone wires and the red wire of one
of the drivers were soldered in place and epoxyed back onto the
flask. I then began driving the PZT's with the function generator and
amplifier, while using the oscilloscope to register the signal picked
up from the microphone. I could alway hear the signal when the PZT's
were oscillating at frequencies below 20 kHz, and could always hear a
fizzing noise when bubble were present in the flask from the
undegassed, vapor distilled water. Indeed this is the type of water I
initially used to try and trap a bubble. This was very difficult
however. Every time I injected a bubble, it would get trapped far off
from the center of the flask and would randomly oscillate; eventually
the bubble would become so unstable that it would fly off to the walls
of the flask. This would occur even if the acoustic field was at or
close to the resonance of the flask. An indication of a successfully
trapped bubble was ripples in the sine wave pattern on the
oscilloscope. This was sometimes never observed, except when the
bubbles were very well centered and stabilized. To see the bubbles, I
had to use a high intensity light source (Fiber-Lite A3200) which was
directed straight onto the flask, which was then placed inside a large
black box that was made by the previous SL student, Ken Lee.
To find the resonance of the flask, I had to watch when the signal on
the oscilloscope reached it's maximum amplitude, as I varied the
frequency from the function generator. I often found this frequency to
be between 25-27 kHz. I also had to reposition the ferrite rod in the
inductor to maximize the signal amplitude. It should also be noted
that I always followed these procedure after first sucking some water
from the flask, as this slight perturbation in water volume would
easily alter the resonance. I also noticed some other interesting
effects of the undegassed water. When I would inject bubbles, they
would all migrate towards an anti-node of the acoustic field near the
center of the flask and combine to form a larger bubble. If I then
violently injected a large concentration of air bubbles, there would
be a small one forming near the center of the flask; and sometimes the
bubble would rapidly orbit some axis and form a tail. This tail looks
very similar to a cavitation vortex, which has been observed in the
work of cavitation researcher Roger Stringham. I also discovered that
for a sufficiently stable bubble, I could manipulate its position in
one axis, by varying the frequency in steps of 10 kHz. This is
probably due to some shift in resonance of the acoustic field in the
flask. Indeed it is somewhat similar to the idea of optical tweezers,
except instead of using light with orbital angular momentum to rotate
a microscopic particle, I am using an acoustic field to change the
position of the bubble along a particular axis. I suspect I could
create an acoustical tweezer very easily then.
After becoming comfortable with bubble trapping, I then proceeded to degass fresh vapor distilled water. To do this, I used the vacuum pump to lower the pressure to 5 Torr and waited for the all the visible bubbles to leave the flask. This took approximately a half hour. After doing so, I then proceeded to trap bubbles in the degassed water. I found however that the bubble would not easily form immediately after degassing, implying that the water was too degassed. However, if I waited a couple hours, I could then trap very tiny bubbles, on the order of the thickness of a strand of hair. I also found in these conditions that by continuously injecting bubbles, they would migrate towards the initially trapped bubble, but they would not combine to form a larger bubble. I also found these bubbles to be far more stable, and very well centered in the flask. The bubbles would remain centered for a couple of minutes, versus a few seconds in the regular fresh water. To reach the conditions necessary for SBSL to occur, I also had to increase the voltage, just below the point before the bubble became unstable and flew away. This also took some practice but was eventually mastered. After understanding these nuiances of trapping bubbles in degassed water, I then proceeded to observe SBSL. On the first attempt, I cleaned the flask with denatured alchohol solvent, found the resonance of the flask, trapped a bubble, set the voltage just below the threshold of instability, shut off all the lights, including the high intensity light source and oscilloscope, and waited for my eyes to adapt to the darkness which took only a few seconds. Lo and behold, I was successful in seeing the bubble sonoluminesce (picture taken by Nilus) and I was so pleased that I cheered at the top of my lungs. Seeing the bubble was a bit difficult however. I had to look slightly off to the side of the flask, like you would in looking at a faint star in the night sky. Only then could I clearly see the dim, luminescing bubble. Indeed this is why it looks like a star in a jar. This was officially achieved with a frequency of 26,586.112 Hz and voltage amplitude of 5.7 volts, at 11:18 pm on Wednesday August 10, 2005.
It should be noted that I worked for several hours into the night trying to trap and stabilize bubbles. You would normally think that failing dozens of times would be frustrating; but surprisingly, I wasn't even phased in the slightest bit. I just kept plugging away like any good, patient scientist and was eventually successful. I have become so immersed in my project that every time I close my eyes, I immediately see vivid images of bubbles being trapped at the center of a flask. It's a bit bizarre, but also an indication of mastery of my domain. And this is of course the goal of every scientist.
At one point I wanted to first and produce MBSL (Multi Bubble Sonoluminescence), but Amol called Moon's cell phone and said he wanted to speak to me. He told me that he wanted me to get SBSL and send him a picture. It was this extra push that drove me to stay on track. After producing SBSL, I took an hour long break and then returned to producing SBSL. I managed to do it 6 or 7 more times, after which I was pleased enough to call it a day (at 2 am). Since Wednesday night, I have been able to continuously produce SBSL and have shown almost everyone in the lab. What was surprising however, is that the following day, I was still able to produce SBSL in the same water that was sitting in the flask over night. You would think that over 10 hours, enough bubbles would dissolve back into the water to make bubble trapping very difficult; but apparently this was not the case. At one point, when showing John, I managed to keep the bubble stable for over 5 minutes!! This was at a frequency of 26.588 kHz at 4.38 volts. I did also try MBSL by matching the resonant frequency of the flask and cranking the voltage amplitude to a maximum of 25.5 volts. By slightly varying the frequency, I could then hear a subharmonic pitch which sounded like a high frequency screetching noise (I can now produce this subharmonic effect at will). I'm not sure if this worked, because the light that I thought I was seeing could have been imagined. Later on, I chilled the flask with water down to 10 degrees Celsus in John's refrigerator and tried producing SBSL, but this was difficult because I did not have an oscilloscope to work with - other students needed it for their projects. Of course, I will try doing this again, and would also like to try using glycerin and Vitamin water. The Vitamin water, which is lemon flavored, is vapor distilled and contains magnesium based electrolytes. I would imagine a very strong SBSL effect if I were to chill the vitamin water down to 10 Celsius and add some glycerin. So this is something to try in the near future....(more to come).
