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Sunday, November 28, 2010

Cambridge College Programme General Relativity and Superstring Theory Essays

This past summer, I attended the Cambridge College Programme where I spent 3 weeks at Cambridge University taking various classes of my choice as well as having loads of fun, of course.  The experience was quite amazing!!!! One of my classes, Superstrings: The Theory of Everything (taught by Dr. Yves F. J.-M. Gaspar) was extremely engaging and interesting; at times, it was so exciting that I got goosebumps just talking about some of the complex topics that we discussed.  Below are two essays that I wrote regarding General Relativity and Superstring Theory.  Even though these complex topics are quite different from kinematics and dynamics, they are topics that I love wholeheartedly with a great passion.  I thought I might post them for anyone who would like a general description of these two topics.  I encourage everyone who is interested to delve deep into these topics for they are very interesting.

Superstring Theory – Essay Questions

1.     Describe the fundamental postulates of General Relativity.  Explain the role of the curvature of Space-time in General Relativity.  Give the experimental verification of General Relativity.

When Einstein was creating his special theory of relativity in response to problems with the Maxwell field equations, Galilean coordinate translations, and violations of the Galilean relativity principle, he probably was not aware of the impact that it would have on cosmology far into the future.  In spite of this astonishing breakthrough, Einstein was still not satisfied; there were still many questions left unanswered.  Special relativity did not include gravity and was not compatible in non-inertial reference frames.  When unifying the heavens and the earth, Newton had “discovered” gravity, defined it to the best of his ability, and wrote equations that described how it affected bodies.  However, there were many problems with his theory.  For instance, it did not describe the nature of gravity (where it comes from, what creates it, nor the speed of propagation of gravity waves), and there were still problems with how his theory calculated the orbit of Mercury.  Einstein recognized that there were problems and gaps in Newtonian gravity and special relativity.  For instance, in Newton’s equation of gravitation (F=(Gm1m2)/r2), mass and distance can be relative and thus can conflict with the Galilean relativity principle.  As a consequence of all this, Einstein created his theory of general relativity.
General relativity is based upon three main ideas or postulates.  The first is an idea that has its roots in special relativity: the equivalence principle.  The equivalence principle states that the inertial mass of an object is equivalent to the gravitational mass of the object (mi=mg).  Basically, this means that if no outside information is being leaked into a system, one could not perceive whether he/she is in a gravitational field being pulled downward or in a cabin accelerating upward (g=-A).  A consequence of the equivalence principle is that inertial effects cannot be differentiated from gravitational effects, a concept that eventually led to the ideas of the gravitational redshift and gravitational time dilation.  The second postulate is the general covariance principle.  This expansion on the Galilean relativity principle states that the laws of nature do not change form in any reference frame, whether they are inertial, non-inertial, rotational, etc.  Thus, the general covariance principle implies that the laws of general relativity are viable in all situations or circumstances that arise.  The third and final main postulate states that at low speeds and weak gravitational fields, the laws of general relativity should simplify down to and be approximated by the laws of Newtonian gravity; basically, general relativity is insignificant at low speeds and in weak gravitational fields.  While special relativity describes the relativity of time and space, space-time, how the speed of light is constant, and other extremely important concepts, general relativity does something entirely different.  It describes gravity not as a force but as a result of the geometry of space-time; it describes gravity in a topological view of the universe.
Essentially, general relativity views our universe as actually a four-dimensional “fabric-like” continuum that is composed of the three well-known special dimensions fused with time.  Masses that are in this “space-time” cause it to bend around the mass, thus causing space-time to be curved rather than flat; the larger the mass, the sharper the curve and deeper the “well” in space-time that is created.  Because this 4D phenomenon cannot be viewed/visualized well in our 3D world, it is best to visualize it with a simpler example.  If one were to view space-time as a flexible rubber sheet (a 2D analogue of 4D space-time), then one could see how placing a bowling ball or other heavy object would cause a dip or dent in the rubber sheet, indicating a curve in space-time.  Also, using this example, one could see how a smaller mass such as a marble would cause less of a dent than a larger mass such as a bowling ball. 
