celtschk
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 Dec 14 comment What are observables? Well, it's already past midnight here, so I won't add math today, and tomorrow I won't have time for it. But maybe on Tuesday I'll find some time to add something about the mathematical description. Dec 14 comment How far can light go? There's not only no reason to just vanish, it even cannot just vanish because doing so would violate conservation of energy. Oct 11 comment Big jump or small jumps? Of course, in real life, our muscles are not 100% efficient, which means we need more energy than the kinetic energy we gain (extreme case: If just holding a heavy weight, from a physical point of view we don't do any work, yet our muscles still consume energy in order to sustain the force; that energy is completely converted to heat). Sep 7 comment Lightspeed (invariance) measurement methods The very first determination of the speed of light by Rømer did not need mirrors. Sep 7 comment Special Relativity, 2nd Postulate — Why? Thank you; I've corrected the spelling errors (and improved some formulations). Sep 7 comment Do we weigh less in the morning? "During the night, the sun is above us, and the earth below us." I think you mean: "During the day, the sun is above us ..." Sep 6 comment Can entanglements themselves be entangled? Most importantly, entanglement is not a relation in the mathematical sense because in general, particles can be entangled in inequivalent ways. That is, there is not only "entangled" and "not entangled", there are different inequivalent ways in which particles can be entangled. Systems consisting of just two systems which have just two states each (that is, two qubits) are special in that regard, since they are the only system that shows only one type of entanglement. Indeed, in the case of more than two particles, there's even no longer an unique maximally entangled state. Aug 9 comment Finding the mass of pure matter I've deleted my comment, since it no longer applies to the current version of the answer. Aug 2 comment Why do physical bodies in the universe follow the law of physics ( or any rule/pattern ) ? Wouldn't that be more appropriate for Philosophy.SE? Anyway, if physical objects would never follow any rules, then the same would also be true for the physical objects making up our brains (or rather, then not making up our brains, because forming brains also requires following rules), and thus there would be nobody there to observe the universe. Aug 2 comment What does the $y$-axis represent in the atomic spectra and what is its significance? "Actually a color CCD will report three numbers" — there is no such thing as a colour CCD. Rather to determine colour with CCDs, you put a colour filter in front of it. For a spectral analyser you wouldn't want to do that because the position already tells you everything about the frequency, so any filter would not add any information. Aug 2 comment How to measure Entropy? @Phonon: But if held at that standard, wouldn't a classic thermometer also not measure temperature, since the measured quantity ultimately is the volume of the mercury in it? Jul 20 comment Does “dark matter” explain how I can have -1 apples? No, that apple would obviously be made of antimatter. Jul 20 comment Interpretation of a density matrix as an observable Why is the identity not an observable? I can even give you a "measurement device" for it: Just write an "1" on the display. And while I'm not familiar with the nLab approach, I'd be very surprised if the identity would not correspond to the constant function with value 1, which clearly is a smooth function. Jul 13 comment could it be possible to create a pentane steam engine? The basic principle of a steam engine (convert heat to mechanical motion through boiling water) is used in many types of power plants. Even a nuclear power plant in the end does nothing but drive a modern version of the steam engine with the heat of the nuclear reaction. However, a low-heat steam engine would be very inefficient, no matter how it is realized, due to the fundamental laws of thermodynamics. Jun 22 comment Classical and quantum probabilities in density matrices A third way to prepare the same $\rho$ is to generate a polarization-entangled two-photon state and send one of the photons. If you retain the other photon, you can turn the sent-out photon into either Alice's or Bob's ensemble by measuring the other photon in either the horizontal/vertical or circular polarization basis. Note that the actual measurement statistics of the sent-out photon won't depend on which way (or even whether) you measured the second photon. Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? It's the Hamiltonian of a harmonic oscillator; the Hamiltonian is used in the Hamilton formalism (another way to derive the equations of motion). Basically, $H=T+V$, except that $T$ is described with the momentum. Otherwise, that's a special case of the potential I've given (with $a=\tfrac12w_x^2$, $b=0$, $c=\tfrac12w_y^2$), achieved by using the main axes of the potential as coordinates. BTW, I just notice that I've got a sign error in the equations of motions; I'll correct it in a moment. Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? @math12: "Two-dimensional harmonic oscillator" means, by definition, "two-dimensional system with attractive quadratic potential". "Quadratic potential" means "potential that is a polynomial of degree 2 in the position", and "attractive" means "when you go away from the equilibrium position, the potential gets greater". Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? @math12: No. A specific implementation (not the most general one) would be a mass that can move on a plane (horizontally, so no gravitation, and frictionless) which is connected through a (frictionless, massless, arbitrarily bendable) fiber through a small hole in that plane to a spring which is in its rest position when the mass is exactly above the hole. Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? $x$ and $y$ are just two directions in which the oscillator can be displaced. They don't even need to be orthogonal. The potential energy $ax^2+bxy+cy^2$ is just the most general possible quadratic form without linear or constant term. It has that form because that's what makes the system a harmonic oscillator (you could plug another potential in here, but then you'd no longer have a harmonic oscillator — well, unless your coordinates are something else than displacements, then it may be a harmonic oscillator in different coordinates). Jun 14 comment How can I find the motion equations of the 2-dim harmonic oscillator? See the edit of my answer.