August 5, 2005
The past four days has been a race to collect data and complete the powerpoint presentation. Both were successful, except that I wasn't able to observe the sonoluminescence since a PZT wire broke off and so did the microphone. Moreover, the wires connecting to the coaxial cable of the inductor and the op amp were crapped out. Thus, they had to be replaced. It was for all these reasons that when I tried driving the PZT's with the function generator, they did not respond. As of right now, the microphone is still detached, but the PZT drivers are repaired, thanks to my masterful soldering skills.
Last night, I spent the whole day creating my powerpoint presentation and rehearsing on my own. So I didn't leave the lab until around 1:30 am. The presentation seemed to have went OK, except for the beginning when I couldn't open my powerpoint on the provided computer. I had to use another REU student's computer to open it and doing all this consumed quite a bit of time. All the subsequent presentations looked very good as well. It is still not entirely certain if I will be able to stay for an extra week, but the hope is that I can. I really want to get to the SBSL.
August 1, 2005
Over the weekend I continued plotting points from the vacuum pump experiment with degassed water. I found that, initially, the rate of pressure rise appeared linear. However, after 2500 minutes, the rise started to level off very slightly. These plots (in red) were also made on the same graph as that of the initial vacuum pump measurements (in blue), where there was no attempt to degass the water. This plot can be seen here. Unfortunately, because these vacuum pump measurements take so long, I did not wait to see if the pressure in the flask would definitely reach equilibrium below atmospheric pressure. I ended the measurements at 202 Torr. The reason this number is so random is because the ZP pressure was scaled at 4 Torr, so I had to subtract 4 Torr from every direct reading from the pressure gauge. Nevertheless, because the pressure rise takes so long, I would conclude that equilibrium pressure is probably very close to atmospheric pressure and that continuously depressurizing the water after it stops bubbling, makes a small difference in the gas content of the water.
I also created 3 powerpoint slides for my presentation and finished writing my REU abstract which can be found here. And today, Dr. Noe and I cleaned my work station and organized the pump, meter, flask, amplifier, etc., in a more functionally efficient way (pictures coming soon). With Dr. Noe's help, I also wired the 36 volt power supply to the amplifier. I connected six outlets on the power supply to three wires from the amplifier, in such a way that there are four potential differences for the op amp. The op amp needs some sort of absolute reference frames, to know what input it is getting. We are now in the process of regluing the PZT's and trapping an air bubble to produce SBSL.
I also want to mention a phone discussion I had with a physicist at Boston University, Dr. Daniel C. Cole, whom I worked with in high school. I had several thoughts and ideas I wanted to consult him on and he was gracious enough to give me an hour of his time to do so. I told him of my research here on sonoluminescence and about some of the other optics projects we have going on. He was quite impressed by it all. We then discussed an experiment I recently designed to test the classical electromagnetic zero-point radiation model of Stochastic Electrodynamics (SED) versus the virtual electron-positron pair model of Quantum Electrodynamics. The idea is this: In the Casimir effect, cavity resonance occurs, like in light amplification in an optical cavity, when integer multiples of one wavelength can fit between two conductive, reflective boundaries. The constructive interference of the waves increases the vacuum energy density between the boundaries and produces a repulsive force between them. Now if one were to oscillate the two boundaries at the same fundamental frequency as the standing wave between the boundaries, that would clearly increase the energy and intensity of the E-field betwen them. If these boundaries oscillate fast enough, on the order of 1017 Hz, then what should emerge from the cavity is real, as opposed to virtual, photons. This could only occur if the energy given to the virtual photons in the cavity is larger than the energy needed to obey the uncertainity principle where dE*dT < hbar. But if the boundaries could amplify the E-field of the standing wave so its energy is greater than or equal to twice the rest mass of the electron, then would we not observe electron-positron pair creation between the boundaries? And what predictions would SED make for this energy range? Would it just predict photon emissions of arbitrarily larger energies? Cole answered in the affirmative and pointed out that SED cannot yet handle particle-pair creation. Moreover, the definition of a photon in SED is still somewhat vague (as it also is in standard quantum mechanics). Nevertheless, he agreed this would be an interesting experiment to do and still holds out hope that SED will be able to eventually deal with these fundamental issues. We also discussed sonoluminescence. I described how SL can be used as an acoustic black hole analogue model and that Casimir effect mechanisms have been proposed for SL (see my websites).