According to Einstein, what is interpreted as gravity is not the result of masses that exert some sort of force or “field” that attract other masses to them.  In fact the answer is far from it.  General relativity states that what is seen as gravity is actually a result of the curvature of space-time.  The trajectories of objects thrown near large masses – like a baseball thrown on the earth – are not curved because of a force originating from the mass that is pulling on them and changing their trajectories; rather, the trajectories are curved because space-time itself is curved.  They cannot travel in a straight line – despite their inertial tendencies – because they are traveling through bent non-Euclidean non-Minkowski space-time.  If space-time were to be flat, the geodesics of particles and objects would be straight lines.  If space-time is curved, then the geodesics of particles moving through it have to be curved as well (thus making their paths in “our” three special dimensions be curved as well).  It can easily be seen that for length contraction and time dilation to be correct, space-time cannot be described with Euclidian geometry because it breaks some of the major concepts of Euclidean geometry such as the definition of pi (Let, for example, a person be standing within a giant ring that is spinning extremely quickly.  He begins to measure the circumference of the ring with a meter stick and then proceeds to measure the diameter as well.  For an outside observer, however, while the measurement of the diameter is correct because the meter stick underwent length contraction in the direction of measurement when measuring the circumference, more meter sticks were “fit” in the ring then there should have been based upon the measured diameter.  Thus, the ratio of circumference to diameter is greater than pi, breaking some of the principles of Euclidean geometry.)
Einstein’s theory of general relativity has been proven and verified directly and indirectly many times.  In 1919, Sir Arthur Stanley Eddington proved that massive celestial bodies could substantially bend light (large gravitational fields can change the trajectory of light).  During a solar eclipse, the position of a known star near the edge of the sun was measured.  This location was then compared to the known position of the star; they did not match.  The star that was seen was, in reality, behind the sun and should not have been seen.  However, as described by general relativity, the mass of the sun caused space-time to curve, bending the light rays so they were viewable from Earth.  Sir A. Eddington’s measurements of the angle between the actual location of the star and the viewed location of the star perfectly matched Einstein’s predictions, verifying his theory.  A second experimental verification is the Pound-Rebka experiment in 1959.  The experiment consisted of placing sources of gamma rays in a tower (one at the top and one at the bottom) and receivers to detect the gamma rays opposite of the emitters.  By performing the experiment, they noticed that rays that were emitted on the Earth’s surface and traveled upward toward the top of the tower away from Earth were slightly redshifted when the rays that were emitted at the top of the tower and traveled downward toward the Earth were slightly blueshifted.  This experiment proves that time dilation and therefore gravitational redshifts and blueshifts described by general relativity are true.  For the rays that are moving away from Earth, they are redshifted because as they move from a stronger gravitational field to a weaker gravitational field, their rates of time speed up making their frequencies decrease and the rays shift toward the red end of the spectrum.  For the rays that are moving toward Earth, they are blueshifted for just the opposite reason.  As they move from a weaker gravitational field to a stronger gravitational field their rates of time slow down making their frequencies increase and the rays shift toward the blue end of the spectrum.  A third experimental verification of general relativity has to do with observations of binary pulsar systems.  When two heavy celestial bodies come close enough together (usually a white dwarf or a neutron star and another giant, heavy, and dense celestial body), due to their large gravitational fields and effects on space-time, they usually begin to circle around each other.  As they swing around and get closer together, they lose energy by emitting gravity waves (ripples in space-time).  Often, the larger body will start to draw matter from the smaller body.  During this exchange, the matter will often heat up, create strong electromagnetic fields, and emit strong radio signals and X-rays at perfectly regular steady rates.  By these X-rays and radio waves, scientist are able to accurately measure the movements of these pulsar systems and prove that they must be emitting some type of gravity waves to account for the rapid loss of energy.  These results have corresponded to the predictions of general relativity to 10-14 orders of accuracy, thus proving its validity. 

2.     What is the origin of string theory?  How is string theory trying to quantize gravitation?  What are the eventual advantages to use strong theory in order to quantize gravity rather than other quantum field theory techniques?

