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jelliott

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Everything posted by jelliott

  1. Nate-- Negative energy - can't really wrap my head around that. Very cool. Justin-- That stuff about the planet rotating under you and forcing you into fixed waves is even scarier than the idea of your traditional tidal wave. Awesome
  2. After watching Interstellar, one can pretty much gather that Miller's planet is weird. On top of the aforementioned super-massive tidal waves and its close proximity to a rotating black hole, Gargantua, it has a very interesting property regarding its time "flow" - one hour on this planet equates to 7 years on Earth. So what does this mean? Are those on Miller's planet aging at a vastly accelerated rate? Is everything in slow motion? Well, the answer can be summarized like this: it's all about perspective. On Miller's planet, the flow of time doesn't feel any different than it does on Earth. From their point of view, time is running normally, and they aren't aging any faster. It's not like if they spent a few days there, they'd come out looking way older, they'd just look a few days older (which is to say, not at all). However, after a few days, if they came back to Earth, everyone they know and love would be dead. Which is kind of a bummer, really, and that's why they wanted to get out of there so quickly - they were looking to save humanity, so time, like fuel and sustenance, was a valuable and irretrievable resource. This time dilation is all due to gravity. Being so near the huge gravity of Gargantua means time would flow much slower (1 Earth hour is .06 Miller seconds). But if someone were to record a video for an hour on Miller and bring it back to Earth, it'd still only take an hour to watch. Now if somehow a live feed were set up, to watch those on Miller experience an hour, it'd take 7 years. So they'd be moving pretty slowly. The second thing I wanted to touch on was quantum data. What was it, why was it so important, and what was it doing in a black hole? The Earth is falling apart due to the blight, massive dust clouds causing lack of food and sickness among Earth's inhabitants. We need to get out of there and fast. So to do this, we need to harness the power of gravitation. With all the additional dimensions and nuances of the Universe as demonstrated in the film, the gravitational constant G is not necessarily true all over, so we need to investigate quantum gravity, the effects that massive gravitational fields have on subatomic particles. And the gravitational field that Gargantua exerts on subatomic particles would be a great way of analyzing quantum gravity and allow Murph back home to complete the equation. Cooper and TARS fall into the black hole, and the quantum data they discover is sent back to Murph; with this data, she can finish the second half of the equation that the late professor failed to do during his lifetime. With the completion of this goal, humanity can finally leave the Earth - the answer lied within gravity. As you may recall when Cooper wakes up, he is inside of a dome-like structure with buildings hanging upside down. This was made possible with the quantum data that the characters in the movie were so fond of mentioning.
  3. The observation of interactions is basically the foundation of science and physics, but often times this observation directly alters the phenomena being observed. This concept is aptly named the observer effect. In circuits, the voltage and current can be measured by the use of voltmeters and ammeters, respectively. However, the placement of these devices into the current alter the actual voltages and currents of these circuits. This is why voltmeters are very high in resistance and wired in parallel, and ammeters are very low in resistance and wired in series. This is to minimize the essential error or alteration they are causing, and since there is really no "zero" or "infinite" resistance, these errors will just have to be diminished by improving technology, though obviously we have come very far in this respect. There are other examples, such as measuring temperature with a thermometer. The thermometer slightly changes the temperature of the liquid it is placed in. Also, electrons are detected by using photons, and this interaction alters the path of the electron. This is often confused with Heisenberg's uncertainty principle in quantum physics, so I'll mention that briefly. Basically, the precision of a pair of physical properties of a particle (complementary variables) can be expressed as an inequality. Here, x and p are position and momentum. As the precision of one gets higher, the precision of the other gets lower, and this relationship can be expressed as a fundamental limit using inequalities.
  4. You wouldn't have too big a problem believing that the past can affect the future, or that the present affects the future. We see it everyday. But if I told you that the future could affect the past, you'd probably be a bit skeptical. Quantum physics is full of these weird thought experiments that are absolutely wild and mind-bending, and one of them is known as Wheeler's delayed choice experiment (prominent in the late '70s and early '80s). John Wheeler attempted to answer a very strange question in the following way. It uses Young's double slit experiment wherein light can either demonstrate wave-like or particle-like properties. But light does not demonstrate these properties both at once, and Wheeler states that the light when passing through these slits "senses" the detection mechanism for either particles or waves, and adjusts accordingly. But by the time the detection mechanism is used/altered, the photons have already entered through the slit. So, is it possible that changing the detection mechanism after the light has already entered the slits affects how the light entered the slit in the first place? This causality doesn't make much immediate sense, but then again, neither does a lot of stuff in quantum physics, and that's what makes it so enthralling, even though experiments such as this one have their detractors. I myself am greatly struggling with understanding this, so if you're as confused as I am and care enough to do so, look into it! It's really cool stuff.