I then asked him about the interpretations of continuity and quantization of energy and spacetime. More specifically, I raised the point that in Einstein's field equation, the curvature and mass-energy tensors are correlated mathematically, but standard general relativity (GR) does not exactly explain how matter and spacetime are causally related, nor does it say whether or not spacetime is some sort of geometric background entity, with an existence independent of matter, or if spacetime is constituted by something more fundamental, like fields. In fact, general relativity assumes spacetime to be a classical vacuum, which is blatantly false according to Quantum Field Theory. Quantum fields isotropically pervade space via the Heisenberg uncertainty principle. However, if one assumes energy quantization, meaning photons, then there is only a finite volume of spacetime that can be occupied by such photons. This leaves momentary spatial "gaps" in between these quantum fluctuations, where the there is briefly some region of empty spacetime. However, the moment you posit the existence of a spacetime vacuum, the question then becomes this: what sort of physical properties does this spacetime vacuum have, independent of the quantum fluctuations? Standard GR says it is just a classical vacuum with no other definable physical properties, other than being able to "interact" somehow with matter and energy. But if it is a classical vacuum with no other definable physical properties, then how can something (matter) curve this nothingness called "empty space", rather than just perturb the quantum fluctuation field of quantum field theory? If on the other hand one assumes a continuous, electromagetic zero-point radiation field, then one could plausibly argue that spacetime is not some geometric entity indepenent of matter; rather, spacetime is the zero-point field fluctuations and what we observe as spacetime curvature is actually perturbations of the zero-point field fluctuations. This idea of mine is similar to the ideas of what physicist Andrei Sakharov proposed in 1967, that gravity may be an emergent effect of one-loop quantum field effects on a dynamically curving pseudoriemannian manifold. The difference of course is that he doesn't explain what causes space to curve. Nevertheless, the idea is very similar and does not require the fundamental assumption of spacetime quantization which is so dominant among most theories of quantum gravity. Of course, such an approach should still explain how matter is quantized and how energy is quantized in its interaction with matter. Standard GR, in my opinion, does a wonderful job of providing an elegant geometrical description of gravity in terms of "spacetime curvature", but it lacks a rigorous, causal, mechanistic explanation as to what this precisely means. Cole essentially agreed with my opinions, which was somewhat encouraging.
We then discussed hidden variable theories in quantum mechanics, and Cole sent me a paper by the physicist Ballentine, who argues that a stochastic or statistical interpetation of the foundational axioms of quantum mechanics is much more physically and logically coherent. I then quickly described a method I designed, to extract useful work from the lateral Casimir effect. I can't go into details about this contraption yet, since it may turn out to be practical and workable, and so I wouldn't want my idea to be "ripped off"! He also found this idea interesting and suggested that we discuss it another time. So the past few days have been quite productive and intellectually stimulating to say the least!
Also, I want to mention that I was fortunate enough to have a string theorist participating in the Geometry of String's Vacua, move into my suite. It'll be interesting to see what sort of discussions come out of this situation.
July 27, 2005
This morning I went to the String theory lecture, entitled "Type IIA Flux Compactification". I managed to understand some of the talk, which was encouraging. It was also exciting to see the exchanges between all the physicists during the Q&A session. Later on in the day, I discussed acoustical vortices with Marty and contemplated the use of optical vortices in a BEC (Bose-Einstein Condensate) to produce optical black holes. I also read an interesting paper which reported on the work of two astrophysicists who have recently suggested that what we think are black holes do not exist and are really just gravastars, which are highly condensed spherical shells of matter in a BEC state, with a negative gravitational pressure pushing outward. Apparently gravastars resolve a number of problems that exist with a singularity picture of a collapsing neutron star. They may also provide a potential explanation for the cosmological constant, since the negative pressure inside a gravastar is equivalent to the cosmological constant value. So essentially, the universe and all the matter inside it would be like a giant gravastar.
I also plotted the measurements of the rate of pressure rise in the flask, after being pumped. I found a linear curve up to 100 Torr, which was most unexpected. Perhaps the equilibrium state is much higher and so the leveling off is still unobservable. Hal suspects that there is a leak, since the pressure should have reached equilibrium at 17 Torr. He suggested that I use vacuum grease and a stopcock to seal the flask. However, when I pumped the flask with just air, the pressure stayed constant, indicating no leak. Moreover, Dr. Noe mentioned that 17 Torr is the vapor pressure of water and does not take into account the air pressure in the flask. This point is still not entirely clear to me, but in the mean time, I will degass the water in the flask and take measurements to compare to this one that I just completed.
July 26, 2005
Much was done today. I pumped the flask, empty, down to zero-point (ZP) pressure (5 Torr) to verify that there was no leak. Indeed there was none. I then pumped the flask with fresh distilled water down to ZP pressure and since then have been recording the increments at which the pressure in the flask increases by 5 Torr, with respect to time. I have found so far that it is taking exponentially longer for this to happen and that these results are very different from the previous run when the pressure increased at a much faster rate and continued to rise, suggesting that there was a leak. Thus, I conclude that this flask is completely vacuum sealed and more accurately shows how pressure increases in the flask.
I also went to the Strings workshop to speak to Rocek about the connections between General Relativity and sonoluminescence, but he was too busy to speak. He did however ask me if I had made any progress on the idea of using PZT's, slightly out of phase, to induce a torque on the bubble. I told him that I had not. However, when I returned to the lab, I went over to Greg's work station where we discussed optical vortices. An idea then hit me. Shouldn't it also be possible to produce acoustic vortices? One possible way to do this I thought was Rocek's suggestions of creating sound waves, slightly out of phase to produce a Topological charge. These acoustic waves could potentially be used to transfer angular momentum to a sonoluminescing bubble, which would be very interesting to study for the simulation of black holes. Later that night, through Google Scholar, I found two papers on acoustic vortices; and it turns out they are produced by a one-sided hexagonal arrangement of PZT transducers, out of phase with each other! This could very well be an interesting project in it's own right.