When first hearing about string theory, many people would think that it is a figment of some writer’s imagination from some science fiction novel.  Its basic structure and elements seem so strange and unconventional to every day life that they can at times seem impossible.  String theory, however, is a viable physical theory that has great potential to solve many of the problems in cosmology and theoretical physics, especially in the fields of quantum physics, quantum field theory, special relativity, and general relativity.  Ironically, for such a complex and heavy mathematical theory, it has some fairly simple origins.  String theory was first created by nuclear physicists who were looking for a mathematical model that would help them understand nuclear interactions by treating nuclei and other objects not as point particles but as extended objects with at least one dimension (strings), thus eliminating many of the problems associated with point particles such as infinities or divergences.  The so-called “string theory,” however, quickly came to the attention of many physicists and cosmologist the world over due to its implications as a possible “grand unification theory.”
When string theory was still in its stages of infancy in the hands of nuclear physicists, there was one major problem that continuously arose from their calculations: the constant appearance of closed strings (loops with no ends, like rubber bands or rings).  This was a major problem for nuclear physicists because closed strings had no physical meaning in their interpretations of their theory; they were simply mathematical nuisances that made things difficult and non-coherent.  Surprisingly, when quantum physicists, cosmologists, and many other physicists began to examine these closed strings, something extraordinary happened; their problem was transformed into a triumph.  These closed loops resembled particles with a spin of two: gravitons.  This discovery was unlike anything seen before.  Not only were closed strings with spin two modes included in the model, but they must be included or the theory is not coherent and violates unitarity, one of the principle concepts of quantum mechanics that describes how in any system, the total probability has to be conserved, or the total amount of information in the system has to be conserved (particles cannot just suddenly disappear forever; something has to happen to them).  This in itself was a stunning revelation.  For the first time in a small way, elements of quantum mechanics (unitarity) were being related to elements of general relativity (gravity).
In essence, the modern goals of string theory were to unify the four interactions (forces) of nature, include a quantum theory of gravity, while at the same time unifying all particles and fields in nature.  One of the largest problems in cosmology and theoretical physics at this current point in history is that every time scientists tried to combine different theories, they ended up with many divergences and infinite sets of infinities.  For example, when quantum mechanical principles were applied to quantum field theory, everything lead to divergences due to the fact that point particles have no dimensional limitations and a field, by its definition, has infinity degrees of freedom.  Take, for example, two point masses that are nearing each other; they can get infinitely close.  According to Newtonian gravity (F=(Gm1m2)/r2), as the distance between them approaches zero, the force between them tends toward infinity.  By Newton’s second law of motion (F=ma), as F approaches infinity and the mass remains the same, the acceleration would have to approach infinity as well eventually surpassing the speed of light, an occurrence that is blatantly a problem.  The same dilemma also occurs if one tries to combine quantum field theory with general relativity; all of the equations blow up and result in divergences.  At the time, these problems were not being solved, possibly due, at least in part, to the fact that general relativity and quantum physics were both non-renormalizable.  When scientists tried to renormalize these two theories, they became stuck with free parameters, an infinity of infinite parameters. 
Conversely, one of the major differences between string theory and many of its contemporaries is that instead of dealing with point particles, it is working with extended objects, thus limiting the number of interactions and creating smoother transitions.  Essentially, there were three main postulates that string theory was based upon.  First, it had to abide and be compatible with special relativity, meaning that it had to be invariant under the Lorentz-Fitzgerald transformations.  Second, it had to follow causality, meaning that the effect of an interaction could not be before the cause.  Third, it had to abide by unitarity, the quantum mechanical principle that was discussed earlier and is related to the conservation of information.  In the more recent years, the addition of supersymmetry to string theory to form superstring theory brought scientists one-step closer to achieving a grand unification theory.  Supersymmetry eliminated the need for tachyons (imaginary particles that move faster than the speed of light and are not coherent with special relativity) and has brought a sense of symmetry to the model between fermions and bosons.  Also, it solved a problem in quantum field theory relating to infinite energy densities in vacuums.
While there are still many roadblocks, superstring theory, which has now been expanded to a more universal M-theory with 6 different sub-theories (all relatable through duality transformations), has many amazing possibilities.  It is quite amazing that in 11-Dimentional Supergravity (one of the low energy limits of M-theory), all forces and particles can be described as different manifestations of the geometry of extra dimensional hyperspace.  M-theory can also solve problems related to the motion of stars in the outskirts of galaxies.  It has been observed that the stars on the outer edges of certain galaxies are spinning faster than they should be according to Kepler’s laws.  On possible explanation of these strange phenomena is that gravitons (closed strings) from other universes that are located in different “brane-worlds” near our own are permeating through hyperspace and affect measurably affecting matter on the edge of galaxies.  Because gravitons are closed strings and not connected to any one brane, they can propagate through hyperspace freely.  This could also be the explanation why gravity seems so weak when compared to the other three forces known in our universe.  Gravity might not be constrained to our universe or brane, but might be distributed throughout all of hyperspace.  Now that superstring theory is being applied in superspace (normal space-time plus extra Grassmann dimensions) and M-theory has been formed, the power of these theories are beginning to grow, it seems as if given time, scientists may be able to complete this theory and finally have a grand unification theory that describes the physical world.  Maybe, those humble nuclear physicists stumbled upon something truly great.

