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About Latro

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  1. You have been missed. I hope your research is moving forward.

  2. Well for one thing, your statement isn't true in classical mechanics either. If a classical object weighs 1 kg, then it takes 50 J to get it to 10 m/s from 0 m/s, whereas it takes 150 J to get it to 20 m/s from 10 m/s. As for special relativity, there is a quantity that appears all over the place called the Lorentz factor, conventionally denoted by a lowercase gamma. It is equal to 1/sqrt(1-v^2/c^2), where v is the speed of the object and c is the speed of light in vacuum. The energy of an object moving at speed v is m gamma c^2, and the rest energy is m c^2, so the kinetic energy is m (gamma-1) c^2. For v less than 0.1c or so, this is within about 1 percent of 1/2 m v^2, because the first correction term is on the order of m v^4/c^2. But there is a divergence as v approaches c; specifically the divergence is of the same character as that of 1/sqrt(x) as x approaches zero. Note that this is not "exponential" at all. Effectively what is going on here is that the mass of an object moving at speed v is not m but rather m times gamma, in both the sense of inertia and the sense of gravitation.
  3. Forward only time travel is already known to be theoretically possible. For instance, let's say you're 20 and you want to get to 3016 by the time you are 21. You get in a spacecraft, accelerate to 0.9999995 times the speed of light, continue that way for 6 subjective months, then turn around and very quickly accelerate back to the same speed, and stop after another 6 subjective months. Special relativity says that you will now appear to be 21 but it will be 3016 on Earth. Of course, the requirements for this are massive: getting a 100 kg object initially at rest to accelerate to 0.9999995c amounts to giving it about 10^25 J of energy--about 20,000 times more than the entire world used in 2012. Your trip essentially has to do this four times (get to speed, stop, get to speed going the other way, stop again). Other than that, it doesn't look like time travel is possible from the perspective of current physics, but we might find that relativistic singularities (black holes and the like) change that.
  4. Discrete optimization is hard. I'm sorry this didn't work out.

    About 30 years ago, I created a discrete filter that should have been great for a particular problem. Should have been... I have rolled it back out on occassion when something came along that might redeem the idea. I tried it again this month on my current project... total FAIL.

    I think everyone who has done any serious work has at least one of these "shoulda' worked" things on the shelf!

    It's good to see you.

  5. It's a long story.

    Last September my previous advisor and I concluded our relationship. I got another advisor in July. It's not going too great. I spent a lot of time on developing and implementing a numerical method scheme which turns out to not match up with the "gold standard" method for the physical problem we're studying.

    To be specific, I work on crystal growth now, and the "standard" method is kinetic Monte Carlo (KMC) methods, usually in a "solid-on-solid" framework. The regime of interest is "step flow", where there are 2D, relatively flat regions called "terraces" which are separated by "steps" of one atomic height. The idea behind the scheme I developed is to average out the diffusion of the terrace atoms while resolving the step sharply. Since KMC spends most of its time on the surface atom diffusion, this should in principle be faster. But for various reasons, my scheme doesn't work: it generates much lower numbers of terrace atoms than KMC.

    So now I'm trying to play with some toy problems instead to find another focus. Hopefully I finish by May 2018. At the moment I'm not looking much past that.

  6. When do you finish your degree? What then?

  7. Except the Laplace transform of the indicator function of [0,1] is actually (1/s)-(e^(-s))/s, so actually proceeding this way is a bit technical (you have to use the binomial theorem and then integrate a rather complicated piecewise polynomial function). What you did amounts to working with the "density" of a "uniform variable on [0,infinity)" (which of course makes no classical sense). It can be cleaned up, but it's more delicate than it seems. You can subdivide the cube into n! simplices. Namely, for each permutation s_1,...,s_n of {1,...,n}, there is simplex given by the points in the cube such that the ith number in increasing order is in position s_i. These are disjoint, except for points where at least two coordinates are equal; but this set has measure zero. So the question then reduces to showing that all n! of the simplices have the same volume. That's geometrically intuitive, though I don't see an easy geometric proof.
  8. The electron is one cloud. It can be represented in terms of a combination of simpler ones in some cases, but it is still just one. While the electron shells are a very useful model for applied problems, they are not "real", but rather an approximation of many-electron phenomena in terms of (mostly) one-electron phenomena. If you were instead trying to talk about the issue of indistinguishability in the Fermi-Dirac statistics of electrons, I would argue that this is too subtle a topic to explain with any analogy.
  9. What ummon actually said is barely even an interpretation, instead it's just "a macroscopic measurement device is a big quantum system, and its interaction with a small quantum system can in principle be described by the laws of ordinary quantum mechanics". The many-worlds aspect of it is where interpretation comes in.
  10. It actually turns out to be worse than that: a quantum measurement of, say, an electron, does not actually require applying any force to it (with, say, a photon). It still triggers the effect of the uncertainty principle even if no force is applied. That is, the uncertainty principle is part of how electrons exist, not a property of how we interact with them. It is also not limited to the Copenhagen interpretation: all interpretations of QM explain the uncertainty principle in one way or another, because it is built into the math itself, not just the philosophy. Or at least so says our current understanding of QM. But we've also proven things like Bell's theorem that say that other understandings of QM would be even weirder than what we already have. For example, we've shown that simply inserting hidden variables can never actually resolve the philosophical concerns that we intuitively have with QM.
  11. I'm a PhD student in math in my third year. I haven't advanced to candidacy yet; the hope is to do so next semester. Honestly, it hasn't been so hard so far. Between teaching duties and classes, I am in a classroom 14 hours a week. Between grading and homework on top of that, I probably work less than 40 hours a week in total. Meanwhile I have a stable job, a roof over my head, and my best friend and girlfriend at home with me. I've met more friends in the first month I was here than I did in my entire time in undergrad, because for once I was truly surrounded by people with similar interests. I do agree with you about the freedom aspect. Probably once a month this semester I've been overcome with the desire to just get out, get some adequate job, and just settle into a life where I have more personal freedom. I'd say there are two main reasons here. First is that I'm now very happy at home. I don't find myself trying to fight with boredom and just make the day pass away anymore, I truly enjoy almost all of my free time now. The other reason is that I discovered that I was lied to about economic needs, which I think is relevant to your concerns. I came to this town with $1000 in the bank. I've earned somewhere between $50k and $60k since I got here nearly 2.5 years ago. I now have $10,000 in the bank. I haven't felt frugal in the slightest, especially in my housing decisions. If my girlfriend and I both had jobs earning even $25k, we would have no idea what to do with most of it.
  12. I don't think that simplification really works. Say the universe consists of two compartments, A and B. I put 1 Joule in A and -1 Joules in B. (Explaining what -1 Joules even means is another issue in explaining this phenomenon.) Although the total energy is zero, there is still nonzero energy density in A and B. So something is there, even though they would cancel each other out if they came into contact.
  13. In the absence of static charge and resistance, voltage is zero. (Strictly speaking, it is an arbitrary constant, but that means we set it to zero by convention.) Hence in the absence of static charge, resistance and voltage can only exist together. So I'm not sure what you mean here.