July 25, 2005
Not too much happened today. Nilus gave a presentation on his optical lever project and we helped him construct the first paragraph of is upcoming report. In the morning, I went to the Geometry of Strings Simons Workshop in the ITP. Today was the first day of the event and it was quite informal. Martin Rocek, and Cumrum Vafa of Harvard, gave a short introduction about the workshop and how it would comprise of only one lecture a day, with the rest of each day being devoted to informal discussions about ANY interesting physics problems, not just string theory. I was very surprised to hear that the event would be this laid back. But I think this will be an invaluable opportunity to interact with the world's top mathematical and theoretical physicists. And that's no exaggeration. Some of the other participants are Ed Witten, Juan Maldacena, and Brian Greene. You can't get much better than that.
In the evening, I read about air solubility in water and found two wepages, one with a formula for Henry's Law for air solubility at STP. The other had an equation allowing you to compute the change in oxygen solubility as a function of temperature. I was unable however to find a general formula to express how air solubility as a function of pressure and temperature. Though it is absolutely certain that temperature decreases air solubility in water. I also did some calculations of the air solubility at ZP pressure, using these formulas.
July 22, 2005
Immediately this morning, Matt, Dr. Noe, and I proceeded to further simplify the expression Matt and I derived yesterday. We found that
I(Load)=(V1/R1)*(R3/R5). At 11 am, Hal gave a talk, ironically, on the Op Amp circuit and the concept of feedback systems; and later on, about laser diodes. Unfortunately, Greg and I could not stay for the second half of the talk as we had to attend our REU lecture given by Prof. Michael Rijssenbeek. His talk was all about the Standard Model of particle physics. He was quite comprehensive, starting from the beginning of quantum mechanics, all the way to discussions of the Higgs field and Quantum Gravity. I enjoyed it very much. I asked a number of questions such as how can the graviton model be consistent with general relativity? At what energies do particle physicists expect to find the superpartners? And how can the Higg's boson itself acquire mass if it is supposed to be a mass giving particle?
Later on, Marty and I discussed the problems with PZT transducer adhesives and the vacuum pump. I came to the conclusion that I should probably try using electricians wax and/or simply reglue the PZT with epoxy.
July 21, 2005
Most of today was spent working on the Op Amp circuit. Matt and I gave a presentation on the Op Amp, but realized during the talk that our answers to the questions Dr. Noe was posing were rather incorrect. After about 2 hours of questions and discussion, I finally developed a deeper understanding of how the Op Amp actually works. Following the talk, Matt and I proceeded to rederive the equation relating output current to input voltage in the circuit (we got I(Load)=(V5/R5)-(V1/R1)).
Other than the talk, I did a complete derivation of energy quanta by applyingg the First and Second Laws of Thermodynamics for monochromatic radiation of low density. Unfortunately, the derivation had to be erased.
July 20, 2005
I spent most of my time today trying to produce a mixture of epoxy
resin and hardener with a texture similar to that of the adhesive that came
off the PZT. This did not seem to work unfortunately. Perhaps it would be best to just simply epoxy on the PZT and see what happens.
We also had the LTC and Metcalf research group picture taken. It seemed to have come out well.
July 19, 2005
Today I got working on the resonance circuit. John told Matt and I to think
about the OpAmp circuit and to try and understand how it works. This took
a while, but we eventually derived a formula for the usable current or the
constant current produced by a circuit with four resistors and an audio amplifier
recieving a signal from a function generator. A problem later arose when
the PZT transducer came off the flask, after it was removed from the water
bath from the previous night. And apparently we could not figure out what
adhesive was used for the PZT. It may have been epoxy, but it had a rubbery
texture and dissolved from being immersed in water.
Other than this, Hal gave a lecture on the history of time and methods of
measuring it. He also discussed how time is one of the most precisely measured
quantities and how a second is defined to be 9,192,631,770 vibrations of
a Cesium atom. We also went into some discussion about quantum mechanics.
I asked Hal whether the transition of an electron from one state to another
is instantaneous orhas duration. Hal said there are experiments suggesting
both possibilities. This was not exactly clear to me. If it is the case that
the transition is instantaneous, this would be a violation of causality since
there would be no time needed to go from one state to another. Thus I am
willing to bet that the transition has duration and can probably be better
explained by quantum electrodynamics. We also had some discussions of measurement
theory. Hal remarked that we can't meaningfully talk about the electron existing
in a definite, until it is observed. The electron is in a superposition of
states. This Copenhagen interpretation is common among experimentalists.
Aside from this lecture, I continued studing the OpAmp circuit diagram.
July 18, 2005
Dr. Noe returned today. He first talked about his vacation and
the places he went. We then went to the pizza lunch in the seminar room where
we discussed the progress made on our projects with Hal. During this lunch,
I read an excerpt to Hal from the Optics text by Hecht, where Richard
Feynman explained why light is made of particles called photons, not waves.
I then asked him what his thoughts were. He replied, "Everybody makes mistakes,"
referring to Feynman. He still maintained that light behaves as waves. I have
to read more about how QED explains interference and diffraction in terms
of photons, but I think there are problems with both models.
Other than this, I read the pressure on the gauge meter and found it to
be at 280 Torr. I then decided to do a test to see if pressure increase when
uniformly heating the flask. This was suggested by John. Of course the pressure
will increase sincean increase in temperature reduces the solubility of air
into water, and also gives the air molecules more kinetic energy, thus increase
the pressure inside the flask. To do this experiment, I first filled a plastic
container with deionized water and measured its ambient temperature which
was 21.1 Celsius. I then heated the water-filled container in a microwave
for 2 minutes to a temperature of 37.8 Celsius. The flask was then immersed
in the heated water and the pressure gauge was carefully observed. In 5 minutes,
a pressure increase of 5 Torr was observed, from 280 Torr to 285 Torr. after
which, the pressure rise in the flask regressed back to the preheated state.
It seems plausible that there is a leak in the vacuum pump, considering that
the pressure inside the flask doesn't seem to be reaching any equilibrium
below room temperature so far. This experiment ended at around 11:30 pm.