  5. Nothing for me proves the ubiquity of physics more than this article I came across in the LA Times. http://www.latimes.com/science/sciencenow/la-sci-sn-popcorn-science-20150210-story.html Yes, that's right; on top of just being tasty, popcorn is a great demonstration of several physics concepts such as thermodynamics. First off, food chemists have determined the ideal moisture content of a kernel to be around 14%, and since the 1950s, plant breeders have apparently fixed that annoying unpopped kernel problem by 75%. So there's evidently a lot of people with some passions for this stuff, and it follows that researchers have looked into the physics here. Most people know that kernels are consistent of water, which when heated expands and pops the corn. But it's slightly more complicated. Only a specific type of corn can actually pop; when the popcorn is heated to 100 degrees Celsius, the water inside turns to steam, which forces its way into a protein matrix called the endosperm. This apparently creates a molten mass similar to bread dough, and this starch mass soon solidifies into a light spongy treat that we all know and love. Also interesting to note: the locomotion of popping popcorn is reminiscent of biological fracture mechanics existent in some plants and fungi, which disperse their seeds in this manner.
  6. One would think that someone who is somewhat knowledgeable in the realm of physics might be somewhat decent at golf. They would be wrong, because I exist. In this particular installment, I will be focusing on the flashiest aspect of golf, known as the drive. A long drive may not guarantee a good score on a certain hole, but it's a good start, and can make you look cool. Martin Paul Gardiner, creator of advanced golf simulators, obviously had to do some research beforehand - I will be citing his findings here. A driver has considerably less loft than other clubs, and typically, a 10 degree driver with an impact velocity of 134 mph will launch a ball at a launch angle of 8 degrees. The ball will then rotate at 3600 rpm. At high spin rates, a magnus lifting effect causes the ball to climb vertically in a non-parabolic fashion. This is achieved by hitting the ball with a very high impact velocity and is only achieved by the "hard hitters" - most often seen in the pros. Finally, I'll touch on two subjects I know very well: the slice and the hook. A slice is a left to right movement of the ball caused by hitting the ball with an open club face, swung from out to in. A hook is a right to left movement caused by a closed club face swung from in to out. (For all three colors, the hooks are on the left and the slices are on the right.)
  7. This is the last blog post (for now, at least) concerning the debate on nuclear fission, and we'll end with the positive aspects. For one thing, it is free of CO2 emissions. This is a big one considering the effects of global warming caused by such gases. In fact, the lack of harmful smog and air pollution is one of the biggest selling points for nuclear reactors. While the wastes can be hazardous, the immediate radiations from fission are harmless to the environment. Although it may not seem like it would be the case, the fuel used in these reactions are quite cost-efficient and generally easy to come by. The use of these fuels could also replace energy sources that would otherwise be imported, potentially making the economy that much more self-sufficient. Not to mention, the energy outputs are pretty massive. It seems as though the major concerns come from safety, which is absolutely reasonable. Ideally, fission should be very safe. It is the human error involved that causes the danger, whether it be poor safety precautions or neglect. In fact, there have been several whistleblowers in the nuclear community, mainly former employees who have spoken out against the unsafe conditions in these reactors. So, perhaps one of the main problems is the fear of persecution, or losing one's job if he/she were to bring these problems to light. To fix the problems associated with nuclear reactors, new technologies/methods of disposal must be used to eliminate the dangers of waste, and improved regulations/safety procedures must be implemented. Employees should be guaranteed to keep their job even if they speak against their place of work - safety must overtake complacency. Hopefully, fusion can be our saving grace in years to come, but until then, nuclear fission should continue to be invested in, so long as safety is the number-one concern.
  8. As mentioned before, nuclear fission generates a pretty substantial amount of energy. And the numbers alone may convince you that fission is extremely efficient. Well, efficiency isn't the only means for debate - it also involves safety, as the process can be very dangerous. The most common nuclear reactor is known as a critical fission reactor. Here, neutrons produced by fission of atoms (such as Uranium) are used to cause further fissions, and so it is generally self-sustaining. One of the main reasons people are against this process is the nuclear waste. Honestly, the term "nuclear waste" sounds pretty foreboding - reactions whose dangerous byproducts stay in the Earth for millions of years? That's pretty scary. Especially considering the world's nuclear fleet generates 10,000 tons of waste each year. These wastes remain deadly to living organisms for a very long time, so treatment is necessary. Byproducts like iodine-129 last for freakishly long times - in particular, this one has a half-life of 15.7 million years. That's a lot. Another concern is the potential for accidents, such as the infamous Chernobyl explosion. The problems with these explosions are not only the initial deaths, but the potential for cancer to afflict the exposed. Decontamination costs can also prove crippling to an economy, as Chernobyl did to the Soviet economy. Many opponents also believe fission is excessive - Helen Caldicott, Australian physician and anti-nuclear advocate, states that nuclear reactors are just dangerous, sophisticated ways of boiling water, "...analagous to cutting a pound of butter with a chainsaw." Aside from just being a fun analogy, she makes a point that many opponents agree with, that it is too costly, excessive, and dangerous to be worth the energy output.
