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Everything posted by joigus

  1. Strange and Janus already have given you excellent illustration and glossary. Just in case what you are looking for is something more mechanical, there are several ways to make ellipses with mechanical elements. One of them is the "nothing grinder" or "do nothing machine," also called "elliptic trammel": But I'm not sure it tells you anything about the foci. I don't think it does. In Italian I think it is "Trammel di Archimede." And the other one is a couple of tacks and a piece of string. The tacks' positions are the foci. It's all in this website: https://americanhistory.si.edu/blog/ellipsographs
  2. So your mind was cross-pollinated. That speaks highly of you. I remember reading Russian calculus and phys/chem books and learning about Gauss' theorem under the name of Ostrogradsky's theorem, and the atomic theory as Lomonosov's. That's about as much cross-pollination as I was able to get.
  3. Maybe. But I remember a conference by Svante Pääbo for CARTA in which, during the Q&A session, somebody asked him why Neanderthals, having such cognitive abilities, failed to become the prevalent human species in Europe and the Middle East 30 000 ya. After some pondering he said something like, 'when we modern humans learn something, we feel the urge to share it with others. That may be the reason why our knowledge started building upon the previous generation's, while theirs became stagnant, as they had to re-discover all the tricks generation after generation' --something like that, I'm quasi-quoting him. So I do think there is an element of sheer delight in teaching that's hardwired in our brain circuitry, in looking at the expression of wonder in a child's face when she understands something or finds out about something with your help. That must be, I think, coded in our genetic sequences somewhere. And, please, nobody say this is cheap sentimentalism. Or if it is, it's reasoned and purposeful at that. Another very important reason why we must take as many looks at the different ways to entice enthusiasm in learners is this: We are living times in which religions in the West are about to disappear for good. Some people turn their eyes to science, others turn to pseudoscience or the occult, others --most likely in other parts of the world-- desperately try to reinforce their religious faith, probably as a counter-reaction. Religions cannot be the way out of whatever it is that we're in. And just pure utilitarianism is plain scary. That's why it's so important, if you are right and passionate teachers are something of the past, we revive them. Sorry I haven't dwelt on biographical details. Some of them've made me smile in complicity, some of them've made me cringe with envy. Lucky you for having grown up in Canada.
  4. Ok. I really must take issue with this, because although I do find some points of agreement with you, like, e.g., the "it would defeat the purpose" argument, or the general intention to reach wider audiences that these shows blatantly target, I really think you're flushing too much down the plughole there. As to school teachers pictured as "exiles,' I really must tell you that I've found sour exiles and leeches at university and school alike. Some of the best were at uni, and some of the worst too. I know enough of science to know that there exist vast graveyards of good-for-nothing sloppy science made by professionals, like some 'glorious' pieces of GR that were just plain wrong because the authors didn't know they were dealing with tensor densities, and messed up the calculations. They're still there, published, 80-odd years afterwards, to the shame of all. It is by no means the rule, thanks to the peer review system, but it just happens to happen. Same goes for papers that are but leading-nowhere speculations dressed with the glories of mind-numbing formalism. Again, not the norm, but there is such a thing as bad professional science and there is such a thing as good popular science. It's not as simple as researchers or university professors = people in the know, versus school teachers or popular science writers = poor idiots who don't know what they're talking about.
  5. Also an excellent point. Let me guess. You either do some refereeing or have been there... Because the modern peer-review system has zero tolerance with sensationalism. AAMOF, it's in the user's manual.
  6. Colour or polarisation state? Sorry, I'm not quite up-to-date in quantum information technology.
  7. Did I see it you say? Saw it several times. Particularly the Walking with Beasts series. I also greatly enjoyed the Walking with Monsters, as it brought to life the things I'd read about in S. J. Gould's Wonderful Life, that had me dreaming for years about the Cambrian and pre-Cambrian oceans. Googled about for all the critters, and further 'investigated' the evolution of whales, which is an amazing story of both natural evolution and scientific perseverance. The animation of Ambulocetus natans is one of the best things I've seen in the genre. https://i.gifer.com/5Bk5.gif
  8. Well, I don't live in North Sentinel island. BBC is, I have to say, my favourite in that respect. Only thing is when they get to me they're not quite so fresh. Plus the BBC blocks some contents outside the UK, unfortunately. Yeah, it's the 'snippets' part I was talking about. Although I quite agree with studiot that asking that people making the films be scientists is perhaps a step too far. Only that the authors be careful about documenting, and maybe allow the scientist to critically review the film so that no exaggerations are put in their mouths by selectively cutting the interview to make a statement sound as a suggestion of something else. So true. Related, although not the same. I remember a CGI film --it was wonderful otherwise-- about the Cretaceous extinction with three dinos killing each other in some kind of Reservoir Dogs of the dinosaur era finale.
  9. Again, imprecise. Non-factorizable pure n-particle states that, once an ideal measurement has been performed on them, become strict mixtures of maximum entropy. I think I got it right now. It is much shorter to say 'entangled,' but dangerously vague. I think I've read 'maximally entangled' somewhere... Otherwise, for pure states, you pick your state as making up the first vector of a basis, and then, the entropy is clearly identically zero. For the GHZ experiment, e.g., if you pick the GHZ state as the first vector of your basis, \[\rho=\left(\begin{array}{ccc} 1 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{array}\right)\] so that, \[s\left(\rho\right)=-1\ln1=0\] Instead, if you perform and ideal measurement, coherences are erased and, \[\rho=\left(\begin{array}{ccc} \frac{1}{3} & 0 & 0\\ 0 & \frac{1}{3} & 0\\ 0 & 0 & \frac{1}{3} \end{array}\right)\] so that, \[s\left(\rho\right)=-3\textrm{tr}\left(\frac{1}{3}\ln\frac{1}{3}\right)=\ln3\]
  10. Silly me, forgot: -Entropy: \[s\left(\rho\right)=-\textrm{tr}\rho\ln\rho\] When most physicists talk about entangled states, what they really mean is maximum-entropy non-factorizable pure n-particle states. They are something more than just entangled --non-separable.
  11. I watch science documentaries quite often. I find most other kind of TV quite unbearable. Overall I think it's a positive experience, because you get a lot of visual information that otherwise wouldn't be accessible to you. Plus you get to hear the researches, you learn some of the story of the scientific ideas... But I've noticed it's a bit dangerous to take some statements from them too literally. There are narrative strictures that sometimes have the unfortunate effect of adulterating the message with a pinch of sensationalism. And why is it that you never get the chance to hear a complete argument by any scientist that's being interviewed? It's like a collage of sentences.
  12. Hi, Mordred. I don't think this should be addressed to me. I was just thanking the moderators for sparing me the trouble to read all that nonsense. It really is a thankless job. That's all.
  13. I agree. And this observation has led me to further reflection. One should also consider the context too. Take, e.g., the term 'conspiracy theorist.' In a context like these forums, such tag would more than likely be pointing at logical flaws in someone's argument, or the lack of one such argument. But taken in a wider context, it would be very easy to dismiss just about any suspicion or reasonable case for conspiracy, the latter being a concept that sometimes makes perfect sense, given the context. I am firmly convinced, e.g., that Elizabeth I of England faced a real Catholic conspiracy led by the Pope and Phillip II of Spain to murder her. Same goes with 'alarmists,' 'bleeding hearts,' and many others.
  14. 🤓 ... 🤔 ... 🤭 "But... what happens at zero?," asked the GR disciple. "Zero is not zero," the GR master replied. "How could that be?," said the disciple. "Coordinates are meaningless," the great master said. "I don't understand," the student declared, utterly puzzled. "Every answer has a question in it; every question departs from an answer, they both build on each other," was the master's reply, and hit him with a tensor on his head. The student was immediately enlightened.
  15. Just to contribute another example of how so-called 'fundamental science' pays off: Einstein-Bose discovery of stimulated emission. Originally was just motivated by studying the quantum properties of photons. Went on to completely change the face of the world when Maiman came up with LASER. It may take decades, but pays off by mega-factors.
  16. (my emphasis) This is a very old post, I realize. But I think it may be worth keeping the fire burning. I'd love to have a go at getting into some details. But I don't think anybody can make it simple. The mathematics is not very hard, compared with, e.g., GR, but the connection with the physical intuition is bizarre at best. It would be nice to be able to dispel some common misconceptions. Very interesting. One of my old teachers --now retired-- changed his mind twice in 48 hours! I changed mine circa 1999 --old geezer-- and never went back. Suddenly realized that you don't need to collapse anything if you keep track of mixed states instead of pure states. Nobody would listen back then, though the real savvies knew about it. Life went on and I licked my wounds. I learnt about Ballentine's approach very similar to my view, although something was wanting: What happens to pure states? Are they a figment of the physicist's imagination? Hopefully, someone might catch me in any possible mistakes, imprecision, ambiguity or digression, misquotation. I've compiled a basic dictionary of everything that might be needed: 1) Dirac bra/ket notation. If not, the row/column complex vector would suffice. 2) Spin eigenstates and eigenvalues, Pauli matrices. For example, does this ring a bell? --no pun intended, \[\left(\begin{array}{cc} n_{z} & n_{x}-in_{y}\\ n_{x}+in_{y} & -n_{z} \end{array}\right)\] 3) The multi-particle formalism of quantum mechanics, otherwise known as "tensor products of states". 2-particle will do. 4) The postulates of quantum mechanics (states, observables, eigenvalues and eigenstates, probability amplitudes as Hermitian products, commutators & incompatibility, Hamiltonian or linear+isometric = unitary evolution, projection postulate.) 5) Yes/No observables, otherwise known as projectors (P linear & P2=P). That is, observables of simple bi-valued spectrum {0,1}. Plus useful lemma: \[A^{2}=I\Rightarrow P_{\pm}\stackrel{{\scriptstyle \textrm{def}}}{=}\frac{1}{2}\left(I\pm A\right)\:\textrm{are mutually orthogonal projectors}\] 6) Completeness relation or resolution of the identity for orthogonal projectors, In a nutshell: as much of the basics of the formalism as possible. To really understand the fundamentals, I would also strongly advise anybody to learn about: -The position/momentum representations of the wave function -The concept of a complete set of commuting observables (CSCO) -Superselection observables (those for which superposition cannot be applied) -The density matrix (distincion between pure and mixed states) -Decoherence -Local conservation principles, in particular, local conservation of probability densities Just for hairy details of measurement, QM of open systems, how states actually evolve in space and time, etc. I do have a feeling of impending doom, though. This topic has brought me unbearable pain in the past. I can no longer feel pain, so I'm thinking what the hell. My intellectual appetizer would be the statement of this common misunderstanding: Quantum mechanics is an out and out local theory. The conundrum is more to do with: systems that look to my rational mind as pairs of things (triplets: GHZ-M) are really one thing in some strange, uniquely quantum sense, because they're internally connected. It's non-separability that's at the root of all this, not non-locality.
  17. Forgot to say hello. I'm Joss, I teach Physics, Maths, Chemistry and English @ some academy in Spain. They sometimes make me teach Bio and Spanish, because they somehow assume I must know everything. I'm a theoretical physicist. My alter ego is Sisyphus. PD: I love Yogi Berra quotes
  18. No offence taken. I gave you an apology too, and I owe you an explanation. I thought this was probably just about a Physics student working on a physical problem looking for mnemonic/algorithm. Looks like the magnetic moment of a given current density. The integrand comes from the geometry of the circuit. The way I see it, physical problems in terms of different variables are just useful parametrizations of something 'real.' If the integrals are not manifestly divergent and simple symmetry arguments tell me it better be zero, the maths probably are telling me I must assume those integrals not to be of physical relevance. There are two peaks in the integrand, one at \varphi = \pi and the other at \varphi = \fraq{3}{2}\pi, with opposite signs. In such a way that, if I further change the variables \cos x = u, the integral formally reduces to a \[\int_{1}^{1}\] That tells me it must be zero. I wasn't going for any kind of mathematical rigor. I'm not cut out for that. And I haven't the faintest idea what the Henstock-Kurzweil integral is.
  19. The expression is familiar to me because I've seen it in lattice problems in physics. Here's a test run of your expression with, \[f\left(x\right)=\sin x\] It should give, \[f''\left(x\right)=-\sin x\] Let's see: \[\frac{\sin\left(x+2\varepsilon\right)+\sin x-2\sin\left(x+\varepsilon\right)}{\varepsilon^{2}}\] Using, \[\sin\left(x+2\varepsilon\right)=\sin x\cos\left(2\varepsilon\right)+\sin\left(2\varepsilon\right)\cos x\] \[\sin\left(x+\varepsilon\right)=\sin x\cos\varepsilon+\sin\varepsilon\cos x\] \[\cos\left(2\varepsilon\right)=\cos^{2}\varepsilon-\sin^{2}\varepsilon\] We get, after simplifications, to, \[-\sin x-\varepsilon\cos x+\frac{\varepsilon^{2}}{4}\sin x\] Works for powers of x, works for sines and cosines, therefore exponentials and products of them. Works quite well I think when things are smooth.
  20. This is what people want you to say: \[f''\left(x\right)=\frac{f\left(x+2\varepsilon\right)+f\left(x\right)-2f\left(x+\varepsilon\right)}{\varepsilon^{2}}+o\left(\varepsilon\right)\] Where, \[\lim_{\varepsilon\rightarrow0}o\left(\varepsilon\right)=0\] Can't be false because it's an identity as long as f(x) is twice differentiable at x. Utter the words and fall on your knees. Sorry, were it not for CoVid-19 I would be sleeping like a baby.
  21. During the first months of LHC running its first tests, I got wind that micro BH formation tested negative. It was an informal conversation, but the source was reasonably reliable. We seem to be stuck at Higgs...
  22. That makes sense. Half the viruses is not so good.
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