Moon was also in the lab at this time, learning how to use Mathematica.
She then assisted me by using Mathematica to calculate the Planck energy density,
and the quantum mechanical zero-point energy density. The purpose of doing
this was to check if my approximate order of magnitude calculations of these
values were correct, and if the ZPE density is greater than the Planck density.
The significance of both these values is that the Planck energy density is
the critical mass-energy density needed to form a quantum singularity or
black hole, and the ZPE density is the theoretically predicted energy of
the vacuum of space, interpreted as fleeting virtual electron-positron pairs.
If it turned out that the energy density of the ZPE was greater, this could
then allow one to interpret the ZPE as being comprised of virtual quantum
singularities. Unfortunately, the calculations showed the Planck density to
be three orders of magnitude greater than that of the ZPE.
July 15, 2005
Today I pumped the flask with water down to the 5 torr
zero-point pressure. I then closed the valve and monitored the rise in vapor
pressure inside the flask. This took a few hours. In fact, the rate of
pressure increase, exponentially decreases; so it is very difficult
to observe the equilibrium pressure since the pressure may still be changing.
For this reason, I used a magnifying glass to carefully watch the needle
as it moves. This first run was necessary test to scale the graph that
I will now use to accurately plot the pressure change with respect to
time. I also noticed that this test seems to require that the vacuum
pump be continually filled with liquid nitrogen every half hour or so.
Aside from the vacuum pump measurements, I taught Lindsey and Matt a
little bitof special and general relativity. This discussion then led to
another about time travel. I first explained how time may not be a fundamental
quantity, but a relational property of one harmonic motion spanning another,
as argued by Aristotle and physicist Julian Barbour. We then
delved into other random discussions about metaphysics and naturalism,
where Matt and I were defending a physicalist view of the universe
and Lindsey was arguing for a more transcendental interpretation. Nilus
was also involved, but he asked questions rather than taking a position.
All in all, I'd say this was a productive day. On another note, I want
to point out Moon's "other"
page which has a very nice collection of quotes and poems. In particular,
I found If by Rudyard Kipling to be very insightful. I disagreed
however with the Einstein quote which said "No amount of experimentation can
ever prove me right; a single experiment can prove me wrong." Theories can
never be falsified for the same reason they can never be proven; they are
only supported by inductive evidence i.e. experiments. It's surprising
how the Popperian concept of falsification still survives among scientists.
I also found it amusing that Nilus, Lindsey, and Matt were able to immediately
recognized the fallacy in Einstein's reasoning.
July 14, 2005
This morning I filled the Pyrex flask with deionized
water and reconnected it to the vacuum pump, in preparation for the measurements
and tests I will run tomorrow. Additionally, I read some of the Hect Optics
textbook and found it to be quite nice. The author seems to provide a very
comprehensive treatements of classical and quantum waves mechanics, as
well as optics. I found some extra sections on scattering phenomena and
its connection to quantum theory. Indeed Hect confirmed my suspicion that
the phenomenon of scattering is much more complex and poorly understood,
which is why Amol and I did not have much success in trying to fully understand
it. I also found the discussions on Quantum Field Theory and Complementarity
to be very nicely treated. Hect adresses not just the physics and
mathematics but also the metaphysics of waves, which is important, I think,
in fully appreciating the complexity of such phenomena.
July 13, 2005
We the LTC students and a group of graduate students,
had our first official pizza lunch. A talk was given by Jan, a German
graduate student studying X-Ray Spectroscopy. Afterwords, John left for
the week, while Marty stayed behind and looked at some of our projects.
July 12, 2005
This morning Greg and I had our REU field trip
to Brookhaven National Lab. The tour was delayed because the bus would
not start, so all the students just hung out in front of the SAC. At BNL
we saw the Synchrotron Light Source and all the experiments it is being used
for. We then had lunch in the BNL cafeteria where I happened to run into
Bob Crease, the BNL historian. Afterwords, we toured the RHIC (Relativistic
Heavy Ion Collider) which was fantastic. We then saw the STAR detector, as
it was being disassembled. It's interesting to think about how such devices
are so complex that no one individual physicist or engineer entirely knows
how they work. After returning, I went back to the lab and brought the two
audio amplifiers over to my work station.
July 11, 2005
Today I developed a simple MBSL experiment, after reading
a paper by Lawrence Crum on the use of an ultrasonic horn to produce cavitation.
I figure that if I were to superheat a flask of degassed water and then
bombard it with ultrahigh frequency soundwaves from a high frequency generator,
I should easily observe SL and with greater intensity than with normal
Other than this, I checked the pressure in the gauge which was
pumped on Friday of last week. On Friday, the pressure was 5 torr at
minimum. I concluded that this should be treated as the minimum
or zero pressure point, since it will not go any lower. Now I will pump
the flask with water and start taking readings of pressure increase. I
also need to start tinkering with the audio amplifier. Time is of the
July 7, 2005
Early in the morning, we all went to the seminar
room for the third of Hal's lectures. This time, his talk was about
the property of waves. We all did a demo where we stood side by side
and moved our fists up and down, following each person to our right.
This demo then led into a philosophical discussion about what a wave
is, since it was difficult to state whether we created a wave in our demo.