  9. A couple posts ago, I briefly touched on the idea of nuclear fusion - the process of merging two light hydrogen atoms to release massive amounts of energy. This concept is awe-inspiring considering our current energy crisis, but it is far from being mastered. A certain nuclear energy source that is utilized, though, is nuclear fission. It's essentially the opposite of fusion - a heavy atom is split, by decay or a nuclear reaction, into two lighter atoms, and a large amount of energy is released. Now, this process has its proponents and opponents, and I'll get to that in a later post. But here, I'm just going to elaborate on the process of fission and how it is used today. To split a heavy nucleus requires a good deal of energy. In order to overcome the nuclear force which holds the nucleus in a spherical shape, about 7-8 million electronvolts (7-8 MeV) are needed. This deforms it into a peanut shape, and from here, the two lobes' positive charges allow them to further separate from each other, and two lighter atoms (fission fragments) move away from each other at high energy. In some cases, 6 MeV of the necessary energy to split the atom is simply acquired by binding an extra neutron to the nucleus. This doesn't work in cases such as Uranium-238, which will sometimes just absorb the neutron and become Uranium-239. How selfish. The typical output is 200 MeV of energy, which seems like a huge efficiency. How could anyone have an issue with this? (To be continued, shortly)
  10. We humans are drawn to the unknown and the mysterious. And what's more mysterious than black holes? Not much. An event horizon (a.k.a. a point of no return) is a boundary in spacetime where an outside observe cannot be affected by anything beyond it. In other words, a gravitational pull is so strong that nothing can possibly escape it. Light emitted from beyond the black hole's event horizon can never reach an observer outside of the horizon. If you, an observer, are looking towards one of these horizons, an object approaching it from your side will never quite reach it - it will appear to slow down as it approaches nearer. However, to the traveling object, no strange effects are felt - it passes through the horizon in a finite time (0.0001 seconds for a black hole of 30 solar mass). This time is proportional to the mass. So, as said before, from an observer's perspective an object approaching a horizon will never appear to reach it - it will just appear to slow down. Interestingly enough, for an object near to horizon to appear stationary to the observer, a force must be applied - and as the object gets nearer and nearer the event horizon, this necessary force increases without bound, becoming infinite.
  11. Besides being fun to say, plasma is a very important concept in physics. But what is it, exactly? Well, it's one of the four fundamental states of matter, alongside our friends solids, liquids, and gases. It can be found even in household objects, such as fluorescent light bulbs, plasma televisions, and the Sun. It is essentially a medium of unbound positive and negative particles, meaning it is generally neutral (the charge is close to zero). When a plasma moves, these charges create current, and therefore magnetic fields. They are in turn affected by the fields of other plasmas. To create a plasma, ionization must occur, meaning a substance must lose or gain electrons. To do this, a gas is either heated or subjected to an electromagnetic field. Since the resulting plasma is a very good electrical conductor, its electric fields are very small, leading to a concept known as "quasineutrality", where over large volumes of the plasma, the density of positive and negative charges are about the same. (There may be charge imbalances when taking into account smaller volumes.) Why is this important? Well, aside from being the most abundant state of matter in the Universe in mass and volume, it is vital in fusion, the process of fusing light atoms together to release great deals of energy. To get these atoms close enough together to counteract their repellent electric forces, researches try to maximize the ion density in a small region. To do this, reactors are heated to levels that even surpass the temperature of the Sun's core, and this converts hydrogen gas into plasma. From here, lasers/magnetic fields confine this plasma into a tiny region where fusion can take place. This, of course, is still a work in progress, but one that is essential to our current energy crisis.
