For all you physics gurus

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AuthorTopic: For all you physics gurus
Master
Member # 4614
Profile Homepage #25
No, I'm just trying to understand these important concepts for an online physics course. I would try to talk to the online professor or whatever, but I really don't see the point in bothering when I have all these experienced students at hand to help.

Whether or not I get the right answer to these particular questions has very little effect on my standing in the course.

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-ben4808
Posts: 3360 | Registered: Friday, June 25 2004 07:00
Law Bringer
Member # 335
Profile Homepage #26
I think you calculated tension wrong. The forces on the inclined plane block are:

F = 2ma = 2mg*sin30-2umg*cos30 - T
So T = 2mg*sin30-2umg*cos30 - 2ma

Your signs aren't quite the same, but there's an easier way to do this.

Gravity only affects the block on the inclined plane, which pulls the other block right and is in turn pulled left by that block. Therefore you know the two blocks are experiencing the same acceleration.

Treat each block separately. F is the force on a block, u is the coefficient of friction (0.2), and T is the tension in the rope.

For the block on the flat plane:
F = ma = T - umg

For the block on the inclined plane:
F = 2ma = 2mg*sin30 - 2umg*cos30 - T

Add these equations together:

3ma = 2mg*sin30 - u*(2mg*cos30 + mg)

a = 1.48 m/s^2

(Check math on this one!)

—Alorael, who knows your way would work too if you keep your directions and signs straight. It's just probably easier to leave T out.
Posts: 14579 | Registered: Saturday, December 1 2001 08:00
Electric Sheep One
Member # 3431
Profile #27
I'm teaching electrodynamics at the moment, and this morning shortly before my first lecture on magnetostatics I made the shocking discovery that the nice conceptual progression from the Lorentz force to the Biot-Savart law was the exact opposite to the historical development. Biot and Savart found the correct expression for the magnetic field produced by a steady current, already in 1820. The correct force on a charge moving through a given magnetic field was first written down by Lorentz in 1892.

In between were such momentous events as the bold hypothesis by Hertz, in 1872 or so, that electric field generated by changing magnetic field is electric field, period; it is precisely the same thing that gets generated by electric charge. It boggles my mind to try to see how this apparent tautology could possibly have constituted an insight, but at the time it surely did. Man, were people confused back then! Just as we are today, about different things. Sometimes, in fact, about the same things.

And, alarmingly, magnetic forces by themselves are frame-dependent, and do not respect Newton's second law (equal and opposite actions and reactions). Or rather, they are a counterexample to the usual rule that Newton's mysterious 'action' really just means 'force'. Somehow I never quite absorbed this last point in particular, back when I was first learning this stuff myself. Textbooks generally waft deftly over these questions, and I can see why.

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Off With Their Heads
Member # 4045
Profile Homepage #28
The backwards-ness of the historical development of E&M has been commented on several times during my upper-division E&M class this semester. It definitely has bothered me that the Lorentz force law came after Maxwell's equations. You'd think that Maxwell's equations would've been the final, culminating summary, after just about everything else was known, but no.

It's also kinda odd that E&M already takes into account Galilean invariance (the frame-dependent thing), which no one really cared about until relativity in 1905. It really could've gone the other way: the principles of relativity in the low-speed limit require that E&M be formulated the way that it is. But no, it happened the other way around.

It has bothered me since high school physics that there's no simple Coulomb's Law for magnetism, that the nearest equivalent we have is the Biot-Savart Law, and that magnetism has to be formulated with these stupid dipoles and current loops. But that evidently is not just some historical coincidence but actually the way that nature works, so I can't complain too strenuously.

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
Infiltrator
Member # 4256
Profile #29
Wasn't Maxwell motivated mostly by 'Ether' in his theory (at least in his emendation of Ampere's law)? The impression I got from the two undergrad E&M courses was that he got rather lucky that his theory was even correct, as he had little to no interest in the concepts that actually proved to be true and important. (for instance charge conservation)

As far as the Magnetism goes, there should be an equivalent to the Coulomb law, but it has/would have no practical use without monopoles.

SoT, what textbook are you teaching from?

Edit: Actually, according to this that wasn't his motivation, but rather an attempt to argue against 'action at a distance' which still sounds like something that he would have used ether to explain.