Thursday, July 15, 2010

A Wonderous Wormhole - Honors Geometry Picture Graphing Project

In the field of cosmology and particle physics, the possibility of wormholes is a very mind-boggling and exciting subject. In essence, a wormhole is a hypothetical "shortcut" through spacetime, a theoretical "tunnel" with its end at two different points in spacetime. Even though there has never been any physical/observable evidence of wormholes in physics, there are some solutions to the equations of general relativity that could support wormholes. One possibility for a real wormhole is the Schwarzschild wormhole. However, this was discovered to be too unstable to last long enough to allow any matter to pass through it. Traversable wormholes, wormholes that someone/something could travel through, would only be possible if some type of exotic matter with negative energy density could be used to make it stable.

When I was assigned a project in Honors Geometry to create an image solely by writing equations and graphing them, a wormhole immediately came to mind. I knew that it was going to be a challenge with the many ellipses parabolas, and curves. However, I knew it was something I could do, and wanted to do. I worked on it by hand and on the computer. For the sake of giving due credit, the final picture was graphed and colored with the application GeoGebra.


Some Wormhole Information:
Wormhole Photo:

Tuesday, May 18, 2010

AC/DC - Not the band!?!?

When you hear the acronym AC/DC, what is the first thing that pops into your head? Is it the Australian rock band formed in 1973 by brothers Malcolm and Angus Young? Possibly. For me, however, it has to be electricity, for AC/DC also stands for Alternating Current and Direct Current.

Ok. So we're talking about electricity here, an obscure subject for some but an important one nonetheless.

For all intensive purposes, electricity (electric current) can be defined as the flow of charges (typically electrons) from one place to another with a capability of doing work. For an electric circuit to be present, there must be a closed path in which an electric current can travel from an energy source (positive terminal), to an element in the circuit, and back to the energy source (negative terminal). Conventionally, the direction of the current is considered to be the movement of positive charges from + to - when in reality, it is the movement of negatively charged electrons from - to +. The common elements of a circuit are a battery (energy source), wires, and loads (lights, resistors, etc.) that are arranged in a closed loop with no breaks or gaps.

A DC (Direct Current) circuit is one in which the current travels in one direction continuously (a constant flow of electrons).  An AC (Alternating Current) circuit is one in which the current is continuously and rapidly changing directions (the electrons are moving back and forth).

A Series Circuit:
A series circuit is one in which the elements in the circuit (lights, in this example) are arranged in line with each other, from end to end. Take, for example, the circuit below:
In a series circuit, the current is the same along all points in the wire.  This is due to the fact that there is only one path for electrons to take (like cars traveling along a one lane road; they cannot pass each other).  The equivalent (total) resistance of the circuit equals the sum of all the individual resistances of all the elements in the circuit.  Even though the current is the same at all points, the voltage (potential electrical difference) across two points in the circuit is not.  The voltage drop across each individual element in the circuit equals the voltage drop across the entire circuit (the voltage drop of the energy source).  Basically, the voltages of the batteries are distributed between the elements in the circuit. In this example, the total voltage of the circuit is 75V. Because the two lights have the same resistance, they both have a voltage of 37.5V. Note: If elements in a circuit have different resistances, the distribution of the voltage will not be equal.