  12. The phonograph was invented by Thomas Edison in 1877 as a revolutionary device to not only record sound, but play it back. Since then, obviously, new music media has become more prevalent (CDs, etc.) and understandably - but a recent "retro" movement has increased the popularity of this seemingly dated form of listening to music. Newer record players are obviously different from the original phonograph, but the components and main concept remains the same. Starting with the record: A master recording is perfected in a studio. Then, a lacquer (disc) is placed on a record-cutting machine. As the disc rotates, electric signals are sent from the master recording to a cutter head, where a needle etches grooves into it. The lacquer is coated with metal to create the "mother" record. This mother is then used to create stampers, which finally are used to create the actual vinyl record. Now how is the record played back? Well, a stylus (the needle) is located on the end of the tone arm. As the record rotates, the stylus, which touches the disc, picks up vibrations from the record. These vibrations travel through a metal strip and wires inside of the tone arm, where it reaches the cartridge at the end of the arm. This cartridge converts vibrations into electrical signals. Electrical signals are carried to the amplifier (which enhances the signal), and finally, the signal is converted into sound which obviously, comes out the speaker. For the first music playback device ever invented, it is extremely involved and consists of several vital components. And although plenty more efficient methods of playback have been invented, some people insist that vinyl is the way of listening to music how it was meant to be heard. And others still view these people as "hipsters" - but regardless, it is an extremely interesting machine, and creates a very enticing atmosphere wherever it is played.
  13. (You, of course, indicating its impact on the Earth and not necessarily you on a personal level.) By essentially sapping energy from an orbital system, gravitational radiation makes orbits more circular and continuously decreases their radii. Overall angular momentum decreases, as this too is essentially stolen by radiation. The decrease in the radius of orbit is given by the following equation: Substitution of the Earth's and Sun's masses for m1 and m2 tells us that the rate of our orbit with the Sun is decreasing by the second: 1.1 * 10^-20 meters per second, to be exact. Not to freak you out or anything, but we're getting closer and closer to the Sun as you read this. In exactly 365 days (that's a year in math terms), we will be MUCH closer to the Sun than we are now. About 1/300 of the diameter of a hydrogen atom. Now that's a bafflingly huge number, but I'm sure we have a few years left under our belt before we collapse into the Sun and die fiery deaths. This equation can tell us the lifetime of an orbit as well, before this collapsing occurs. However, since the rate of change depends on the radius and not time, integration of the equation is necessary. So the lifetime of an orbital radius is brought to you by this guy here: Again, substituting in the Earth's and Sun's masses, we find our orbit to be about 1.09 * 10^23 years. Seems pretty massive, especially considering this is 10^13 times larger than the age of the Universe itself. Well, I hope you learned something, and I'll see you next quarter.
  14. Relativity, as we know, explains the intimate connections of space and time, since they are essentially components of one larger entity, the spacetime continuum. One of the more elusive byproducts of this theory is the concept of gravitational waves. To explain, first understand that the spacetime continuum has curvature, and this curvature is directly affected by the mass of an object. For instance, large masses like planets will actually cause spacetime to "bend" around it. And gravitational waves are like any other waves, in that they are ripples that travel outwards from the source - these in particular, though, are ripples in spacetime, which travel away from the source carrying energy in the form of gravitational radiation. Again, this is just a theory by Einstein, but I'd keep an open mind about it. Because, you know, he's Einstein. So what objects produce these waves? Well, they have to be accelerating. But more than that, this motion cannot be spherically or cylindrically symmetrical. Gravitational waves HATE symmetry. For people like myself who love seeing equations related to things, here is the power developed due to gravitational radiation in a system of masses m1 and m2: Just by looking at these numbers (G^4)/(c^5) these are extremely small numbers we're dealing with. For instance, the Sun-Earth system gives off a whopping 200 watts - absolutely paling in comparison to the electromagnetic radiation emitted by the Sun (3.86 * 10^26 watts). Tune into my next post (which will be in about 10 minutes) and I'll discuss gravitational radiation's implications on orbits n' stuff.
  15. We all know now that the Universe is expanding, and at an accelerating rate. What happens, though, if it expands too far? Well, it turns out that if the Universe's density exceeds its "critical density", all of its matter will be mutually gravitationally attracted to each other, causing the expansion to cease and then reverse. This phenomenon, that all matter will eventually collapse in on itself into a black hole singularity, is known as the Big Crunch. What happens, though, after all matter has dissolved into this black hole? It's possible that another Big Bang could occur, thus indicating an infinite cycle of Big Bangs and Big Crunches, meaning the Universe lasts forever in this fashion. There are obviously scientific debates surrounding this theory. One camp believes the Universe will forever expand, and the other believes in this Big Crunch idea. So what if the Universe's density is less than the critical density? Well, it will keep on expanding until its matter becomes thinner and thinner. By this point, the Universe will become essentially lifeless. Finally, if its density is equal to the critical density, the Universe will expand to an equilibrium point and then come to a halt. There are obviously several other theories, some of which involve the role of dark energy and matter that stimulates cosmic acceleration and leads to creations of other separate universes.
