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Phys(ics)Geek
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Research...
Not done with homework yet... but when I finish I'll be dropping dead so I thought I'd update nice and early. Today was okay... done with quantum, I have my geometry work done, now I have to study "All My Sons" (Arthur Miller)in prep for "discussion" tomorrow... Ugh... Tired. I have to do some stuff for my research tonight too... I'm kind of stuck on deciding what I want to do... I basically have three options... 1.) Continue my work with Two Loop Self-Energy Basis Integrals (Feynman Basis Integrals...), which would be most familiar to me... I'd most likely end up completely rewriting all of the code I currently have written in C, in C++, and then using the C++ code to do some actual calculations of particle interactions. 2.) Renormalization of and Solution to the Quantum Chromodynamical Hamiltonian. This would involve me learning a ton of new physics, including but not limited to: Quantum Field Theory, Gauge Theory, a shitload of new Quantum Mechanics, and Quantum Chromodynamics. So I'm interested in the a whole lot. Plus, I could sort of split it up into two research projects: write my thesis on the renormalization of the Hamiltonian and then, during my senior year write a paper on the solution. Plus, according to Dave I might be able to get this published. 3.) Analysis of the Collapse of the Quantum Mechanical Wavefunction. This... alright, I'll explain it. Take in your mind, the classic quantum mechanics wavefunction, Psi(x,t). What does it tell you? It tells you the probability of finding the "particle" at point x at time t. Well, say I set up a detector, and I "see" the particle at x. Because I've interacted with the particle, I've now changed its wavefunction. Whatever the shape of the function, it has now gone from that to being a sharp peak around point x (so that if I were to make a second measurement shortly after the first, the probability that I'd find it near to x is high). Now, as more and more time passes, presumably (thank Heisenberg), the wavefunction collapses back down to what it originally was, that's the "Collapse of the Wavefunction". Alright, now, imagine I turn my detector on, and I don't find the particle. What do you expect to have happened to the wavefunction? I make the claim that were I didn't detect the particle (x), the wavefunction now has a valley, such that if I were to make a second measurement in an extremely short amount of time after I made the first, the probability of finding the particle at x is extremely small. So... if the explanation for the peak in the detection case was that, in detecting the particle I interacted with it, and indeed somehow changed it, what does this imply for the non-detection case? Well... clearly in not detecting the particle I interacted with it... but HOW? That's the question I'd try to answer if I chose that as my research topic. As you can see... It's one of those weird quantum mechanics "things" and it has me fired up. Of course, there's a chance that if I choose that, that the answer will become trivial and I'll be in trouble when it comes to writing the honors thesis. So yeah... that took longer than I thought... but these are the things I've been pondering over the last few days... great huh? Feeling:
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