A Parallel Circuit:
A parallel circuit is one in which the elements are connected in parallel, meaning that each have a direct connection to the energy source (the lead from the energy source is split into many paths that lead to the elements).
In a series circuit, the voltage drop across each "branch" equals the voltage drop of the total circuit (voltage drop of the energy source).  Even thought there are multiple paths, the voltage in each path is the same because it has, in essence, a direct path to the energy source (battery). However, the current drawn by each branch varies with the the resistance of each branch. Furthermore, as can be derived from Kirchhoff's current law (Conservation of Charge), the total current of the circuit equals the sum of the currents through each branch.  The equivalent resistance of the circuit can be found by taking the inverse of the sum of the inverses of each individual resistance (each new resistance added decreases the equivalent resistance).

A Complex Circuit:
A complex circuit is a combination of elements in series and elements in parallel into one circuit.
In a complex circuit, things become more complicated. To find the equivalent resistance you combine the resistances of individual components (parallel segments and series segments). For this example, the equivalent resistance would be found by adding the resistances of the two series lights and the resistance of the parallel segment (as described above). The total current would be found by dividing the voltage drop of the energy source by the equivalent resistance of the circuit. To find individual voltage drops and currents at specific points, look at each component as a single entity and incorporate it into the larger arrangement. In this example, the parallel segment can be considered in series with the two other lights. In general, in situations similar to the one pictured above, to find the voltages of series elements multiply the individual resistances by the total current.  To find the voltage of the parallel branch, subtract the series voltages from the total voltage. Now, you can find the different currents in the individual branches of the parallel segment: divide the voltage of the parallel branch by each individual resistance.

When working with circuits, do not memorize a certain method that can be used in every situation. Circuits are like puzzles; they take thought to work through every situation.

Have Fun!!!

AC/DC Photo: Photo by Yannick Croissant -
Lightning Photo: Photo by Fort Photo -
Electric Circuit Pictures: Screen shots while working in PhET simulation: 

Saturday, April 24, 2010

A “Green” Idea: Optical Phenomena with a Green Laser

Warning!!!! Laser Ahead!!!!

When beginning to think about what to do for my photo project, lasers immediately entered my mind. From hand held lasers that can be seen for miles and miles, to extremely high powered lasers used for science or military purposes, something about lasers peaks my interest. Interestingly, the word laser originates from the acronym LASER, or Light Amplification by Stimulated Emission of Radiation. The basic premise of lasers is that they emit "coherent" light, or light that has waves of identical phase (in-step), polarization, and frequency, rather than "incoherent" light that is totally random, in various phases, frequencies, and positions at various times. The common components of a laser are a gain medium inside of a reflective optical cavity (a mirror on each end, with one mirror having a small hole or being semi-translucent).  As light travels through the gain medium and bounces back and forth between the mirrors, it is exponentially amplified and is released as a narrow "beam" of light.  Simply, energy (typically electricity) is "pumped" into the gain medium, causing all of its atoms to be at a higher energy state. Next, "ignition" photons are tuned to a specific frequency (a similar wave function), so when they skim the atoms in the gain medium, they stimulate the release an additional photon in the same direction as the incoming photon. These two photons go on the stimulate further atoms, and they will stimulate even more atoms, etc., creating a chain reaction. Affter emmiting these photons, the atoms fall back down to a ground state to be re-energised by the energy being pumped in. Through this process, the light can be exponentially amplified, creating powerful "rays" of electromagnetic radiation (light).

Here is my photo:

A “Green” Idea: Optical Phenomena with a Green Laser
This contrived image demonstrates common optical phenomena that are not typically observed with conventional light sources (incandescent lights, fluorescent lights, or sunlight) because the rays are too spread out. The image was created using a 5mW, 532nm green laser, water tank, small mirror, and light bulb. Greater visibility of the beam was created with the dispersal of a small amount of milk throughout the water and the introduction of fog into the air above the tank. The laser demonstrates several optical concepts: reflection (Law of Reflection), refraction (Snell’s Law), and diffraction. When the ray strikes the water, two things occur. First, the majority of the ray passes through the air-water boundary, refracting (bending) and traveling through the water at an angle less than the incident angle of the aerial ray (with respect to the normal, perpendicular to the waterline). Second, a substantial amount of the ray reflects off the water’s surface, obeying the Law of Reflection (angle of incidence equals angle of reflection). Next, the ray is reflected off a mirror on the tank’s bottom where it then hits the water-air boundary again, some of the ray reflecting back into the tank (barely visible) while most passing through, refracting, and striking the light bulb. Some of the beam reflects off the bulb’s shiny surface while the rest is transmitted through the glass where it is refracted, reflected, and diffracted (due to the frosted coating), making it visibly illuminated from the inside; a “green” idea comes to “light.”