I suggested that it is not a wave since a wave carries energy and momentum
plus information. The latter concept is difficult to define, but I argued
that it was related to causality. Basically, for information to be communicated,
there must be a causal connection throughout a wave. And this causal
connection arises out of a transfer of energy. But since no energy was
transmitted, it did not fit the definition or properties of a wave, so
I argued that the "wave" in our demo was an illusory perception. Metcalf
challenged my implicit assumption that all physical processes are causal
by bringing up quantum mechanics and radioactive decay. Nevertheless, I
am still convinced that the concept of a wave is clearly definable. We
then went on to quantitatively define waves using the sine function in the
z direction. Afterwords, when John and Hal left, Greg gave a mini-talk
on modern physics to Lindsey and Moon, after being asked about what photons
are. He discussed the photoelectric effect and quantization of energy;
I then said a bit about GUT's (Grand Unification Theories). Moon seemed
particularly interested in these ideas.
In the afternoon, I tried pumping the SL flask to take measurements
of pressure change, but found that there was a leak somewhere. John
then came over and tried to find the leak, but somehow ended up sucking
water into the pressure gauge. Thus, I had to take the gauge apart, clean
it, and reassemble it. We then found the source of the leak which was
a torn valve. After replacing the valve, we then discovered that the rubber
stopper was also leaking air; so I ran the vacuum pump without the flask
and was able to lower the pressure to as little as 4 torr. I then left the
gauge meter at that pressure over night.
July 6, 2005
In the morning, John talked to us about the lab's DOS computer
and its spreadsheet program.
At around noon, Greg and I went to the
second REU lecture titled, "Imaging the Surfaces of Rotating Stars".
The speaker, Dean Peterson, is an astrophysicist and was showing us how
rotating stars can bulge out at their equator and also produce jets at
their poles, with temperatures hotter than the surface of the star. He
also talked a fair bit aboutinterferometry and diffraction. His discussion
about the star properties was very interesting because it reminded me
of my theories about how angular momentum would affect the behavior of
a SL bubble. Indeed at the Q&A session, I had an exchange with him
on whether or not these data of rotating stars could be used to help predict
how a SL bubble would be affected by spin. He acknowledged the similarities
in SL and the differences, noting that stars are stabilized by their own
gravitational and magnetic fields. Nevertheless, he suggested experimenting
with the idea.
July 5, 2005
Today was the second of Hal's lectures. This time
it was about noncommutable operations such as matrix transformations.
It reminded me of my linear algebra class, but was not at all hellish.
Indeed it was nice to see the application of matrices in describing
the effects of polarizers. Following Hal's lecture, we attempted to
find a general polarizer matrix by which we could multiply an electric
field vector and achieve the resultant electric field vector after
polarization. A contrived solution was found by Amol, but the actual
one was discovered by John and Lindsey and can be seen on either Amol
or Matt's journal webpages. I continued tinkering with with the vacuum
pump, trying to decide how to scale the measurements of pressure increase,
since it takes much longer than I anticipated.
In the evening, Nilus, Moon and I did an experiment to determine
the pitch of a screw behind a mirror mount indirectly via an optical
I have been contemplating methods to enhance sonoluminescence,
using microwave radiation. Over the weekend, I was playing around with
superheated water, which is water heated past its boiling point without
boiling. The potential energy tensioned in the water molecules, make
the liquid very unstable; and the slightest perturbance will cause
bubbles to nucleate and to release large amounts of thermal energy. My
idea is to first tension a liquid with negative acoustic pressure in
the same way that Taleyarkhan did with his sonofusion experiment. A small
volume of liquid in the node of the acoustic field would then be irradiated
with a focused beam of low energy microwaves, thus nucleating a cluster
of small bubbles. These bubbles will then expand in volume because of
the negative pressure field, and the subsequent collapse of the bubbles
will occur with much more force. The advantage, I think, with my approach
is that for any sonofusion experiment, the use of microwave radiation, rather
than neutron radiation, will make any subsequent measurements of neutrons
or thermal energy, much more reliable since there is no spurious neutron
source. It's also easier to do, though probably a bit dangerous.
June 30, 2005
This morning, Hal Metcalf took us all over to
his conference room and gave us a two hour lecture on the logic and philosophy
of complex numbers, as well as his own philosophies about teaching.
On one particular question, he asked me to prove that (8)(1/3)
= -1 + isqrt(3)/2. Unfortunately, it did not work out; not because
I made any error in my algebra, but rather, because the statement
is wrong, as Greg and I later realized. It's the division by two
that's incorrect. This became a "homework" problem after
it did not work out. Hal also kept on emphasizing how i is not
a number; but this is dependent on the definition of a number. So
I asked him what his definition of a number is, but there was no clear
answer. For this reason, my question of "what is a number?" also
became a homework problem. Considering his comments about the "magic"
of complex numbers, I asked him if he thought mathematics is invented
or discovered. His answer was not very surprising. He is a mathematical
realist, meaning he believes that mathematics is tautology and so
exists independent of our minds. He then went on to talk to us about
how polarizers work. Afterwords, John discussed Euler's Formula of
eix=cosx+isinx and how it can be used to derive most trig
identities. Moon then found a very elegant derivation of the Euler
formula using integration.
In the afternoon, we discussed a variety of topics
including the dispersion relation, group and phase velocity,
reflection, and the feasibility of making a light-saber. I should
point out that all these discussions were initiated by Amol. One
thing that also continues to bother me about reflection is how reflected
light can have the same intensity, if only a fraction of the light
that is isotropically scattered, is constructively interfering.
I also don't understand how information is defined and how it is stored
in the signal velocity rather than the phase velocity. In the evening,
I took some time to read another paper on sonoluminescence from the red
June 29, 2005
I spent the morning reading two long papers on
SL and sonochemistry. Later on, an acquaintance of John Noe,
who is a physicist working with Tom Weinacht, came to say hello.
Afterwords, John further discussed the small angle approximation,
as well as variations of multiple-slit diffraction. Greg and I then
went to the REU tour of the Nuclear Structure Laboratory (NSL). There,
we met and spoke to the two other Stony Brook REU students. I've seem
the NSL twice before, but it was nevertheless nice seeing it again.
