Here is the in-class Modern Physics Final that I took today. I call each question an essay because that's what the assignment sheet said. He specified that each "essay" should only be a few paragraphs.
Oh, and by the way, I didn't revise this at all so ignore any semantic mistakes or poor use of language -.- And note that I really started to tire during the end. But that's perhaps because the questions got less interesting and because I had less time -.-
Modern Physics Final Exam -- 5/25/07
Essay 1: Special Relativity
Special relativity is Einstein’s theory concerning the distortion of space and time at different relative velocities. It describes a transformation that allows to observers to agree on what each other saw, based on the calculation of the gamma factor. A crude yet useful summary of it is the three words short, fat, and slow. That is, as one approaches relativistic speeds, distance contracts, mass and energy increase, and time slows down. From the perspective of a beam of light, the light is everywhere at once (due to the contraction of distance), time is just a single moment (due to time dilation), and energy is infinite (due to energy increasing by the factor of gamma, which is infinite).
The difference between special relativity and classical physics can be seen in Einstein’s famous thought experiment r eferred to as the Train Experiment. A still observer relative to the ground is placed halfway between two points at which lightning eventually strikes. The still observer sees the lightning strike the two points at the same time. Another observer, moving on a train, is passing the still observer. The observer on the train sees the lightning strike the point towards which he is moving earlier than the point towards which he is moving away. This different order of events can be explained by a Galilean transformation, i.e., classical physics. What cannot be explained by a Gallilean transformation, however, is what the two people observe each other seeing. In classical physics, the two observers would agree on what each other sees. On the contrary, Special Relativity states that the two observers would not agree on what eachother sees, because they have such different definitions of time and space.
Special Relativity has momumental impacts on our scientific understanding of the universe. It not only advances our knowledge of physics, but it practically reinvents physics. It explains phenomena that used to puzzle us, such as the Michelson-Morley experiment. It provides the foundation for quantum mechanics and modern physics in general, and enables technologies such as GPS which would not have been accurate and thus would not have worked under the supervision of classical physics.
In addition to the scientific advancement that it is has induced, Special Relativity has profound philosophical impacts on how we view the universe. It grants credibility to possibilities in one’s wildest imaginations. It presents the possibilities of living to see the end of the universe, returning to a world thousands or billions or however-many years later in a relative time span of two years, travelling through time using wormholes. It also shows how everything is relative, how everything is subjective -- the worst nightmare an objectivist like Ayn Rand could have had.
Essay 2: Duality
The double slit experiment presents the “single mystery in physics” (Feynman). When shooting single photons at a wall of detectors through a double slit, one would expect the photons to align on the wall in two places, forming two vertical lines. This does not happen, however. Instead, the photons form an interference pattern on the wall. This presents the paradox known as duality. Light can behave as both a particle and a wave. Louis DeBroglie later showed that this phenomena applies not just to light but to everything else, i.e., every particle has a wavelength.
Duality is not the solution to a paradox, but rather the name of a paradox. It is impossible for light to be both a particle and a wave because this would imply that the photon in the double-slit experiment is both spread out in a region of space and at one point in the same time. We do not know the solution to this paradox; the question is at the very heart of modern physics.
We know that light has both of these attributes due to how it behaves in different circumstances: like a wave in the double-slit experiment and like a particle in the photoelectric experiment. We use these two competing natures of light to our technological advantage. For example, we use the wave nature of light in optics. Our eye glasses make use of the property of refraction. We use the paraticle nature of light for its photoelectric effect in television, through use of the cathode ray tube. Of course, this is not the first time we have exploited a physical phenomena in technology without yet understanding it. We used electricity to power our country before we even knew what it was, and we know ways to live to see the end of the universe without having the technology to launch us at relativistic speeds.
Essay 3: E = mc^2
Einstein’s equation E = mc2 basically says that mass and energy are equivalent. It applies to the creation of the universe because it verifies that the universe could have been pure, massless energy at the start -- nothing but energy -- before condensing into mass.
This equation is essential to particle physics because it explains how particles can annihilate eachother, convert into pure energy, and then condense back into matter that is not necessarily the same matter. This allows for the discovery of new particles; it is the reason behind the Standard Model, which is basically the new periodic table.
This equation is also essential to particle physics because we use it in our measurements due to the conservation of energy. It is from our measurements that we deduce the existence of new particles; we simply track a particle, collect information on its properties, and then decide what kind of particle it is, and whether it is new or not.
Essay 4: Fast, Cheap, and Out of Control
In the movie Fast, Cheap, and out of Control, the director Errol Morris, likens each of his four human characters to the animals they are describing. In order to explain this, we will examine George Mendonca, the topiary gardener. Morris likens George to the insects because of how he works for the lady tenant of the mansion, just like worker insects work for a queen. It is especially ironic that George uses insect-like cutters to shape the bushes. Morris likens George to the cats in how just as the circus is the cage for the cats, the garden is the cage for Geroge. George and the cats’ worlds are inside their cages; everything outside is just the cage itself. Furthermore, Morris likens George to the naked mole rats because he, like the mole rats, is an example of an insect society infiltrating the mammal world. Morris likens George to robots by asking the question: is George really alive, or is it just a bunch of programming -- sensors, signals, and “falls” -- that makes George do what he does?