[ Wednesday, November 28, 2007 12:07: Message edited by: Sticky ]

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"Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'."
Posts: 564 | Registered: Wednesday, April 14 2004 07:00
Off With Their Heads
Member # 4045
Profile Homepage #30
Lorentz was going by the ether theory, IIRC. That's what the Lorentz transformations in relativity originally were.

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
Electric Sheep One
Member # 3431
Profile #31
In principle I'm supposed to be using Jackson, but so far I'm actually using a combination of Nolting (German) and Reitz, Milford and Christie.

The history of electrodynamics in the 19th century is apparently a total minefield. I had always thought this stuff was pretty simple, and in the rationalized reconstruction that one is supposed to learn in courses like mine, it is, at least by modern standards in physics. But how people actually came up with this stuff historically is quite another story.

Yes, there was all that ether stuff, for most of the time. But I don't think it really made all that much difference. Late in the century someone apparently observed that the only real function of the ether was to provide a subject for the verb 'to oscillate', and as far as I see this was a sound insight. People were not much attached to any particular notion of what the ether was like. They made careful observations, and formulated mathematical theories of fields that could reproduce them. Then they felt obliged to construct material models of a space-filling substance whose mechanical stresses and vibrations would in turn reproduce their field theories. But experiments and field equations between them were doing all the actual physics.

Did anyone really believe in the ether? I'm not sure. From an old popular book I once read, I believe everyone acknowledged that it was only an unproven working hypothesis. It was a motivation for some work, and an apparently obligatory afterthought for most. Eventually it became clear that ether models were both extraordinarily difficult to construct and essentially irrelevant. Yet there was no really damning evidence that there did not exist some very peculiar form of ether. So the proposal that there was no ether at all would really have been just as irrelevant to actual physics as any other ether model. Denying the ether would not have been bomb-throwing radicalism, but pipe-smoking punditry.

An invisible material medium is not so hard to believe in, after all, since we are all familiar with air, wind and sound. To entertain one further invisible medium would not be hard in an age that was discovering many new substances. To state as we do now, that electric and magnetic fields are not made of anything else, but are themselves fundamental entities alongside matter, might well have seemed a greater violation of Ockham's Razor than the ether was, since it introduced an apparently unnecessary new category of fundamental objects, rather than just one more object of an established class.

I think that perhaps the first person to really take electromagnetic fields completely seriously as fundamental objects in their own right may have been Albert Einstein. Instead of thinking of the fields as being made of something material, he thought of matter as made of them; and this led him to change space and time themselves in order to make all of physics agree with Maxwell's Equations.

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Infiltrator
Member # 4256
Profile #32
Yeehaw, got my first abstract sent to APS yesterday. A small step towards... who knows what.

Anyways, if you're supposed to be teaching from Jackson, are you teaching a grad level course? I've never heard of undergrads being taught from Jackson, but for some reason I always thought of you as a grad student yourself, or perhaps a post-doc student. Are you an assistant professor or something now? Or have you always been that, and I was just delusional.

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"Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'."
Posts: 564 | Registered: Wednesday, April 14 2004 07:00
Electric Sheep One
Member # 3431
Profile #33
I've been a professor for three years now. Before that I was a post-doc for an unusually long time. (Post-docs aren't students, by the way, but junior researchers on fixed term contracts.)

Jackson is fairly common for senior undergrad courses, though usually the whole book isn't covered. And the German system is kind of different from the North American. Students often cover essentially the same material twice, once in a course taught by an experimentalist professor, then in a course taught by a theoretician. The perspective is expected to be more advanced in the theory version, but the subject matter generally overlaps a lot. I'm not sure yet whether this is excellent pedagogy or appalling inefficiency.

[ Thursday, November 29, 2007 04:00: Message edited by: Student of Trinity ]

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Off With Their Heads
Member # 4045
Profile Homepage #34
quote:
Originally written by Student of Trinity:

Yes, there was all that ether stuff, for most of the time. But I don't think it really made all that much difference. Late in the century someone apparently observed that the only real function of the ether was to provide a subject for the verb 'to oscillate', and as far as I see this was a sound insight. People were not much attached to any particular notion of what the ether was like. They made careful observations, and formulated mathematical theories of fields that could reproduce them. Then they felt obliged to construct material models of a space-filling substance whose mechanical stresses and vibrations would in turn reproduce their field theories. But experiments and field equations between them were doing all the actual physics.

