joigus

This is just my two cents, for whatever it's worth. You can live a long, healthy, and fulfilling life without ever thinking about the 'weirdness' at all. Even become a very valuable person in the scientific community. Further go on to win a Nobel Prize and have a university named after you. But, if you are a compulsive thinker, if you can't make peace with yourself until you've made as much sense of it all as it's humanly possible (in other words, you are a 'theorist,' you should ask for something more. Send your papers and accept the peer-review system. Above all, if your ideas meet the criteria of acceptability and make it to the laboratory (that's something you must always ask yourself: Can this be brought to the laboratory?), it's still OK if you make some room for the possibility that there's an error in the interpretation of the experimental results, because it could still be right in some sense. But in the end, if your idea is rejected by Nature (and I don't mean the publisher,) and you're going against all odds to save it, then it's probably wrong, no matter how beautiful or plausible it looks in your mind, and it belongs in the rubbish can. Why must we, or anyone at all, keep thinking about the QM rationale? IMO, because there is the possibility of understanding a little bit further. Theoretical physics (that's my perspective) is about mapping the world with mathematical tools. So in that sense it's like the geometer looking at geometry from the other end. As a geometer, you depart from a differential manifold (fancy name for an n-dimensional surface, with dashes of more sophistication) and study its properties. As a theoretical physicist, you're compelled to look at the world rather more like the cartographer: You are given the landscape at different scales and from different vantage points, and you (and others like you) must try and figure out what the underlying 'space of variables' is. If you squarely deny yourself the possibility of understanding deeper and further, you're probably looking at the world from a vintage point rather than a vantage point.

and adding them up.

I wonder why I wonder why I wonder why I wonder why I wonder why I wonder Richard P. Feynman https://i.pinimg.com/originals/b3/8c/15/b38c152b06f4fb26298b56983c107ded.jpg

I agree that what you really want to say is COM, not COG. LOL. But it really is the best example I can think of. Thank you, but not your fault in any case. I've got myself in lots of trouble throughout the years for not reading the wording of a problem carefully. The question, I think, is very reasonable. The wording without mathematical formulas or diagrams, is generally tricky.

LOL. There's also the 'minor' problem of slowing the hell down from near to 3x10^8 ms^⁻1 to near 0. That takes some braking capacity.

Also, eigenstates are always associated to observables = properties that you can measure. When the particle has a definite value for that observable (dispersionless, it's called) then it is in one of those eigenstates, which is German for "proper state." But in a general situation, observables have dispersion (statistically speaking; they are "blurry" in that observable) so what quantum mechanics assigns to those instances is a linear superposition of all those eigenstates with a statistical "probability amplitude," which is the corresponding coefficient. By squaring the absolute value of all the amplitudes in a range, you get the probability that the observable falls within that certain range. I hope between Studiot's beautiful analogy and my attempt at telling what QM is in a nutshell, we've shed some light. But QM is very abstract, that's for sure.

Oh, yeah, divisibility by 11 criteria give you that, right? I'd forgotten about that. Must go over that again. But don't get me into other numbers.

Yeah, I was pigeonholed in my theoretical mind. Couldn't think about fluids and the like. The OP I think was talking about sth. like biomechanics. Sorry on my part: Yes! Everything rotation-based in physics changes when you displace the centre of mass, or the centre of gravity if you rotate about the same axis. The best example I can think of is a pole dancer. These girls must really get some joint lesions from the stress of rotating out of centre.

Gravity won't do the trick. There's just not enough energy and nothing can move faster than light, locally speaking. As Strange says, gravitational waves need really powerful sources to be triggered, as black-hole collisions, plus they're really feeble, and don't really induce linear accelerations in clusters of matter, but just space-time distortions in two mutually perpendicular directions. It's just like a blip on the radar screen, so to speak. The Alcubierre metric is another far-fetched possibility AFAIK, not free from inconsistencies. And then the only reasonable possibility in principle that I can think of is getting work from the huge storage of mc^2-energy in matter, maybe by capturing free antiparticles from cosmic rays and guiding them to ordinary matter that would act as fuel/target. But that is a far cry, I suppose. I'm a theorist, so I really can't tell with any degree of accuracy. There are many experimentalists/engineers here that can judge much better than me how much of a crazy idea the latter would be.

