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Caleb's 4x4 Contest - Round 5: "Heisenberg's Uncertainty Principle" . My entry for Round 5 (final round) of Caleb's 4x4 Contest. The category is "Paradox" . This is my entry to Round 5 of Caleb's 4x4 Contest. The category for this round is "Paradox". The paradox I have chosen to represent here is Heisenberg's Uncertainty Principle. Quantum mechanics and relativity are two branches of physics that are replete with apparent paradoxes. While the princples and theories are all backed by strong experimental evidence, many seem paradoxical to those of us familiar with the Newtonian mechanics that govern most of our everyday activities. Heisenberg's Uncertainty Principle asserts that it is impossible to simultaneously know position and momentum of an object. In the "normal world" that proposition seems absurd and paradoxical. In fact, under Newtonian mechanics, knowing the position of an object at two distinct nearby points in time would allow one to get a very accurate estimate of the object's velocity (and, coupled with knowledge of the object's mass, its momentum). But in the world of quantum mechanics, where interactions take place at an infintessimally small scale, the wave-particle duality of matter dominates, and the paradoxical becomes the norm. I'll go into detail about the components of this MOC below, but first let's take a look at the front and back of the entire MOC. You'll notice that at the top of the MOC is a bust of "Heisenberg" from "Breaking Bad", the chemistry-teacher-turned-drug-dealer who borrowed this moniker to describe his elusive nature. First, my apologies to physics majors out there. Since I am just a lowly electrical engineer, I am probably about to commit all kinds of atrocities on the laws of physics with the following description. Feel free to correct me. Beginning at the bottom of the front, we have a wave packet composed of a single discrete frequency (in blue). While I have shown only two cycles of this wave, it continues on infinitely. The graph above this wave packet is the frequency plot corresponding to this wave packet (in red) -- an impulse of just a single frequency. Since frequency directly corresponds to momentum in the quantum mechanical world, we have very good knowledge of the momentum. However, since the wave packet has essentially infinite extent, the particle could be anywhere -- we have no certainty about its location. These two plots could be reversed to describe the opposite situation. If the probability distribution for a particle's position is an impulse, we know exactly where it is, but then the plot of its momentum distribution would be the blue graph, so we would have no certainty at all about its momemtum. The back side shows a less extreme case, in which neither the position of momentum of the particle are known exactly, but where there is some "confidence range" for each of them. Both the particle packet and the momentum distribution have the shape of a damped sinewave (in digital signal processing terms, we'd call them "wavelets"). These plots do extend infinitely, but they quickly taper off, so that with very high confidence, one can conclude that the particle's position/momentum lies within the middle few lobes of the appropriate plot. Just below "Heisenberg" in the front is a diagram showing how Heisenberg's Uncertainty Principle makes itself manifest in an experimental situation. The electron beam (purple) is hit with a photon emitter (the yellow cone). The incident photon collides with the electon beam and scatters (the green lines), causing the electron to deflect, but it an unknown direction. It is possible to use higher-frequency (i.e. smaller wavelength) light to get a more accurate location of the affected electron, but higher frequency light has higher energy photons, which will disrupt the path of the electron more and create more uncertainty about its momentum. Shorter wavelength, lower energy light will allow for better observation of the electron's momentum, but will make it more difficult to isolate it spatially. Finally, we have the two pictures to prove that the MOC fits within the limits of a 4x4 stud footprint and a height of 50 stacked bricks.

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