What keeps electrons spinning around their nucleus?
in [Relativity]
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From: Daryl McCullough on 29 Mar 2005 12:53 Gregory L. Hansen says... >Daryl McCullough <stevendaryl3016(a)yahoo.com> wrote: >>I guess whether or not the ball accelerates when you let go of it >>depends on how you define "acceleration". Here's the way I see >>things, mathematically: Letting V be the velocity vector, and >>A be the acceleration vector, we have: (where e_k = the kth basis >>vector) >> >> V = V^k e_k >> A = (d/dt V^k) e_k + V^k (d/dt e_k) >> = (d/dt V^k) e_k + V^i (d/dt e_i) (changing the dummy index k to i) >> >>Now, we can rewrite d/dt e_i as follows: >> >> d/dt e_i = dx^j/dt d/dx^j e_i >> = V^j (d/dx^j e_i) >> = V^j G^k_ji e_k >> >>where the matrix G^k_ji is defined via >> >> d/dx^j e_i = G^k_ji e_k >> >>Putting this altogether, >> >> A = (d/dt V^k) e_k + V^i V^j G^k_ji e_k >> >>Or in component form, >> >> A^k = (d/dt V^k) + V^i V^j G^k_ji >> >>If you release a ball while sitting on a spinning carousel, >>the first term (d/dt V^k) is nonzero, but the second term >>V^i V^j G^k_ji exactly cancels it, to give zero acceleration. > >The way I see that, you have declared "There shall be no mechanics >performed in an accelerated frame!" Why do you say that? I'm telling you *how* to do mechanics in an accelerated frame. There is no way to do it without connection coefficients. The question is whether you call them "force terms" or "acceleration terms". >What makes you think the e_i have a time dependence? Well, in order to compare vectors at different times, you have to have some operational way to do parallel transport. For spatial vectors, you can use gyroscopes: Set the gyroscope into motion pointing along a particular vector A at time t1. At a later time, t2, you compare A at time t2 to the direction that the gyroscope is pointing. >On a spinning carousel, if I define e_1 by a line >extending from the center to the black horse, and >e_2 from the black horse to the red one just ahead, >then they're not going to change. The coordinates of the black horse don't change with time, but the basis vectors do. -- Daryl McCullough Ithaca, NY
From: Bilge on 29 Mar 2005 13:15 mmeron(a)cars3.uchicago.edu: >In article <slrnd4h9dg.6h5.dubious(a)radioactivex.lebesque-al.net>, >dubious(a)radioactivex.lebesque-al.net (Bilge) writes: >> mmeron(a)cars3.uchicago.edu: >> >> >I don't see anything in the formulation of newton's laws saying that >> >forces must be traceable to fundamental interactions. What should be >> >taught is that there are "physical forces" which are, indeed, a >> >measure of interactions between objects, and there may be additional >> >"inertial forces" which are an artifact of the choice of reference >> >frame. But being an artifact, does not mean that they've no >> >> ``Inertial force'' is an oxymoron. If ``inertial forces'' are >>to be considered forces, then the word ``force'' is nothing but >>a placeholder for a noun, since anything is then a force. >> >Not "anything". Just anything that can be plugged into f = ma to >yield equations of motion. That would be anything, if you admit ``inertial forces'' to be forces. ``Fictitious force'' would be a lot more apt. >You can use, say, the Coriolis force in >this way, but I doubt very much that pepperoni pizza will work. Sure I can, just by balancing the electromagnetic force with the ``force of gravity'' to treat the pizza oven as an inertial frame when explaining why the pizza is (supposedly) at rest.