Centre of mass, moments of inertia (there are 6 of them for a rigid body) and any other average of any power of the coordinates with respect to the mass distribution will change if or when you change the mass distribution. If you think about it, it will make sense, I believe. Rotating a body around an axis that is not a principal axis will lead to mechanical stress that could result in breaking it. In general, having a rigid body rotate around any axis that is not an axis of "inertial symmetry" will lead to such mechanical stresses and tend to break it, if it's rigid. One simple way to do that is by forcing one such body to rotate around any axis that is not a principal axis of rotation (the axis the masses cluster around as symmetrically as possible, so to speak.) Whether the balance of forces would realign the rotation depends on the detailed study of the solutions to the problem. It would be very surprising to me that the situation you are proposing lead to a point of stable equilibrium in the phase space (the space of all dynamical configurations.) Stability and predictability are exceptions, not the norm. On the contrary, if you do the same with a blubbery gooey kind of object, the rotation would lead to deformations, although the moment of inertia as such would not be well defined. Or you could perhaps work out some kind of instantaneous moment of inertia definition. I hope the previous was helpful. If not, just ignore me. Yeah, probably MigL is right that it could realign the rotation. I'm just not sure right now. I think that had to do with the combined action of gravity and friction. Ditto. Ditto. For big angular velocities, not necessarily accelerations, as rotations always induce non-inertial forces.

Right you are. My doctor told me to stay away from factorizing numbers that are too high.

I honestly don't think they expect anything to happen as a consequence of their prayers. If they ever do such a thing, they must be impervious to disappointment.

Studiot is absolutely right AFAICT now, and has given a very thorough discussion AFAICT. Maybe you mean the 'principal axes.' But even in that case I don't think it's necessarily true, although I would have to think about it. What is true is the (mathematical) fact that, when you refer the motion to the centre of mass, the eqs. of motion adopt a particularly simple way in terms of the moments of inertia relative to the principal axes. They kind of split in to translation and rotation in a simple way. Maybe it's true. But then again, I would have to think about it.

-Today I've learnt about: Einzel lenses and viral load in aerosols. Indebted to: Swansont -Today I've learnt about: colour-entangled W states Indebted to: Studiot -Today I've learnt more details about: quaternary-structure protein dymers and palindromic character of RNA sequences Indebted to: Dagl1 and CharonY -Today I've learnt about: Intricacies related to atmospheric CO_2 absorption by weathering at the Himalayas Indebted to: Area54 and Studiot -Today I've learnt about: phenomenological/heuristic aspects of cosmology in general Indebted to: Mordred -Today I've learnt about: geons Indebted to Strange There's quite a bunch of 'todays' there. And I'm still learning. And counting...

I haven't followed the follow-ups very closely, as first answers were very satisfactory IMO. If you're going to spend any length of time thinking about photons, be careful, though. I just want to point out that #(photons) is not a conserved quantity. Photons are very 'dangerous' to think about in terms of little bundles of 'something.'

Easy. If what the survey says is actually true --see below: Analogy --not to be taken literally: Go to a prison and ask all convicts for murder crimes whether they're guilty or not. You end up with a list of: 10 % say they did; 65 % say didn't and 25 % don't remember. Conclusion: Only 10 % of convicts for murder crimes actually did commit a crime. Explanation: In the words of Daniel Dennett; American Philosopher and scientist, outstanding at exposing many religious (and other) logical fallacies IMO, "they believe in believing in God." I.e.: They live in a social environment in which it would be far more costly for them to declare themselves atheists than to keep on pretending. Dennett, e.g., takes no prisoners when it comes to theologians. They all fall --willingly or not-- in the use/mention fallacy: "A history of God," "God in our society," etc. Religion is absolutely rife with fallacies, half-truths, and conveniently spun arguments and data. Besides, as iNow says, . Excellent point.

It never crossed my mind. Well, it did, but it was a virtual process.

Now, if \mathcal{F} (LateX for script F) were not a friction, the discussion would be more complicated. I'm not sure that's the case you're interested in. Ghideon is considering a force that acts just at the moment initial forces stop acting, I believe.

OK. I think I understand the problem, but I concur with studiot, MigL, and Ghideon that the conditions are less than clear. Sorry for changing your notation, Ghideon, but it's clearer to me if I set, m, M, f, F. And initial acceleration a_0, positive. Eqs. of motion: \[f=ma_{0}\] \[F=Ma_{0}\] We get, \[\frac{f}{F}=\frac{m}{M}\] Now comes the braking force. I'll call it script F. You don't say it's constant, you don't say anything except it's equal for both masses. I will assume the forces f and F keep acting as before. \[f-\mathcal{F}=ma\] \[F-\mathcal{F}=MA\] Where a and A are the new accelerations. Using f/F=m/M, we get, \[\frac{a_{0}-a}{a_{0}-A}=\frac{M}{m}>1\] This leads to, \[a_{0}-a>a_{0}-A\] or, equivalently, \[A>a\] As script F is a friction, it can never overcome either f or F. So m stops further away, I believe.

Disegnare ellisse con una corda (youtube-URL)+ watch?v=YGygq98xDjI

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

Thank you so much.

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.

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.

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.