  16. My previous blog post took a look at the far future - a timeline of events predicted to occur in our known universe assuming it exists infinitely (no Big Crunch). Well, if it exists for an infinite amount of time, there will logically be an infinite number of physical occurrences/interactions. So theoretically, though seemingly improbable, there could potentially be the formation of what's known as a Boltzmann brain. Entropy is increasing in our universe as it expands - chaos - and according to this particular hypothesis, it is possible that a self-aware entity could emerge from all of this disorder. Random quantum fluctuations can result one of these brains floating into existence, complete with thoughts, memory/data storage, etc. As a matter of fact, there's a slight paradox going on here. It would seem as though the probability of us, self-aware entities existing within an organized environment, is far less likely than those of single, dispersed entities existing in thermodynamic "soup" - again, another term for chaos and entropy. So our evolved brains are technically pretty unlikely compared to a Boltzmann one - feel special, you've earned it. How did he even come to this conclusion? Well, our observable universe is fairly low in entropy - lower than it seems it should be. So it's possible that we inhabit some bubble of lower entropy. After all, entropy is constantly fluctuating, though it's generally on the "up" trend, as the universe slowly tends towards heat death. Yay! Not to creep anyone out, but I'll end with a question. What if you were merely one of these Boltzmann brains, imagining yourself in a physical body that doesn't really exist? And what if everything we see in our observable universe is nothing but a hallucination? No, that's silly. Now if you'll excuse me it's about time to dissipate back into the void.
  17. Science and technology have grown exponentially within the past century alone. Even today, the concept of predicting the future using empirical evidence seems mind-boggling, despite all the advancements we have made. I bring this up because I recently stumbled upon a Wikipedia page chronologically organizing the series of events that will occur within our solar system, and it spans an immense period of time. Note that, being somewhat of a cosmic weather forecast, it isn't exact - but it does use trends that physicists notice and are aware of in order to map out these events. Being a physics blog, I'll focus on the physics-y implications of this timeline, namely astrophysics and particle physics. To start with, these predictions take into account the laws of thermodynamics, and assumes a universe that does not experience a "Big Crunch" (which is a concept that states the universe will collapse in on itself in a finite time, and perhaps then lead to another Big Bang). The year is 52,000. (Approximately.) The gravitational forces exerted between the Earth and its moon will alter the Earth's rotation (slowing it down) causing the length of our day to increase from 86,400 seconds to 86,401 seconds. In other words, a leap second must be added to the clock each day (or we could just alter our time system). The year is 502,000. A meteorite of diameter 1 km will likely hit us. Unless, by then, we have the technology to avert it. Where's Jimmy Neutron when you need him? It's about 7.6 billion years in the future. The Sun has reached the peak of its Red Giant phase, and is 256 times larger than it is today. The Earth and Moon are "very likely destroyed" by being engulfed in the Sun. I hope you've packed your SPF 50 sunscreen. That's our planet in seven billion years! Cool, huh? Looks hospitable. Ooooh, this next one's exciting. A particle physics one. In 10^(10^56) years (that's a 1 with 10^56 zeros after it), it is estimated that random quantum fluctuations will cause another Big Bang. Something interesting about this number: even though it's stated in years, it is so unfathomably large that you could list it in nanoseconds, or the lifespan of a star: and the numbers would barely change. Now, we humans are self-centered. What's in it for us? Well, if we're not extinct by this point, in 100,000 years it is possible that we could have colonized Mars by altering its climate, creating a human-friendly environment. Pretty cool stuff. There is so much more to be seen here, so check it out if you're interested; it's wild. http://en.wikipedia.org/wiki/Timeline_of_the_far_future
  18. ...(But probably not.) In light of the holiday season, I bring to you a Christmas-themed blog post, with a pinch of love and some hints of gravitation. I came home from school today and stepped into the living room, astutely noticing that the Christmas tree had fallen. Obviously, the first thing that ran through my mind was that gravity did this. I mean, gravity's everywhere - it's a pretty likely culprit. You may or may not notice the lamp just above where the tree fell, but I believe it to be of great importance in this investigation. I have deduced that, at any time from 10:00 AM to 2:00 PM on Tuesday, December 16, the gravitational attraction between the tree and lamp created a gravitational orbit that forced the tree out of its holder, and onto the cold ground. Let's take a look. First off, the tree had to begin in static equilibrium - it was still at first. Due to Newton's first law, an outside force had to act upon this tree, and I do believe that the placement of the lamp near this tree provided an IMMENSE GRAVITATIONAL FORCE. So let's dive in. We know that the magnitude of this force is given by GMm/r^2, where G is a constant, M is the tree, m is the lamp, and r is the distance between the two. G = 6.67E-11 Nm^2/kg^2, we know this. The average mass in kilograms for a Christmas tree is about 70 pounds at this height of tree, or 31.75 kg. The mass of the lamp is about 8 pounds, or 3.63 kg. I can already see this force is about to be massive. And the distance between the center of mass of the tree and lamp? About 5.5 feet, or 1.68 meters. Time to calculate. F = [(6.67E-11 Nm^2/kg^2)(31.75 kg)(3.63kg)]/((1.68m)^2) Therefore, the force due to gravity is a whopping 2.72 NANONEWTONS. This incredibly large force undoubtedly caused the displacement of the tree; therefore, gravity ruined Christmas. You may be subconsciously pointing out the holes in my story, like how did a gravitational orbit just occur if the lamp was there the whole time, or perhaps just pointing out the fact that two objects on Earth will likely only apply negligible forces to each other. Fair enough, but keep in mind that there is absolutely no other worldly explanation for this phenomenon. So it's either gravity, or ghosts. You decide. Or maybe the cat just knocked it over.