Amol asked two more interesting questions
today. The first was about why certain objects are black in
color. The other was how reflection of light in one direction
is possible if the atoms comprising a surface scatter light waves
in all directions. Since me, Greg, and John couldn't adequately
answer his questions, we had to recruit the expertise of Hal Metcalf,
who was able to answer the questions much more adequately; although
the problem of why light doesn't scatter laterally or backwards
in a dense gas medium, still remains a mystery.
Afterwords, John assembled the vacuum pump
and showed me how to handle the liquid nitrogen that was needed
to make it work. This was pretty fun, as I later got to mess around
with large quantities of it. Greg and I then degassed the flask filled
with water. This was the first day of doing something hands-on with
the SL equipment and I look forward to more of it.
June 28, 2005
Today, Dr. Noe did a review of calculus and discussed
Rayleigh's criterion. At lunch, we had some discussions about
random physics topics like which father-son combo won the Nobel
prize. Afterwards, Dr. Noe gave us a long spring which we created
longitudinal and standing waves on. Greg discovered an interesting
phenomenon where a longitudinal wave turns into a transverse wave
after a certain time and back to a longitudinal wave.
Amol also asked Greg and I a question about
why in a dense gas medium, a propagating beam of light will
only be scattered in the direction of motion and not laterally
and backwards. We tried answering his question but am not sure
if we were successful. For this reason, we will ask Dr. Noe tomorrow.
I then went to a meeting with Fred Goldhaber
and Robert Crease, about the Quantum mechanics and philosophy
course we are creating for spring of 2006, so I didn't get back
to the lab until much later. However, I did manage to speak to Martin
Rocek and Fred Goldhaber about my idea in treating a sonoluminescing
bubble as a black hole analogue. They both said they were intrigued
by the notion and found it to be plausible, though they admitted
to not knowing enough about fluid mechanics and analogue models in GR
to give much more feedback. Rocek did however brainstorm some ideas
with me on how to rotate a bubble, using perpendicular pairs of transducers,
and about what other liquid solutions might be interesting to test.
So both Rocek and Goldhaber's reactions seem very encouraging and I will
continue to communicate with Martin on these ideas. Ideally, I would
like one of them to help me quantitatively analyze how a spinning,
sonoluminescing bubble would behave.
June 27, 2005
The high school students started at the lab today.
After meeting them, Greg showed them the basic bash commands.
Dr. Noe then spoke to them about what would be required of them
and what sort of thinking is necessary to be successful in their
research. All the students seemed intensely interested and asked
a number of insightful questions.
After returning from lunch, I showed the
students my SL experiment to-be and suggested to Greg that
he show them the Fresnel Spot that he produced. After doing so,
Dr. Noe showed us a number of different optics phenomena such as
variations of the Fresnel Spot, diffraction, interference, polarization,
and a number of others. I then continued reading papers from
the red SL binder that Noe has here.
June 24, 2005
Not much happened today for us the students.
After lunch at the Curry Club, Greg and I went to Dr. Metcalf's
group discussion, where we heard about the research his team was
conducting and the problems they were facing. The way they seem
to deal with many technical problems appears to be plenty of brainstorming
and improvisation, which was quite interesting.
Dr. Metcalf even asked me and Greg to
give future talks about the research we are doing, which
is something I certainly look forward to. At the lab, I brought
over all the SL equipment such as the function generator and the
vacuum pump, in preparation for next week when I actually begin
doing hands on research.
June 23, 2005
Today I spent most of my
time reading more papers on SL and also learning the bash
commands. I also continued to think about the possible extensions
to the sonoluminescence experiment and about the plausibility
of the alleged sonofusion effect. To this extent, I read a couple
of sonochemistry papers by Ken Suslick while also reading about how
viscosity and vapor pressure affect the sphericity and temperatures
I am contemplating methods involving the
use of a pulsed YAG laser to induce a cavitation bubble and
then driving its implosions with the acoustic field generated
by PZT transducers. I have also thought about the use of various
liquids and think that nonpolar organic liquids with high viscosity
and low vapor pressure would be interesting to try. I also read parts
of the first book of the Feynman lectures that Dr. Noe owns. Feynman's
style is exactly what I like. Some good historical background mixed
with precise, physical explanations of the concepts, all of which
lead to elegant mathematical derivations.
June 22, 2005
Last night I had a most interesting
thought. The imploding behavior of SBSL appears very
similar to that of a collapsing neutron star which will eventually
form into a black hole. And when bubble implosions occur close
to a solid boundary, the cavity collapse is very asymmetric
and generates high speed jets of liquid that move through the
bubble's interior and penetrates the opposite bubble walls like so
This form of cavitation looks
very similar to a static black hole with the jets of liquid
being the analog of the jets produced from a black hole
and the cavitating center of the bubble being analogous to
the event horizon. Of course the difference in the analogy is that
the collapsing SL bubble is not stable and in the case of spherical
collapse, will eventually re-expand. Nevertheless, I wondered
if sonoluminescence could be treated as a general relativity
analog model and if there is a way to produce these "black hole"
like asymmetrical cavitation bubbles without using a solid boundary,
while also prolonging the collapse time.
out I was partially correct! General relativity theorists
often talk about analog models of black holes in condensed
matter physics. And after doing a google search on "sonoluminescence
analog model", I found a lecture by GR theorist Matt Visser,
from a conference on analog models in GR, about acoustic black holes!