Did anyone really believe in the ether? I'm not sure. From an old popular book I once read, I believe everyone acknowledged that it was only an unproven working hypothesis. It was a motivation for some work, and an apparently obligatory afterthought for most. Eventually it became clear that ether models were both extraordinarily difficult to construct and essentially irrelevant. Yet there was no really damning evidence that there did not exist some very peculiar form of ether. So the proposal that there was no ether at all would really have been just as irrelevant to actual physics as any other ether model. Denying the ether would not have been bomb-throwing radicalism, but pipe-smoking punditry.

You know, I'd be inclined to believe this, except that all of my textbooks say something rather different. If I may quote Griffiths at you, in the part in which he describes the term that Maxwell added to Ampere's law:

"[i]n Maxwell's time there was no experimental reason to doubt that Ampere's law was of wider validity [than just in magnetostatics]. The flaw was a purely theoretical one, and Maxwell fixed it by purely theoretical arguments.... (Maxwell himself had other reasons for wanting to add this quantity to Ampere's law. To him the rescue of the continuity equation was a happy dividend rather than a primary motive. But today we recognize this argument as a far more compelling one than Maxwell's, which was based on a now-discredited model of the ether.)"

As far as I can tell, that means that Maxwell's reason for adding the term was primarily his own model of the ether, not experiments or some general view of the way that fields work.

IIRC, the paper that Michelson and Morley published on their experiment that disproved the ether said that they had failed to detect it, but they must have just not had sensitive enough measurements. Even when they did the definitive test that people later cited as disproving the ether, they believed in it enough that they didn't disregard it.

While getting rid of the ether concept didn't actually destroy all of physics up to that point, I think it was a fairly radical notion. Enough people believed in the ether enough that the formulation of physics without it was a significant step.

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
Electric Sheep One
Member # 3431
Profile #35
I'm not really any kind of expert on this chapter of physics history. Maxwell himself probably did believe in the ether, with at least a fair degree of seriousness, because he went out of his way to describe it in startling terms as (I paraphrase a passage from memory) "the largest object in the creation". Thinking of it as a thing, rather than a substance, is to me a sign that he really took it seriously. But I also read a popular science chapter from about 1902 which clearly presented ether as an unproven hypothesis. I figure that if this viewpoint had reached that level then, it must have become common in scientific circles, if perhaps not universal, a generation earlier.

And I wouldn't be so quick to distinguish between Maxwell's commitment to his ether models, and his interest in current continuity. I would think that his ether models (about which in fact I know nothing) were probably constructed to have continuity built into them, so that his faith in his models would to some extent have been based on his faith in continuity.

As I said, people drew inspiration from ether theories, and Maxwell was certainly the leading example of this. But only a few years after his theory was published, Hertz could declare, as he tried to judge empirically between rival electromagnetic theories, that 'Maxwell's theory is Maxwell's equations'. The equations were clearly testable, and the ether models that supposedly underlay them were irrelevant.

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
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Profile #36
Random break from studying for a question! Does QFT ever incorporate general relativistic mechanics at all? There seems to be some inconsistencies. Is there some name to theory that combines the two? There probably is little to no application of such theory, though from a simple google search, in the 70's someone found it significant to gravitational research.

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"Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'."
Posts: 564 | Registered: Wednesday, April 14 2004 07:00
Off With Their Heads
Member # 4045
Profile Homepage #37
Heh.

Well, to be a little bit more plain: There is actually a fairly significant need for a good theory that combines QFT and GR (a quantum gravity theory). That need is in, for example, the field of astrophysics, in which we basically fail at describing the interior structure of a black hole (for instance) or what happened in the first few fractions of a second after the Big Bang.

But how on earth are you deep enough in this material to know that there are inconsistencies and yet not deep enough to know what I just said? :P

[ Tuesday, December 04, 2007 20:52: Message edited by: Kelandon ]

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
Electric Sheep One
Member # 3431
Profile #38
GR mechanics, no: there are horrible problems. Curved spacetime as a static background: sometimes, at least. The results from this are very interesting (poster child: Hawking radiation).

The problem is that, deep down, quantum mechanics lives in Hilbert space, and evolves only in time. Hilbert space and time evolution are the OS of quantum mechanics; space is a feature of some of the apps that it can run.