  19. jelliott

    Delaney's G

    That's my house in the back (the green one), I really don't remember this picture ever being taken
  20. My last one, I promise. When I stumbled upon Mr. Grimes' paper regarding all of these guitar applications to physics, I had already known that things like harmonics had to do with basic string/wave physics - but all of these other applications have really interested me, as someone who loves the instrument. If you're interested at all, visit the source material; he obviously worked very hard on it, and his hard work shines through. http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0102088 This final post focuses on yet another vital guitar technique that is prevalent in so many solos - Hendrix and Van Halen were masters at it, and Stevie Ray Vaughan's subtle uses of the tremolo bar added so much character to his already impressive blues playing. The whammy bar in a typical Fender Stratocaster fits directly into the bridge as shown above, and by applying a torque to the whammy bar, the bridge experiences a slight rotational acceleration in order to change the frequencies of the strings. As we know, a force exerted closer to the bridge would provide less torque, and thus, less rotation. However, apply that same force near the bend in the bar (close to the white tip), and your torque is significantly greater. (Net torque equals force times length.) Well, the new frequency provided by a whammy bar can be determined from this equation derived by Grimes: This is a manipulation of his previous equation, determining frequency of a stretched string. The whammy bar equation is essentially identical, except in the numerator of that radical fraction, the force applied to the whammy bar (F subscript W) is added to the tension of the string. The plus and minus indicates that the whammy bar can go both ways, although on the typical Stratocaster, it is much harder to pull up on the bar and raise the pitch than it is to depress it and lower the pitch. If you don't have a locked-in bridge, though, you're not likely to use this tool as frequently - otherwise, the forces applied onto the bridge alter the tensions of the strings, in other words making them very out of tune. For those using a Strat, remember to whammy in short bursts and with much smaller rotational forces, so that you don't have to stop to tune in the middle of a song. Citation: Grimes, David R. "String Theory - The Physics of String-Bending and Other Electric Guitar Techniques." PLOS ONE:. N.p., 23 July 2014. Web. 23 Nov. 2014.
  21. Continuing with the applications of physics to the guitar: Vibrato, like bending, is a staple in every lead guitarist's arsenal. It is very similar to bending, as a matter of fact, and is basically just bending up and down repeatedly to alter the frequency. Last post, I ended with a monster equation used to determine the frequency of a bent string as it relates to a bend angle theta. This equation was derived by physicist David Robert Grimes who did an excellent job of condensing these techniques down into comprehensible equations. Here's the bend frequency equation again: So, to find the rate of change of frequency caused by vibrato, we'll need an all-new equation. How do we deal with rates of change in equations? Well, we describe them using derivatives. Therefore, to find the rate of change of frequency brought on by constant vibrato, the derivative of both sides of the equation was taken: Keep in mind that the (t) following some of these terms just means that the terms are functions of time. We can see at the very least the relationship between the derivative of the angle with respect to time...as dθ/dt increases, dv/dt increases. dθ/dt may look familiar, and that's because it's the angular velocity equation - so we can mathematically prove something that common sense would already have us believe. If one were to bend the string up and down faster and faster, the frequency would also change faster and faster. But as every guitar player knows, it is way harder to bend an acoustic guitar's strings, or a classical guitar's, than it is to bend the string of an electric guitar. Therefore, since the bend angles on classical guitars are exceedingly small, Grimes developed a specialized equation specifically for them. This equation relates not the bend angle with frequency changes, but the tension in the string, as a classical guitar's strings are mostly bent using varying tensional forces. Time for an example to break up the monotony: When the guitar kicks in around 2:08 until the end of this intro part is full of vibrato. It's also awesome. One of the best guitar songs of all time. Citation: Grimes, David R. "String Theory - The Physics of String-Bending and Other Electric Guitar Techniques." PLOS ONE:. N.p., 23 July 2014. Web. 23 Nov. 2014.