And it turns out he had a discussion about oscillating
bubbles like in SBSL which form an acoustic apparent horizon,
meaning that as the bubble collapses at supersonic speeds, the
sounds waves are swept along with the flow and cannot escape
from that region, just like light cannot escape from the event
horizon of a black hole. But the reason the term apparent horizon
is used is that, as I said, the bubble eventually stops collapsing
and re-expands, so the acoustic horizon is only temporary. Of
course, if someone could figure a way to prolong the collapse time
or increase the speed of collapse, it is theoretically possible that
one would observe the analog of Hawking radiation! So you wouldn't
see real photons, but rather phonons, which are quasiparticles or quantized
sound wave packets.
perhaps giving a cavitating bubble a lot of angular momentum
will induce this effect. If the imploding bubble has a supersonic
angular velocity, then this will cause the equator of the spherical
bubble to bulge out and expand, while the top and bottom ends
collapse into each other and form the subsequent liquid jets. What
would hopefully form is a continuous cavitating vortex of water,
spinning at supersonic speeds. I don't know if these conditions would
be sufficient to observe phonon radiation, but it may be worth a try.
Water would seem like the first liquid to test, but probably organic
liquids which have a high phase change coefficient would be better, as
the bubbles would be much more stable and won't prematurely cavitate.
So this is certainly an unconventional idea for a project with the phenomenon
of SBSL, and one that I will keep in mind for the future.
terms of what went on today, Fred Goldhaber gave the first
REU seminar talk entitled "A new way of Introducing Quantum
Mechanics - The Einstein Way". Prof. Goldhaber personally gave
me this talk before, but nothing wrong with hearing it again. It
centers around the idea that after Einstein published the 1905
paper on the Photoelectric effect, he should have been able to make
the creative leap that though light behaves like a particle when
it is absorbed and emitted, only a wave model, which was already
experimentally confirmed, could accurately explain the behavior
of light in the intermediary state. In other words, light does not
follow definite trajectories as in Newtonian mechanics, but rather,
has a position defined by a probability amplitude. So in other words,
just from the observation of the photoelectric effect and the wave
behavior of light, Einstein had should have been able to derive the
schrodinger wave equation, as well as the Compton effect and the
deBroglie wavelength. Indeed had he done so, it would have been
20 years earlier than when these discoveries were actually made.
Though much of my education of quantum mechanics is self-taught, I
very much like Goldhaber's approach, as he was able to axiometize the
foundations of QM in a very elegant way. Indeed it then makes the formulation
of QM seem much more logical. Of course, I do think that Einstein
contemplated this approach, but then backed off from it as soon
as he saw where it was heading. Einstein was very much a local realist
and wanted the preserve the ontological assumptions of causality
and classical determinism; and this was why he disliked quantum mechanics
so much, because quantum theory reshaped these assumptions in
a very bizzare way that seemed very illogical from the point of
view of his classical physics intution.
June 21, 2005
For the past couple of weeks,
I've been reading a number of different papers
on SBSL (Single Bubble Sonoluminescence) and laser induced
cavitation by Seth Putterman, Rusi Taleyharkan, Ken Suslick,
and others. Some of these papers can be found on my links
webpage. Without a doubt, I would like the end result of this
REU project to be a replication of Ken Suslick's
experiment in sulfuric acid
. What could be more
exciting for this project than to produce a cavitation
bubble as bright as an incandescent bulb! Of course the even
longer term goal of this project is to lead into a replication
attempt and variation of the alleged "sonofusion"
experiment conducted by the ORNL and RPI teams.
But that will come even later in the future.
long as I can consistently produce SBSL in light water,
with some slight variations like the addition of glycerin,
then replicating Suslick's work is just a matter of acquiring
an aqueous sulfuric acid solution. Chances are I can acquire
this stuff from the Chemistry department; but I will worry more
about that only when the time comes. I have also thought of
using lasers to produce Mie scattering so as the measure the
size of the SL bubble, and to observe its general effects on bubble
cavitation. It might also be interesting to see how or if the
SL bubble is affected by magnetic fields or by angular momentum.
The reason to suspect the former is that recent studies of SL by
Putterman and Suslick suggest that molecular dissociation of the cavitating
fluid may be taking place and forming an opaque plasma. This implies
that there are also charged particles and strong electric fields,
which would be affected by magnetic fields. The latter consideration
results from observations that bubbles can implode by flattening into
nonsperhical, pancake shapes and produce water jets from both
ends. So, it might be possible to increase the force of such a collapse
by spinning the bubble. Another problem to think about is the apparent
subharmonic pitch that was observed by Dr. Noe and his previous students.
We've considered looking at how the "glass harmonica" works to possibly
help us understand this subharmonic anomaly. For now though, the
most important task is to produce conventional SBSL.
here appear to be first repairing the microphone transducer.
Dr. Noe already deattached it by cutting through the
layer of epoxy glue that was attaching it to the bottom
of the spherical Pyrex flask. I'll have to solder the wires
back on now and then reattach it. It would also be a good
idea to clean out the flask with alcohol, since it looks quite
The picture all the way to the
left is the Pyrex flask where SL occurs. The latter
three are of the microphone transducer.
Aside from all this, Dr.
Noe spoke to Greg and I about the high school students
and what else we need to do to get the ball rolling on
our projects. Certainly one thing I must work on is familiarizing
myself with all the Bash commands and becoming comfortable
with creating new webpages through Linux. Otherwise, Dr. Noe
asked us a deceptively simple question about how one would measure
the "size", or really the diameter of a laser beam, with a fan
and photodetector. After a couple ideas from both of us, Greg
seemed to have figured out the way to do it and with the help of
Dr. Noe, he derived an integral formula which models the intensity
of a laser beam as a function of its radius. It's amazing how you
can derive such an elegant mathematical model just from the initial
thought of "how would you measure the size of a laser beam?" That's
why physics is beautiful.