In GR space and time are on an equal footing, and there is in general no preferred notion of exactly which spacetime direction is Time. Except in cases with a lot of symmetry, there is no unique global concept of time, even modulo some finite-dimensional transformation group, along which the entire universe together evolves.

So this pretty much stinks. GR is a classical theory, and while we've had good luck translating all other classical theories into quantum versions, GR seems to conflict fundamentally with QM in its treatment of space and time.

There are a few practical consequences to our ignorance about the resolution to this apparent paradox, for example in the early universe or in small black holes. More important though is the issue of principle: the discrepancy between QM and GR is so profound, that it means we simply do not really understand space or time or anything, at all. Resolving the paradox would almost certainly require a revolutionary change in our understanding of reality.

Or so those of us hope, at least, who want the good time to roll again in our lifetimes.

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
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Profile #39
quote:
Originally written by Kelandon:

Heh.

But how on earth are you deep enough in this material to know that there are inconsistencies and yet not deep enough to know what I just said? :P

I'm not! Though those do sound like the high energy density situations where the inconsistencies are supposed to arise. In fact, I'm barely into a differential geometry book, and only using it because because some of the basic theorems are good for (and provable from) the simpler needs of a differential analysis class. That, an overdose of μν notation, and browsing through the QFT book off the bookshelf of the guy I share an office with, inspired the question. Besides, its just interesting stuff, since its an issue that isn't resolved.

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"Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'."
Posts: 564 | Registered: Wednesday, April 14 2004 07:00
Off With Their Heads
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Profile Homepage #40
It's interesting, for sure, but since I've never seen real QFT and have only glimpsed real GR, it's a little hard to follow the issues in more than a purely conceptual way.

It was a revelation when my quantum professor pointed out one of the reasons why basic quantum mechanics is not compatible with special relativity (and thus we need QFT): If you localize a particle by measuring it and then wait an arbitrarily short amount of time, the Schrodinger Equation predicts a finite probability of it being arbitrarily far away. That probability is incredibly small, but it is non-zero, and that means that basic QM predicts that particles have some chance of traveling faster than light. This is no good.

Obviously, there are other, more fundamental problems, but the thing that made that one cool was that it was an equation that I knew and a result that I could actually calculate.

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
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I've been taking a QFT course this semester, which has been awesome, but we haven't come anywhere near discussing gravity and why it doesn't work well with QM. It's a little disappointing, because I'd really like to know about that stuff, but there's just so much background necessary.

I'm also becoming quite confused about some of the stuff with string theorists and so forth suggesting that the universe is 9, 10, or 11 dimensional. From the QFT I've seen so far it matters a lot how many dimensions you have, and the simplest theories break completely and become unusable if you move them to the wrong number of dimensions (since we're doing scalar fields this semester we've done almost everything in 6 dimensions in my class because the really simple theory we've been working with only works properly in 6 dimensions). From what my professor tells us, though, theories of spin 1/2 fermions and the like work best in 4 dimensions, so I'm not sure how these suggestions of much higher number of dimensions are supposed to keep them working properly.

As an aside: My spellchecker thinks that 'fermions' should be 'freemasons'.

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Überraschung des Dosenöffners!
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Posts: 627 | Registered: Monday, March 7 2005 08:00
Electric Sheep One
Member # 3431
Profile #42
It's true that the Feynman propagator does not vanish outside the light cone. But this is not actually a problem. Relativistic quantum mechanics exists and is perfectly compatible with special relativity. It's just that you have to learn a new understanding of what particles are. Then you realise that the hypothetical problem of having a particle certainly localized in one region, then unambiguously detected in another, is not really physical. It involves naive assumptions about the process of particle detection which themselves violate special relativity. These violations are local to the detector, and have nothing to do with how things may reach the detector from distant places. Remove these flaws and consider a fully relativistic detection process, and the possibility to obtain acausal detector clicks miraculously disappears.

The details are not trivial, and although both profound and interesting are not well covered in any book I know, because like everything else in interacting QFT, they are appallingly complicated for such a simple question.

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We're not doing cool. We're doing pretty.
Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Electric Sheep One
Member # 3431
Profile #43
Dimensionality matters a lot in QFT, because it controls just how infinitely many are the short-distance degrees of freedom present, and thus how important they are in comparison to the long-wavelength modes. In my own recent and upcoming stabs at teaching QFT I've chosen to stick with QED in 3+1 dimensions. My feeling is that I've got to get there eventually, so I may as well just go straight to it. The big disadvantage with this approach is that you have to learn to quantize a gauge field, which is quite tricky, before you can really do anything else. You're also dragging around all the vector and spinor indices from the beginning. So far I still think it's worth it, to be able to talk about real phenomena that the students already know, right through the course.