  22. I made a post a while back about the physics behind pinch harmonics - but, since there is a multitude of other guitar techniques, there's a lot more physics to be explored with this instrument. Think about your all-time favorite guitar solo, and I'll guarantee you that there is bending somewhere in it. It's the technique that must be mastered to make a decent solo, and it's in all of the best ones: it's ever-present in legendary solos such as Pink Floyd's "Comfortably Numb", Lynyrd Skynyrd's "Freebird", and Eagles' "Hotel California", just to scratch the surface. Surprisingly, there's a whole bunch of complicated equations to describe the nature of bending, relating the bend angle theta to a change in frequency. An impressive and detailed paper was written about all of these techniques by David Robert Grimes, an Oxford scientist who obviously has a passion for this stuff. I'll be referencing his findings throughout these posts. First of all, the fundamental frequency for a bent string can be described by where l is string length, T is its tension, and u is its linear mass density. With the application of an extending force, its bend frequency can be given in terms of the bend angle. Theta is the bend angle, and F subscript E is the perpendicular force exerted on the fretboard. Note that this equation only holds up when assuming that the increase in string length caused by bending is negligible. But as we have learned, the magnitude of the restoring force of an elastic object is given by F = kx, Hooke's Law, where k is the elastic constant and x is the displacement. This can be rearranged using Young's modulus (E), which depends on material, and the string's cross-sectional area (A). kx and EA both represent the stiffness of the string. Therefore, we can replace F subscript E with known variables, and with some simplification, end up with an equation for the frequency of the bent string: Some side notes are that 1. Young's Modulus, a measurement of stiffness, vary due to string material. 2. The area also varies from string to string - some guitarists prefer thicker strings than others. 3. According to Grimes, the typical bend angle does not exceed 1.5 degrees. Next time, we'll look at vibrato, which, excitingly enough, involves derivatives. Woohoo. Citation: Grimes, David R. "String Theory - The Physics of String-Bending and Other Electric Guitar Techniques." PLOS ONE:. N.p., 23 July 2014. Web. 23 Nov. 2014.
  23. You're reading this blog post, which means you're alive. Good. I'll begin by assuming that you believe you're living on Earth as of now - a reasonable conclusion to draw, I suppose. But what if I told you that we were nothing but computer-generated simulations, living in an artificial world? I doubt you'd be very willing to believe me, and I don't blame you - it's an impossible thing to prove. Well, nearly impossible. To get a little philosophical on you, since the beginning of philosophy itself many have speculated that our reality is nothing but an illusion - something fabricated by our own minds. Obviously, it seems ridiculous to assume that we are just simulants, artificial intelligence living in a digital world, but this is in fact a theory. The modern form of this simulation theory was postulated by Nick Bostrom, philosopher at Oxford University, in the aptly named paper, "Are you living in a computer simulation?" He states that, due to the enormous computing power that humanity will likely develop in the future, it is more probable that we are simulations, living in a world generated by "posthuman" technology, than the belief that we are carbon based organisms inhabiting the "real" universe. This seems like an absurd claim to make, but he does use several probability calculations to back this claim up. This theory corresponds with the "holographic principle" which implies that our three-dimensional Universe is a hologram/illusion, projected from information encoded on a two-dimensional chip. But sane people have criticized this argument on the grounds that such a computer, with the power to artificially create our Universe, would have to be larger than the Universe itself, and would require more energy than the entire Universe has. Which is a valid claim - but as others quickly pointed out, it would take a heck of a lot less computing power to create an "imperfect" Universe, where the simulation is just good enough to fool us into thinking it's real. In other words, parts of the Universe would only be programmed as we observe them - like, for example, far-off galaxies only exist while we simulants are studying them with scientific equipment. And the second we look away, it's gone. This is reminiscent of solipsism, where things only exist as we observe them. Of course, this again delves more into philosophy. Yeah, it's a creepy thought, and it lies just at the border of physics and philosophy. But don't let it worry you too much - I'm sure we're all real. -Simulation complete-
