What keeps electrons spinning around their nucleus?
in [Relativity]
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From: mmeron on 28 Mar 2005 19:20 In article <d2a0ma0td8(a)drn.newsguy.com>, stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: >mmeron(a)cars3.uchicago.edu says... >>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. > >To me, the part that is misleading is the treatment of *acceleration*. >The use of "inertial forces" amounts to defining acceleration to be >the quantity > > A = e_i d/dt V^i > >instead of defining it to be > > A = d/dt (e_i V^i) > >If you use the first definition of "acceleration", then you >have to introduce fictitious forces in order to preserve F = mA. >If you use the second definition, then no fictitious forces are >needed. I think that for more advanced physics, it is a mistake >to equate a vector with its components, which is what is happening >in defining acceleration component-wise as A^i = d/dt V^i. > For more advanced physics you write the Lagrangian and solve the resulting equations of motion, and forces become an unimportant concept (as Bill Hobba mentioned), so it is a moot point. Still, in practical terms, you'll often choose, even then, a non-inertial reference frame and you'll like your answers to be relative to same frame as well. In such case, it'll be a waste of time and effort to transform to an inertial frame and back and, assuming you already chose to work in the accelerated frame, it'll be a waste of mental energy to keep mumbling to yourself "terms 2 and 4 are not really forces, I just pretend they're":-) Take the simple problem of calculating the impact point of a projectile fired from some point at Earth with some initial velocity form some point P, (ignoring, for convenience, both air resistance and the motion of the earth around the Sun). So, is anything gained in the process by first picking an inertial frame with an origin momentarily coinciding with P at the launch moment, calculating the initial velocity in this frame (by adding the momentary velocity vector corresponding to the earth rotatoin, at the elevation and geographic latitude of P, then solving the orbital equation of motion, finding at what location (relative to the inertial frame) the trajectory crosses the Earth surface, then translating this location to a location in the Earth coordinates (taking into account how much the Earth rotated in the meantime). Sure, you can do it. But, why? It is much simpler to work in a frame corotating with the Earth, all across. Sure, you'll have additional terms, centrifugal (gasp, the horror) and Coriolis forces, but it is still simpler. Seeing how Landau wasn't above mentioning both centrifugal and coriolis forces in his Mechanics, is see no reason for purism here. Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: Bill Hobba on 28 Mar 2005 19:29 <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 > > Mati Meron | "When you argue with a fool, > meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: Bill Hobba on 28 Mar 2005 19:34 <mmeron(a)cars3.uchicago.edu> wrote in message news:XQ02e.15$45.3352(a)news.uchicago.edu... > In article <d2a04r0riu(a)drn.newsguy.com>, stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > >mmeron(a)cars3.uchicago.edu says... > > > >>There is ***nothing*** wrong with centrifugal force. The term > >>"fictitious" is misleading. True, it doesn't stem from interaction, > >>just from choice of reference frame. So? It is quite often convenient > >>to deal with a problem in an accelerated frame, rather than transform > >>to an inertial frame and back. And when you want to deal with a > >>problem in the accelerated frame and still use Newton's laws, you > >>include inertial forces (i much prefer the term "inertial" than the > >>misleading "fictitious"). > > > >I don't think that there is anything wrong with using noninertial > >coordinates, but I think what is misleading is to call the correction > >terms "forces". > > Only if you attach more meaning to the term "force" than it deserves. Ahhhhhh. Yes. As Feynman says it is half a law. It gains its full meaning when combined with other laws and/or concepts such as Coulombs law or the introduction of non inertial reference frames. Thanks Bill > > > >I know that's just terminology, but the way I see it, inertial > >forces result from using noninertial coordinates, but *pretending* > >that they are inertial. > > Yeah. So? > > > What I mean is this: Noninertial coordinates > >mean that your basis vectors e_i are not constant. So if you define > >the acceleration vector A to be the time derivative of the velocity > >vector V, you get > > > > A = d/dt V > > = d/dt (V^i e_i) > > = e_i (d/dt V^i) + V^i (d/dt e_i) > > > >The use of "fictitious forces" amounts to pretending that > >the second term is a *force* term, rather than what it really > >is, an *acceleration* term. If we start with > > > > F = m A > > > >and move the second term to the other side of the equation, we get > > > > F - m V^i (d/dt e_i) = e_i (d/dt V^i) > > > >and then the extra acceleration term looks like an extra force term, > >if we define > > > > F_inertial = - m V^i (d/dt e_i) > > > >So, while I agree with you that using noninertial coordinates can be > >convenient, there really is no *convenience* benefit to treating the > >extra term as a fictitious force, instead of what it is, an acceleration > >term. > > > Now, why should I make a distinction. I'm solving an equation of > motion, meaning my goal is to obtain r(t), not some "inner truth". > And, in the equation of motion I've various terms, some resulting from > interactions, other from my choice of reference frame, but all > entering at the same standing and treated the same. So, I would say > just the opposite to what you said above, namely that there is > *absolutely* no benefit in treating the extra term as something > different, instead of just as forces. > > Mati Meron | "When you argue with a fool, > meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: mmeron on 28 Mar 2005 19:44 In article <Rj12e.16030$C7.2138(a)news-server.bigpond.net.au>, "Bill Hobba" <bhobba(a)rubbish.net.au> writes: > ><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. > Well, here is the rub, how much they can initially handle. For most of them the answer is "not too much". Keep in mind that education is, by and large, a processes involving quite average students being taught by quite average teachers. I've no doubt that if you'll pick the cream of the crop of high school students, top 1-2%, and hand them to a teacher of Feynman's caliber, you'll see some truly amazing results. Unfortunately, you cannot use this as a general purpose model:-( That said, there is certainly room to analyze the way things are being taught. The natural tendency is to teach things in the historic order in which they were developed (an educational equivalent of "ontogeny recapitulates philogeny"). That may not necessarily be the best course of action. Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: mmeron on 28 Mar 2005 19:48
In article <Mo12e.16031$C7.902(a)news-server.bigpond.net.au>, "Bill Hobba" <bhobba(a)rubbish.net.au> writes: > ><mmeron(a)cars3.uchicago.edu> wrote in message >news:XQ02e.15$45.3352(a)news.uchicago.edu... >> >coordinates, but I think what is misleading is to call the correction >> >terms "forces". >> >> Only if you attach more meaning to the term "force" than it deserves. > >Ahhhhhh. Yes. As Feynman says it is half a law. It gains its full meaning >when combined with other laws and/or concepts such as Coulombs law or the >introduction of non inertial reference frames. > Yes, it is a rather complex issue. I wrote some stuff about it in the past, here, but I never kept a copy. But it certtainly needs some sort of broad framework, to make sense. Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same" |