For your enjoyment, here is a fun puzzle game on laser reflections:

Laser Radiation Picture:
Some Laser Information:

Saturday, March 20, 2010

March 14th: Pi Day and Einstein's Birthday Celebration: A "Mysterious" Quote

Now that its March 14th (3/14), Pi day and Albert Einstein's Birthday have fallen upon humanity for another time. To commemorate these two events, I have written a little description of one of my favorite Einstein quotes and have given you a little "pie" treat:

Albert Einstein - "The Father of Modern Physics"

"The most beautiful thing we can experience is the mysterious.
It is the source of all true art and science.
He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe,
is as good as dead: his eyes are closed."
-Albert Einstein

        Despite his mind-blowing achievements in the field of physics and cosmology, Albert Einstein was a profound philosopher and intellectual on life. He put in writing many thoughtful quotes about science, education, the universe, and life; many of which are based around the concept of “imagination and creativity.” In 1931, the quote above was published in one of Einstein’s essays, “The World As I See It,” that was originally published in “Forum and Century,” the thirteenth in the Forum series, Living Philosophies. In this quote, Einstein explains that it is human nature to seek answers to problems that arise or things that humanity does not understand; he is showing how mankind is inclined to be curious and how it is this curiosity that drives people to hunt for justifications and explanations for the many complexities of life.
        In the first two sentences, Einstein describes how mystery is beautiful because it makes people engage their mind and actively think, search, and look for answers to the most complex problems in life. Furthermore, it is this unwavering desire to solve problems and explain mysteries through graceful inventiveness and ingenious, tedious scientific research that causes spectacular discoveries in science and works of art to be discovered or created. For the problem-solving scientist, although the best achievement would be to find a life changing answer to a long debated question, true fulfillment and pleasure arises from the path and steps that one takes to move toward the final goal. Artists, nonetheless, use their mind, imagination, and creativity to create wondrous works of art for generations to take pleasure in. Both are trying to answer humanity’s favorite question, “What if . . .?” It is that small spark of curiosity and intrigue that is inside every human being that allows for the creation of magnificent pieces of art, the pursuit of the highest levels of education, the solving of complicated puzzles, and the discovery of new scientific inventions. Mystery is beautiful because of the wonderful things that are created when humans engage on a quest to find answers.
        In comparison, the last two lines of the quote has Einstein issuing a warning to all of mankind about what will happen to humanity if people refuse to see the wonder in everything around them. For human beings that do not have curiosity or any interest in solving mysterious occurrences, the world to them may well be dead, and thus, they are dead to themselves. If people do not see any beauty in mystery or any remanence of grace in the unknown, then what is there to motivate or drive them to achieve something great? Why should an artist pour out his/her soul into a work and try to express themselves to others? Why should a scientist spend hours scouring his/her mind, trying to find the solution to a snag in the research? The answer to these questions is “human nature.” Humans strive, desire, and need to find meaning in the things they comprehend and even in those things that cannot be easily observed. If people are not able to just stop their busy schedule and stand for a moment, amazed with the “awe”-some world, then their eyes are closed; they cannot see the world in its true value or make any contribution to society.

And now sit back, grab a piece of pie, and enjoy the first 500 digits of pi:
Pi = 3.
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912

Smells good!!!!
: )

Albert Einstein Sitting: Public Domain -,_by_Doris_Ulmann.jpg
Albert Einstein Signature: Public Domain -
Pie Symbol: Public Domain -
Apply Pie: Public Domain -
When quote was published -
Digits of Pi -

Wednesday, March 10, 2010

"The Fastest Ice on Earth" - Conservation of Momentum in Short Track Speed Skating

On February 12, 2010, the stunning opening ceremonies to the 2010 Vancouver Winter Olympics were held at BC Place in British Columbia. This ceremony opened the 21st Olympic Winter Games in which the USA was awarded over 37 medals and Canada got its first gold on home land (over 14 golds, leading the gold count for the Olympics). For me, one of the most exciting sports to watch and one that I knew little about was Short Track Speed Skating. These athletes need to have speed, agility, athleticism, and aggression in order to excel in the races. Not only is Short Track exciting to watch, but it is also filled with physics, like all of the other sports in the winter Olympics.

