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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]

#31

Post by tntn »

ncmncm wrote: post #25
k9s9 wrote: post #2

Interesting. And makes me wonder what else we are missing and misunderstanding, as we waste so much time trying to express the complexity of the world in spoken language rather than math. Not just physics but in sociology, psychology, economics etc. Faraday purely from experiments 30-40 years before Maxwell, intuitively understood electromagnetism. Nobody serious believed it because he didn't have the training to exp…

[retracted]

Lord? Faraday was no lord. He was also dead by the time Maxwell gave this presentation.

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

#32

Post by Gibbon1 »

tim333 wrote: post #19
k9s9 wrote: post #2

Interesting. And makes me wonder what else we are missing and misunderstanding, as we waste so much time trying to express the complexity of the world in spoken language rather than math. Not just physics but in sociology, psychology, economics etc. Faraday purely from experiments 30-40 years before Maxwell, intuitively understood electromagnetism. Nobody serious believed it because he didn't have the training to exp…

Spoken language has a lot going for it. I note the featured article and it's discussion are all words not maths. By the way looking at Maxwell's paper it seems awful complicated https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1865... compared to the modern form of the equations https://ethw.org/w/images/d/d6/Maxwell_image_02.jpg

Heaviside thought that too which is why he invented the modern form. Not that he just used a different set of math to describe the problem, he invented the math too.

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

#33

Post by tntn »

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…

Interesting article by Wilczek on the subject of aether: http://ctpweb.lns.mit.edu/physics_today/phystoday/Ether.pdf

Einstein also gave a talk in the late 20s (?) in which he discussed how spacetime in GR could be considered a kind of aether, though stripped of most of its physical properties.

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

#34

Post by earthicus »

tntn wrote: post #15
earthicus wrote: post #9

Earlier quoted context omitted.

This is something of a myth. Maxwell actually uses both to ease the mathematical pain for his readers - he writes the equations out coordinate by coordinate, and he also compresses them using Hamilton's (quaternion) model of vectors. In fact Maxwell was the one who introduced the gradient, curl, and divergence (actually he used convergence) operators, and he addressed precisely your concern in his book by giving both…

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…

Maxwell explicitly uses the imaginary part of a quaternion as a model of vectors, just as Hamilton did:

> A german letter denotes a Hamilton vector, and indicates not only its magnitude but its direction. The constituents of a vector are denoted with roman or Greek letters. [1]

Gibbs and Heaviside or course use a different algebraic model of vectors, which is the one used in introductory courses now. But the more significant change made to get to "maxwells equations" as we know them now is not a slight change in the mathematical formalism.

The big difference is a change in the underlying physical model: Maxwell's original treatment is largely in terms of potentials, which Heaviside modified to focus on the E-M force fields directly. This change is what gives the familiar four equations we know today, not fiddling with your parameterization of the rotation group, or similar games. Nowadays physicists frequently use a tensor or forms model of vectors in addition to the gibbs model.

[1] https://archive.org/details/ATreatiseOnElectricityMagnetism-...

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

#35

Post by srean »

tntn wrote: post #15
earthicus wrote: post #9

Earlier quoted context omitted.

This is something of a myth. Maxwell actually uses both to ease the mathematical pain for his readers - he writes the equations out coordinate by coordinate, and he also compresses them using Hamilton's (quaternion) model of vectors. In fact Maxwell was the one who introduced the gradient, curl, and divergence (actually he used convergence) operators, and he addressed precisely your concern in his book by giving both…

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 Gibbsian vector calculus and geometric algebra. Not that javascript or Gibbsian vectors are bad, quite the contrary, they are astonishing in their own right and scope, but one still feels they could have been so much better.

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

#36

Post by iorrus »

ncmncm wrote: post #21

It is unfortunate that Dyson neglects the role of Oliver Heaviside, again. This is in a long tradition of English neglect, ultimately traceable to Heaviside's status as a commoner. Heaviside invented the mathematical tools we still use to understand and teach Maxwell, and most of the important consequences of the theory, but Pupin, Hertz, Marconi, and deForest used his methods and took got the credit. Today Heaviside…

Exactly, one of the main reasons why maxwell is so hard to understand is that everything is expressed using quarternions unlike Heaviside who expressed the equations using the vector notation we see them expressed in today. In reality ‘Maxwell’s’ equations are in fact Heaviside’s.

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

#37

Post by hopler »

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.

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

#38

Post by iorrus »

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…

Maxwell’s works all assume an ether so it’s not really true to state that the equations don’t need one.

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

#39

Post by pm90 »

k9s9 wrote: post #2

Interesting. And makes me wonder what else we are missing and misunderstanding, as we waste so much time trying to express the complexity of the world in spoken language rather than math. Not just physics but in sociology, psychology, economics etc. Faraday purely from experiments 30-40 years before Maxwell, intuitively understood electromagnetism. Nobody serious believed it because he didn't have the training to exp…

> Pupin went first to Cambridge and enrolled as a student, hoping to learn the theory from Maxwell himself. He did not know that Maxwe ll had died four years earlier. After learning that Maxwell was dead, he stayed on in Cambridge and was assigned to a college tutor.

It wasn't that people spend all those years actually working on this problem. There wasn't an internet nor modern travel to share/disseminate/argue about these ideas.

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

#40

Post by scabarott »

ncmncm wrote: post #27
tim333 wrote: post #19

Earlier quoted context omitted.

Spoken language has a lot going for it. I note the featured article and it's discussion are all words not maths. By the way looking at Maxwell's paper it seems awful complicated https://royalsocietypublishing.org/doi/pdf/10.1098/rstl.1865... compared to the modern form of the equations https://ethw.org/w/images/d/d6/Maxwell_image_02.jpg

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'.
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