  24. Since the beginning of it, we have tried to measure it: time. The concept in itself is intangible and pretty abstract, though we perpetually experience it and find it to be one of our biggest issues. I made an earlier post regarding additional dimensions, noting that many consider time to be the 4th dimension, one that is unbound by spatial constraints - but here, I'll take the topic into something even more abstract. I knew before researching that people have different outlooks on time, whether or not it is flowing continuously or if it has certain fast points and slow points, ebbs and flows. Generally speaking, due to the advent of digital clocks, we have time down to very specific and accurate intervals. But that's boring - so I looked into it. I found out that what I wanted to know is worded thusly: "Is time continuous or quantized?" And before I get deeper into this, I'll explain both of these terms. Continuous is fairly self-explanatory - time flows without intervals, and the intervals we assign to it (seconds, etc.) are entirely arbitrary. In other words, think of it as a number line: from t = 1 second to t = 2 seconds, every possible number of seconds in between these values occurs, therefore meaning time flows in infinitessimally small values, so small they are incalculable and essentially nonexistent. Quantized is the opposing viewpoint. Think of the base word, "quantum", meaning a minimum possible value. Does time have a minimum interval, the same way matter has a base unit of an atom? Well, such a unit has been proposed for use in quantum physics. It is known as a chronon, and its value has been theorized and calculated. The idea of such a unit existing was brought up by Robert Lévi in 1927, and in 1950, German-American physicist Henry Margenau suggested that a chronon could be the time it would take light to travel the radius of an electron - so you can already see how small a chronon is. A comprehensive model for this subject was put forth in 1980 by Piero Caldirola, where one chronon is about 6.27×10 −24 seconds for an electron. Note that the chronon varies due to the charge of a particle - the equation is given like this: . However, this is not the smallest amount of time ever theorized. There is a unit much smaller known as a Planck time. It is known as the amount of time it would take for light in a vacuum to travel one Planck unit, which is 10−20 times the diameter of a proton. (An incredibly small value.) A Planck time is about 5.39×10 -44 seconds - so what's the point of such a small interval? Well, many physicists believe that this is around the smallest value of time where an event, or change of some sort, can be noted. Any smaller unit is useless, since nothing would really occur in such a miniscule interval. What do I think of the whole thing? I think time is continuous, but I also think that the breaking down of units of time into small intervals becomes increasingly useless as you go along. In other words, smaller units of time than this exist, but they are scientifically insignificant values. Hopefully this stretches your mind a little bit - time is an incredibly interesting thing, especially at these quantum levels.
  25. No, not that 5th dimension. I'm actually here to talk about five-dimensional space, not soul music - but regardless, I hope this piques your interest. Last post, I researched the 4th dimension, and attempted to break it down in a concise, easy-to-understand, yet informative manner. This is pretty much impossible to do, especially throwing a new dimension into the mix; so again, you'll have to look for yourself to get a more comprehensive view. (Known as a 5-cube) Several branches of physics, namely particle and astrophysics, studies and debates whether or not the universe we inhabit is, in some way or another, five-dimensional. Essentially, the 5th dimension is a hypothetical dimension beyond the three spatial dimensions which we know, and the dimension of time brought to us by relativity. Several theories were developed around such a dimension; for example, shortly after the theory of relativity came into fruition, an extension of it emerged concerning the 5th dimension. It was developed over the course of two decades, and was known as the Kaluza-Klein theory. Initially, it unified gravitational forces with electromagnetic forces - then Oskar Klein came along to give this theory a quantum interpretation, stating that this dimension was "rolled up" and microscopic. This "microscopic" view actually corresponds with string theory, which relies on the existence on 11 dimensions. In this view, 7 out of the 11 dimensions would be rolled up and existent only at the subatomic level. Some speculations occur in this respect - one of these being that the graviton, a particle said to carry the force of gravity, may somehow permeate into the 5th dimension or higher. This would supposedly explain why gravitational forces are weaker than the other 3 fundamental forces - strong nuclear, weak nuclear, and electromagnetic. So how should we view this 5th dimension? A "holographic principle" was put forward by Dutch theoretical physicist Gerard 't Hooft, which states that a dimension can be viewed as curvature in a spacetime with one fewer dimension. For example, a hologram is a 3-D picture on a 2-D surface, giving it the visible curvature that we all notice. Likewise, the fourth dimension would be the curvature path of a test particle in three-dimensional space. 't Hooft also speculated the 5th dimension to be the spacetime fabric - that continuum which can be distorted by large masses/gravity. A hypersphere in five-dimensional space, the volume enclosed by the set of all points in 5-space equidistant from a central point, is given by the equation , where r is that distance from the center point. (I just added this for the people like me who want to see some tangible math to break up the crazy theoretical stuff.) That's about all I have, so remember to research further if you're interested - I can't do this stuff justice!

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