Below is a link to and an embedded "Prezi" that gives a little history of Short Track, describes its rules, equipment, winners, and illustrates how the Conservation of Momentum and the Conservation of Energy apply to the sport that moves at a lightning speed:

I could not have done this project without my partner Cyrus. Thanks so much for your help and collaboration. It was such an enjoyable experience. Here is his Blog: "A Phlight Through Physics"

Sunday, February 21, 2010

Reflection: Energy - The Fuel of the Universe

"Hubble Ultra Deep Field"
A look back in time nearer to the "Big Bang" 

According to the commonly accepted theory of the big bang, approximately 13.73 ± 0.12 billion years ago, the universe started expanding from an infinitesimally small point into the visible universe that we know of today, over 93 billion light years wide. After one Planck time (about 5.39124*10^(-44) seconds), gravity separated from the electronuclear force. After one picosecond (1.00*10^(-12) seconds), the “weak” force separated from the electromagnetic force resulting in the four forces we know today. By one hour, helium nuclei formed. In 370,000 years, hydrogen and helium nuclei captured electrons and formed stable atoms. By 100 million years after the big bang, the first stars began to shine. It may seem surprising, but all of the energy in our universe at this moment, was present from the very beginning. Some of what I have learned during this unit about energy is explained in the following "Glog":

Energy - The Fuel of the Universe

Big Bang Technical Information:,
Hubble Ultra Deep Field Photo:

Monday, February 1, 2010

Extra!! Extra!! Read all about it! Finally the secret behind the death-defying "Sphere of Fear" explained!

Have you ever been to a circus, amusement park, or stunt show? Well, all of those air defying and gravity smashing stunts are just good applications of physics and an understanding of motion. Not to say that these tricks are not dangerous and don’t risk life and limb, they do. However, the physics principles behind them are rather simple. Take for example the “Sphere of Fear,” “Globe of Death,” or “Circle of Doom” that is a staple in many circus acts. The stunt is fundamentally composed of a large spherical metal cage with one or more motorcycles and riders driving around on the inside. Created by Herb “Daredevil” Durkin after WWII, he and his wife believed that the public would pay good money in order to see the death defying “double loop.” For more than 30 years, they continuously added new tricks to their repertoire such as sidecars, more riders, and eventually, they decided to cut off the bottom half of the sphere in order to increase the risk and make it more exciting for the audiences. In the early 70s, Herb Durkin and his wife retired and left their “Sphere of Fear” to rust into scrap metal. From then on, fresh and innovative performers, entertainers, and daredevils have created similar acts and amazed audiences with their fearless acts of bravery.

Now onto the Physics!!!
Here is a “Prezi” that can explain everything: "The Sphere of Death" - Prezi
 In this "Prezi," you will find a description and analysis of the motion of the riders and motorcycles when riding in the "Sphere of Death." It includes a detailed description of both vertical and horizontal loops, what would happen if the riders go too fast, too slow, or just the right speed, and multiple FBDs and diagrams in order to help you understand what is the physics behind this amazing feat. To navigate the "Prezi," move the mouse to the bottom right of the "Prezi" and use the arrows to step forward or backward in the path.

Now that you know how it works, test you skills with the Homer Simpsons "The Ball of Death Game".

Black and Blue Colorful Fractal:
Blue and White Waves:
Dark and Gloomy Sphere of Death:
Green Sphere of Death in Motion:
Blurred Motorcycle in Motion:
Sphere of Death in Daylight:
Inside Sphere of Death:
Bright Colorful Blue Fractal:
Roller Coaster:
LED Circle:
Snail Cartoon:
Specific Tricks:
YouTube Long:
YouTube Short:
Homer Simpson Ball of Death Game:

Sunday, January 10, 2010

Reflection: Newton's Second Law of Motion including Friction

In this Prezi (a "digital napkin/ presentation tool" if you will), I give my reflections on Newton's Second Law of motion including friction and describe some of what I learned, some of my difficulties during this unit, and some of my problem solving skills as well.

Attribution for Prezi: