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joigus

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Everything posted by joigus

  1. I must have missed it. I made a mistake. The SG experiment is not about charged particles. It's about particles with a permanent magnetic moment. They'd better be non-charged if you want to show just the beam-splitting effect without any qE Lorentz dragging term. Anyway, the force (classically) is a vector gradient of the effective potential energy term. You can do quantum mechanical calculations to show that --quantum mechanically--the beams split into 2S+1 levels. No purely classical calculation can give you that. The essence of this calculation is that (1) There is an inhomogeneous magnetic field in the window of the Stern-Gerlach device, and (2) the states of the particles can be described with a quantum-mechanical function that has 2S+1 distinct basis states. Use of vector identity, ∇(A⋅B)=A⋅∇B+B⋅∇A+A×∇×B+B×∇A allows you to expand, \[ \nabla\left(-\boldsymbol{\mu}\cdot\boldsymbol{B}\right)=-\left(\boldsymbol{\mu}\cdot\nabla\right)\boldsymbol{B}-\boldsymbol{\mu}\times\nabla\times\boldsymbol{B} \] where μ is the magnetic moment of the particles --you can think of gaseous paramagnetic Ag atoms as an example-- and B(z) is the z-dependent magnetic field inside the window. Because the window is very small, you can do a Taylor expansion, \[ \boldsymbol{B}\left(z\right)\simeq\left[\boldsymbol{B}\left(0\right)+z\boldsymbol{B}'\left(0\right)\right] \] Because quantum mechanics of spin introduces a discrete set of states --e.g., S=1/2 has 2 states--, you can expand the incoming states with, \[ \boldsymbol{\mu}=g\frac{\hbar q}{2mc}\left(\begin{array}{cc} 1 & 0\\ 0 & -1 \end{array}\right) \] Use of the quantum mechanical evolution operator with, \[ e^{-iHt/\hbar}\simeq e^{\left(\boldsymbol{\mu}\cdot\nabla\right)\boldsymbol{B}\tau/\hbar} \] (valid only for the small time τ the particles spend inside the window), you can show that the salient states are waves deflected in momenta by amounts --S=1/2--, \[ \triangle p_{z}\simeq\pm g\frac{\hbar q}{2mc}\boldsymbol{B}'\left(0\right) \] So part of the beam goes up, and the other goes down. You can see a more detailed discussion of this in David Bohm's Quantum Theory. No part of your calculation shows this. Instead, as @exchemist said, a classical situation would have the beams deflect in every other intermediate direction, as I said too.
  2. Yes, that's true. My comments were really meant about the prevailing direction. But, as you said, this is a huge subject, with many exceptions and several levels of "turbulence" around the average tendencies.
  3. I apologise for mistake when I said, It should've been "westward migrations throught the steppe." That's apparently the prevailing direction of migrations through the steppe. And it is no accident. Sometimes geography introduces an element of predictability to migrations, if not complete predictability. There's very intesting material by Oxford archaeologist Barry Cunliffe pointing out how the landscape there kind of invites you to go westward. I seem to suffer from some kind of mild --I hope-- directional dyslexia. I promise to get up to speed as to present discussion too ASAP. The latest arguments about Australia and Polynesia I find fascinating. Apparently there is a paleoanthropological mystery/gap in our knowledge as to populations of South Asia during the Middle Paleolithic[?]. There's also the quite puzzling presence of Denisovan genes in people from Melanesia and parts of South-East Asia[?]. Sorry for imprecision. The take-home lesson is --I think-- we still do not completely understand what happened in South Asia for too long a time to be sure about any kind of big picture of what happened there. There are far more uncertainties about this than there are answers or any kind of big picture. @studiot was indeed right when he said this is a huge subject.
  4. As pointed out above, there are many factors, depending on time and place. People follow herds, rivers change their course, lakes dry out, advance of ice sheets force populations southwards, etc. The dynamics of population change are, I think, as varied as can be. Some migrations take place in one generation --example: eastward migrations through the steppe--, others take many generations to advance significantly.
  5. It only does that if you assume quantum mechanics is valid for the charged particles and classical field theory is valid for the EM field. If you combine quantum and classical attributes, it's possible to obtain relatively satisfactory models for some quantum behaviours. You have to put in QM by hand at some point. If charged particles can adopt any orientation --they are classical too--, it's obvious that you would get the continuous range of deflections I was talking about.
  6. The whole point of the Stern-Gerlach experiment is to disprove the classical theory of radiation. You get two or more (2S+1), separated, clearly defined spots where the charged particles end up, corresponding to the different values of spin. If the phenomenon could be interpreted classically, you would get a continuous range of arrival positions, which is never the case. That's why the SG experiment is considered to be one --among many-- confimation of quantum dynamics, as opposed to the expectations of classical-field dynamics.
  7. No. If AI were able to "create" a herd of antelope or a coral reef, plus the long-term incremental changes in the fossil record that led to them, I may change my mind. Then we would have gone full circle in the generation of intelligence by intelligence, which is only the first step that it would take to convince me. IOW: Evolution is obvious once you understand its principles and let the facts sink in. And it is impossible to grasp if you have a very concrete, atavistic prejudice that obstructs your understanding, by ignoring the facts and misunderstanding its principles.
  8. I'm rather confused by your use of the term "a number's territory." You obviously mean something you're finding difficult to define --I infer that from your repeated use of quote marks. Can you be more precise? It's obvious there are numbers so big that you would be hard pressed to find anything physical that makes them relevant. Or so I think. Is something like that what you mean?
  9. My pleasure. I don't know how Graham's number is constructed either. A good principle to organise (integer, counting) numbers by scale (in physics) could be perhaps considering this: Small numbers: Number of people in a room (somewhere between 10 and 102=100) Moderately big numbers: Number of atoms in a typical piece of matter (1023) Big numbers: Number of photons in the universe (1090) Really big numbers: Permutations of big numbers or number of ways to re-arrange big numbers: (close to NN/eN) The last one is called Stirling's approximation. It's a way of "taming" really big numbers by avoiding them directly (knowing all their digits) and using instead a ballpark way of dealing with them.
  10. You might be interested in this: https://en.wikipedia.org/wiki/Graham's_number https://en.wikipedia.org/wiki/Large_numbers The thing about these large numbers is not just, of course, how big they are. You could always talk about Graham's number +1, and that would be bigger. It's rather about humongously big numbers that somehow are significant in one part or another of mathematics. Graham's number is really really big in the sense that people seem to be quite uncertain about most of its digits. So in that sense it's very peculiar. Not at all like powers of ten. It's kind of unwieldy in the extreme.
  11. My feelings exactly.
  12. I don't think it's a coincidence. It's obvious that our anatomy seems to favour use of 10-base number system. The Babylonians had a preference for 60-based number system. And the reason is the high number of divisors that 60 has: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. One problem is that you need sixty symbols or digits, which becomes cumbersome. But still, there are traces of the Babylonian system in our 12-based hour system, as well as in measuring angles.
  13. A good starting point could be, Can you explain in terms as simple as possible how information compression could be relevant to QM?
  14. Yes, but that's on another level. I thought you meant freedom for investors. A regular job is not the market.
  15. I'm afraid 100 % free and 100 % ethical is impossible. The moment you introduce freedom, you also introduce the potential for non-ethical behaviour. It's the law of unintended consequences at work. 100 % free would be like the savanna. 100 % ethical --by regulation-- would stall most enterprising iniciatives. So it's a compromise we must reach. It's always been like that. Would an algorithm be possible to limit the potential damage of guaranteed unethical behaviour? Sure. But I'm afraid people wouldn't like it, plus there's no money in it for algorithm designers. When I say "people wouldn't like it" I mean rather the tens who hold billions than the billions who hold tens.
  16. I'm assuming you're made of matter, so no. I reckon you would have to make an antimatter copy of yourself and send it to an antimatter version of the past environment you would like to be in. Here's the answer, in the form of a well-known poem by physicist Harold P. Furth, A.E.C. stands for "Atomic Energy Comission, and the poem refers to the certainty that any close interaction between matter and anti-matter would end up in a burst of gamma rays. You touch any sizeable amount of antimatter, and you're done.
  17. Agreed. There is such a thing as punctuated evolution, and the concept can be applied to some extent to scientific progress too, I think. Abrupt changes appear out of complex scenarios that could not have been predicted in any analytic way with the tools at hand. AAMOF, they are to be expected somewhere along the way. Alexander Fleming's discovery of penicillin is a perfect example. We are in the middle of a massive data-gathering phase now, measuring things we could barely have dreamt of only decades ago. That's why something new is to be expected. That's also probably why, I think, no continuous model like the law of diminishing returns really applies when it comes to predicting this kind of abrupt changes.
  18. In the words of George Costanza (Season 3, episode 9, The Nose Job), "You can't stop modern science. You can't stop it. You can't stop it. Can't stop science. Can't be stopped. No way, no how, science just marches..."
  19. So do I. There are silent, progressive revolutions, and you understood my point perfectly.
  20. Topological insulators Quantum computing High-precision tests of the standard model (not science-spectacular, but extremely important) Neutrino physics (flavour-changing neutrinos) Observational cosmology (gravitational waves, supermassive BHs, accelerated expansion, exoplanets, etc.) Negative tests of proton decay (negative-result test are extremely important) Non-linear optics And the list goes on... As to other sciences, Ancient DNA Gene therapy Stem-cell therapy Ribozymes Cloning techniques And the list goes on... I think it's the other way around: It's very hard to keep up, really. It's because we're piggybacking on the shoulders of giant breakthroughs that it's so hard to tell how fast we're going --relativistic metaphor-- and even harder to relate the information in order to get a glimpse of any kind of big picture. I think there hasn't been a major change of paradigm, and that's easy to be misinterpreted as no advance. Whether these major advances will coalesce into a paradigm shift is neither certain, nor necessarily the case to be expected.
  21. Maths is the proper language to describe/ascertain uniqueness and/or complexity. What makes you think there is a better language? Approximate calculations without maths? And how would that go?
  22. It is my opinion that words themselves are worthless without the world of meaning behind them. It's what it means what's been, I'm sure, essential in human evolution. Long-distance trade, collaboration, etc. would have been impossible without the phatic function of language. Having others know the communication line is open even if you didn't completely understand the full import that they're trying to get across is a priceless function of language. I learnt that word, as usual, by carefully listening to others. I wouldn't have understood it by just reading a book. Thanks for appreciating...
  23. I personally don't parse every sentence I hear or read through propositional logic. That's all I meant. Language has a phatic function too, you know.
  24. There's nothing wrong with seeing with your mind's eye what your heart feels. It's not science, that's all. And it certainly isn't a scientific speculation.
  25. You have no basis to assert this. All we have is endocasts and certain genetic sequences. How do you know?
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