From: PD on 29 Mar 2005 13:17 Bill Hobba wrote: > <mmeron(a)cars3.uchicago.edu> wrote in message > news:yr02e.13$45.3299(a)news.uchicago.edu... > > In article <hT%1e.15978$C7.12491(a)news-server.bigpond.net.au>, "Bill Hobba" > <bhobba(a)rubbish.net.au> writes: > > > > > ><mmeron(a)cars3.uchicago.edu> wrote in message > > >news:4q_1e.11$45.3008(a)news.uchicago.edu... > > >> In article <1112038910.784307.230090(a)o13g2000cwo.googlegroups.com>, > "PD" > > ><pdraper(a)yahoo.com> writes: > > >> > > > >> >Gregory L. Hansen wrote: > > >> >> In article <1112035436.549412.84900(a)z14g2000cwz.googlegroups.com>, > > >> >> PD <pdraper(a)yahoo.com> wrote: > > >> >> > > > >> >> >TomGee wrote: > > >> >> >> Wormy, Bilge, PD, and all you other lemmings, > > >> >> >> > > >> >> >> you cannot understand that it is the _measurement_ of the force > > >> >which > > >> >> >> is fictional and not the feeling of being pulled out as a > carousel > > >> >> >> spins. > > >> >> > > > >> >> >Nope. You feel the force pulling you *in*, which is a force you are > > >> >> ... > > >> >> >Let me ask you another question. As an elevator suddenly starts to > > >> >> >descend, you feel lighter. Are you in fact lighter? Why should > > >> >Earth's > > >> >> ... > > >> >> >Let me ask you another question. You are on a road making a > circular > > >> >> >bend left in your car. What force acting on the car enables you to > > >> >> > > >> >> Reference frames, Paul. TomGee feels, TomGee is in, TomGee turns... > > >> > > > >> >> Who's making the measurement? A hypothetical 2nd observer > stationary > > >> >with > > >> >> respect to the Earth, or TomGee? > > >> >> > > >> >> In those three situations, TomGee is in an accelerated frame. If > > >> >TomGee > > >> >> is pushed to the left against a wall, there's an inertial force > > >> >pushing > > >> >> him to the left. A 2nd, inertial observer might say no, TomGee is > > >> >REALLY > > >> >> being pushed to the right, but so what? He's not in the car. He's > > >> >just > > >> >> asserting that there's something special about his reference frame > > >> >such > > >> >> that he can make valid observations but TomGee can't, and pretending > > >> >> there's no valid way to transform between them. > > >> >> > > >> >> Centrifugal force is called a force because it acts like a force. > It > > >> >will > > >> >> cause something to accelerate relative to the stationary observer > > >> >who's > > >> >> already pinned against the wall. The stationary observer is, of > > >> >course, > > >> >> spinning madly about if viewed by the hypothetical 2nd observer > who's > > >> > > > >> >> at rest relative to the Earth, but so what? There's nothing special > > >> >about > > >> >> the Earth frame, nothing wrong with the accelerated frame. If > TomGee > > >> >is > > >> >> pinned to the wall of a centrifuge, then TomGee is still at rest > with > > >> > > > >> >> respect to himself and he can define a reference frame from his > > >> >> perspective. > > >> >> -- > > >> > > > >> >Yeah, but I'm opposed to this kind of presentation, especially to the > > >> >uneducated. I really believe that forces should be taught as being > > >> >characterized by interactions between two objects, and those > > >> >interactions should be traceable to one of the four (or less) > > >> >fundamental interactions, and that forces are the cause and > > >> >accelerations are the effect. > > >> > > > >> I don't see anything in the formulation of newton's laws saying that > > >> forces must be traceable to fundamental interactions. What should be > > >> taught is that there are "physical forces" which are, indeed, a > > >> measure of interactions between objects, and there may be additional > > >> "inertial forces" which are an artifact of the choice of reference > > >> frame. But being an artifact, does not mean that they've no > > >> observable effects on motion relative to said reference frame. I see > > >> no reason to treat it as some sort of a dangerous knowledge that > > >> should be kept away from the uninitiated, else their mind may > > >> explode:-) > > > > > >Which is just another reason force should be considered as a secondary > > >concept - the PLA is the primary concept. End of rant. > > > > > Oh, the PLA most certainly is ***the*** primary concept. So primary, > > in fact, that it serves as foundation not only for Newtonian mechanics > > but (with appropriate generalizations) for most of physics. No > > argument about it. > > > > This said, the fact remains that, for applying the PLA, a level of > > mathematical knowledge and sofistication is required which is way > > beyond the capabilities of a beginning (high school) physics student > > and, in fact, way beyond this that most people ever reach. So, we > > maintain forces as a crutch to be used till more is learned. That's > > really their remaining role. > > Most certainly. But if we are to use forces then I think we need a > discussion of what they really mean along the lines of what Feynman did in > the lectures. In fact I consider that to be compulsory reading even for > grade 8 students (at least the chapters they have the mathematics to > understand - other chapters can be added as their mathematical knowledge > grows). Having understood what Feynman wrote I think a lot of confusion can > be avoided. In my case I always wondered why a definition could be a law. > It confused me for many years until I read a rather nifty old book on > classical mechanics. It clearly explained the real import of Newton's Laws > was in his third law. That was the start of actually understanding what was > happening. The full resolution came with Landua - Mechanics. I think it > would be great if students did not need to go through this process and were > taught what was happening right form the start - at least as much of it as > they can initially handle. > > Thanks > Bill > IMHO, the number-one problem students have in physics is making a connection between physics and reality. You can appeal to them about what they've all seen about the flight of a baseball, and then you ask them to draw the trajectory of a fly ball in a physics problem and you get straight lines, you get trajectories with corners, you get crazy stuff. And I've *asked* them, "You've been to baseball games, right? Does this look like what you see?" And they'll look at me blankly and say, "But this doesn't have to look real. It's physics." The number-two problem is ill-formed and overlapping concepts, like distinguishing displacement, acceleration, and velocity in the catch-all "to go", or the distinction between force, momentum, kinetic energy, and power. Teaching students to be careful and precise in their definitions is asking a lot of them. The number-three problem is pre-existing misconceptions, like thinking that a bullet falls to the ground because it is slowing in flight. None of these would be addressed by pulling out a Power Tool, making a Tim-Allen guttural grunt, and saying, "Now THIS is REAL physics!" IMHO, we do our students a service by teaching them to * check against their intuition * recast their intuitive ideas with carefully defined terms * recognize places where the edges of their intuition are a little fuzzy * be rigorous in making explicit predictions they can check with observation, and thereby incorporate those observations into an expanded intuition. To me, this is teaching them to think like a physicist. PD
From: PD on 29 Mar 2005 13:25 TomGee wrote: > PD wrote: > > TomGee wrote: > > > Wormy, Bilge, PD, and all you other lemmings, > > > > > > you cannot understand that it is the _measurement_ of the force > which > > > is fictional and not the feeling of being pulled out as a carousel > > > spins. > > > > Nope. You feel the force pulling you *in*, which is a force you are > > unaccustomed to, and so you mistakenly associate that with a force > > pulling you out. Your naive interpretations are what's tripping you > up. > > > > > Next time you're on a carousel, PD, let go and fall in toward the > center ofit, ok? Now, if I let go and my head and shoulders go in a straight line, and my feet that are pulled toward the center by the friction with the surface of the carousel, what's going to happen? > I am glad you agree that it is the measurements which > are fictional and not the force (though Otherwise you would have made > some attempt at disagreeing with that, right?). > > > > > > Let me ask you another question. As an elevator suddenly starts to > > descend, you feel lighter. Are you in fact lighter? Why should > Earth's > > gravity pull on you less just because the floor of the elevator > started > > to go down? Answer this one, Tom. > > > > Let me ask you another question. You are on a road making a circular > > bend left in your car. What force acting on the car enables you to > > change your straight-line motion? You hit an icy patch in the middle > of > > the turn. What happens to your car? Does it go *straight* or does it > go > > *outward*? What force has disappeared when you hit the icy patch? Answer this one, Tom. > > > > > You cannot make the force disappear just by invalidating your > > > own measurements. You should not think that websites are the > > ultimate > > > authority on anything, either, as subjective opinion runs rampart > all > > > through it. > > > > Which is why I reference textbooks, Tom. Which you refuse to read. > > > > > No, I don't. I already read them, and they did not support your > claims. You are so full of ****. Write down the 2nd, 3rd, 4th words on the second line of page 938 of Fishbane, Gasiorowicz, Thornton, 3rd edition, if you've read it. > > > > > > > You will learn that, Bilgy, when if ever you get to the > > > fifth grade. > > > > > > > You call us lemmings, Tom, but we're pointing out things that really > > are basic, classical physics. > > > > > No, you're not. Your claims are even wilder than mine, and you refuse > to support them. Your interpretations of common terms are so far off > that they don't even make sense. That is because you only read > opinionated wefsites claiming to be factual Like what? I've been referencing books and articles, not websites. > when they are > misinterpretations of the facts. And you with the others fell right in > step without looking for the flaws in the fallacious claim that because > the measurements are false, the force is false as well. > > > > > > If you want to uproot that, then > > advertise that what you're doing is uprooting not only special > > relativity, but also Newtonian physics, classical kinematics, and > just > > about everything else too. But if you don't want to claim that, then > > learn a little physics so you know where the dividing line is. > > > > > But it is you, PD, who needs to learn a little physics more than I do > since you seem to always get it wrong. > > TomGee
From: TomGee on 29 Mar 2005 14:25
Yes, PD, but none have anything to do with our subject specifically nor do they support your claims. TomGee |