I'm also old-fashioned in spending a fair while at the beginning with Hamiltonian operators and Hilbert spaces, rather than rushing into path integrals and Feynman diagrams. It quickly shows students why Feynman's specialized formalisms are worthwhile. It is just gruesome to compute the simplest things. But it also makes a few important things much more clear, if you already understand basic QM.

For instance I believe I can clearly explain so-called (and badly called) 'wave function renormalization', which is pretty much dealt with in all the texts I know by saying, 'Look, a monkey! And now we have a factor of Z!' The better ones are the ones that follow their lousy argument for it with a short paragraph admitting that it's lousy, then shuffling their feet and mumbling.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
Off With Their Heads
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quote:
Originally written by Student of Trinity:

For instance I believe I can clearly explain so-called (and badly called) 'wave function renormalization', which is pretty much dealt with in all the texts I know by saying, 'Look, a monkey! And now we have a factor of Z!'
Ah, the monkey argument. I am well familiar with it. :P

Out of curiosity, how deep into a physics education does one normally encounter QFT? I get the feeling that it's not taught in any undergrad course here at Cal. Is it a first- or- second-year graduate sort of thing, or is it later than that?

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
Electric Sheep One
Member # 3431
Profile #45
Not sure. I first took a formal course in it as a PhD student, after finishing a Master's. But you pretty much have to do non-interacting QFT in any relativistic QM course, since the basic relativistic wave equations actually make no sense as single-particle Schrödinger equations. So this baby step of QFT is often offered as a first-year grad school course. It's pretty hard to squeeze it into undergrad, since usually people are just getting through something at the Cohen-Tannoudji level by senior year.

It's turning on even weak nonlinearity that makes QFT really brutal. You try a trivial computation, like the leading perturbative correction to the ground state energy, and you discover it diverges. Understanding what this really means, and why it's actually not at all the end of the world, is quite hard. In my experience only a minority among people who have been using QFT in research for years fully understand what they are doing. Learning QFT seems to be a task more on the scale of learning Latin than of learning Lagrangian mechanics. One course will only scratch the surface.

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Posts: 3335 | Registered: Thursday, September 4 2003 07:00
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Here, the full blown course is a '7000' level course, which would fit with SoT's description of post-masters, or second year at earliest.

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"Let's just say that if complete and utter chaos was lightning, he'd be the sort to stand on a hilltop in a thunderstorm wearing wet copper armour and shouting 'All gods are false'."
Posts: 564 | Registered: Wednesday, April 14 2004 07:00
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Profile Homepage #47
As I study for my E&M final, this bothers me yet more. Without the Lorentz force law, what the hell did anyone think these fields meant? I mean, I'm told that quantum and relativistic electrodynamics attribute a great deal of reality to the fields as entities unto themselves (they have energy, momentum, etc.), but lacking that, the fields exist only to create forces. But without the Lorentz force law, you don't know how the fields actually create forces.

They must've had a primitive version of the Lorentz force law before they had the real thing. That's the only plausible explanation I can manage. Otherwise, the fields they were working with were meaningless.

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Arancaytar: Every time you ask people to compare TM and Kel, you endanger the poor, fluffy kittens.
Smoo: Get ready to face the walls!
Ephesos: In conclusion, yarr.

Kelandon's Pink and Pretty Page!!: the authorized location for all things by me
The Archive of all released BoE scenarios ever
Posts: 7968 | Registered: Saturday, February 28 2004 08:00
Electric Sheep One
Member # 3431
Profile #48
Well, they could measure electrostatic forces with small objects charged by friction. And they could measure magnetic forces between permanent magnets, or (after 1820) between current loops. And the pattern of iron filings around a bar magnet, for instance, certainly suggests some sort of field picture.

Whether the forces were in fact attributed to local fields, or to direct non-local forces, was a matter of philosophic prejudice, until Faraday's discovery of induction. Once Maxwell's displacement current was added, it was very clear that the fields had their own energy, momentum, and so on, and were not simply bookkeeping devices for forces acting instantaneously over distance.

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