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Why is Maxwell's theory so hard to understand? (2007) [pdf]

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Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#41

Post by tntn »

srean wrote: post #35
tntn wrote: post #15

Earlier quoted context omitted.

Quaternions are not a "model of vectors." Maxwell used per coordinate equations and quaternion equations, but never wrote out what are now known as "Maxwell's equations," which were first formulated by heaviside using Gibbs-Heaviside vector calculus. Gibbs-Heaviside vector calculus formulations proved far more valuable to engineers and scientists than the equivalent quaternion formulations - despite the criticisms fr…

> Quaternions are not a "model of vectors. I dont think I agree. Yes they are not the Gibbsian vector but they are a pretty damn good model of what we want to model as vectors. Its already a little closer to geometric algebra / calculus than Gibbsian vectors. Its a pity that Grassman and Clifford's work gained attention much later. Once javascript is out of the bag one cant do much about it. Thats how I feel about Gi…

I think geometric algebra is a very cool and elegant approach as well, but it has not yet proved useful or valuable to working engineers.

If we want to compare to programming languages, perhaps Haskell vs. C. One is beautiful and elegant, the other is down to earth and conceptually simple for "normal" people. One is primarily used by academics and researchers, the other is used to build the world. Both are admirable.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#42

Post by hopler »

NotAnEconomist wrote: post #20
bsder wrote: post #18

People didn't really get Maxwell because Maxwell's equations don't need a medium aka "aether". Waves propagating without a medium is a shocking message in this time frame. Maxwell published his equations in 1861/1862 in first form. In 1887, the Michelson–Morley experiment gave the first experimental disproof of the "aether". It also doesn't help that you have things like "displacement current" and have to find strang…

> In 1887, the Michelson–Morley experiment gave the first experimental disproof of the "aether". In what way is LIGO not a bigger, and successful, version of the Michelson-Morley experiment? I'm honestly asking, because from my limited understanding, it seems to be. From Wiki: > This result is generally considered to be the first strong evidence against the then-prevalent aether theory, and initiated a line of resear…

Ether is an independent absolute entity, and other objects move relative to it. Per GR, spacetime is an embodiment relations between objects, not an independent absolute entity.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#44

Post by srean »

tntn wrote: post #41
srean wrote: post #35

Earlier quoted context omitted.

> Quaternions are not a "model of vectors. I dont think I agree. Yes they are not the Gibbsian vector but they are a pretty damn good model of what we want to model as vectors. Its already a little closer to geometric algebra / calculus than Gibbsian vectors. Its a pity that Grassman and Clifford's work gained attention much later. Once javascript is out of the bag one cant do much about it. Thats how I feel about Gi…

I think geometric algebra is a very cool and elegant approach as well, but it has not yet proved useful or valuable to working engineers. If we want to compare to programming languages, perhaps Haskell vs. C. One is beautiful and elegant, the other is down to earth and conceptually simple for "normal" people. One is primarily used by academics and researchers, the other is used to build the world. Both are admirable.

> has not yet proved useful or valuable

They would have, had they been the "first mover". Hence my Javascript analogy

Had a better language been released at that time it would have been just as useful and valuable. In fact much more so. But as is usual, a "worse_is_better" first mover accrues so much head start in the mind share and in the tooling / literature that it becomes impractical to switch, especially when both can express the same set of things (just that one does it more concisely than the other). Another shallower example: imperial vs metric units.

I dont think its like Haskel::C at all. Haskell is way more mathy and has a steeper learning curve than C. One who can master curl divergence and vector stoke's theorem can master geometric algebra with less effort

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#45

Post by aj7 »

Say what? Start with the integral representations of the equations a la Halliday and Resnick. You can do tons of useful problems. Once you understand vector calculus, you will understand the equations as written in differential form. Then, pick up a copy of Purcell to see how magnetism comes out of the Lorentz transformation of electrostatics. If you are mainly interested in applied problems, go through Corson and Lorraine. Finally: 1. Realize that the treatment of ferromagnetism is much too limited in most E&M texts. 2. Optics is also worthless in those books. It is a field unto itself, with theoretical, applied, and quantum parts all handled by different books. 3. You don’t use Feynman’s Lectures to learn anything the first time. You use them to see if you understand physics as well as Feynman (you don’t.). All the problems have to have been done BEFORE this step.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#46

Post by aj7 »

hopler wrote: post #37
gumby wrote: post #6

I am struck by the clarity and simplicity of Dyson's writing. As to the substance: yes, hiding your work under a bushel does nobody any favor, but it's understandable when it feels like the alternative is the strident trumpeting of trivial "advancements". But also cautionary is the constraints due to the wrong metaphors. We often see this today in linear predictions as to the impact of some new idea. It's easy to moc…

Why would you say Apple, whose main business was an extensive traxk record in creating, promoting, and selling next generation technology, that their major investment in a new field was blind speculation? In contrast to Microsoft whose business was providing stable solutions and extracting monopoly rents.

This is (1) False, or a venomous mid-80s position. (2) Irrelevant to the theory of electromagnetism.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#48

Post by aj7 »

nonbel wrote: post #16
wmnwmn wrote: post #14

E&M is far from "simple". It contains special relativity, for starters. Also it is incompatible with thermodynamics: solving this problem is why Planck invented quantum mechanics. Also point charges have infinite energy: this problem leads to renormalization theory. Also it introduces gauge invariance, an essential but complex part of all modern theories. And lastly, the mathematics of E&M is a big step up from Newto…

>"E&M is far from "simple". It contains special relativity, for starters." A theory (which is just a set of assumed first principles and rules of logic) can be simple but allow you to deduce vast complexity from it. In fact, it is ideal for a theory to be as simple as possible. The "game of life" is not really a theory, but it demonstrates that simple rules can lead to surprising complexity: https://en.wikipedia.org/…

I reflexively downvote the game of life. I have never heard of a single useful application or analogy of “finite automata.” Yes, there are speculations about extremely small Planck lengths, by no new physics has panned out. Finally I am sad that one of the greatest computer scientists and polymaths, Ed Fredkin, got sucked into this. We all have weaknesses.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#49

Post by twtw »

aj7 wrote: post #45

Say what? Start with the integral representations of the equations a la Halliday and Resnick. You can do tons of useful problems. Once you understand vector calculus, you will understand the equations as written in differential form. Then, pick up a copy of Purcell to see how magnetism comes out of the Lorentz transformation of electrostatics. If you are mainly interested in applied problems, go through Corson and Lo…

You seem to be responding to the title, not the essay.

Dyson describes the theory as "simple and intelligible" once you accept the concept of fields, which was very much foreign in Maxwell's time.

Re: Why is Maxwell's theory so hard to understand? (2007) [pdf]

#50

Post by ncmncm »

scabarott wrote: post #40
ncmncm wrote: post #27

Earlier quoted context omitted.

The modern form of the equations was worked out by commoners, so had to be filtered through the work of others before it could be taught.

You're really caught up on this commoner/non-commoner dynamic (from your other comments). Was it really that important? - many of the well known scientists of that time were 'commoners'.

I'm not, but they were. But it was not discussed openly in print at the time, and so must be inferred.
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