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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]

#11

Post by MichaelZuo »

bsder wrote: post #3

Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…

I've always thought the Heaviside notation is a bit bizarre... is there any advantage to them at all?

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

#12

Post by DrDeWitt »

GolDDranks wrote: post #10
DrDeWitt wrote: post #8

Earlier quoted context omitted.

Which are the two things that combine to nothing?

Particles and antiparticles. But I think he's trying to make a slightly more general point: why are "parities" (2-fold symmetries) so common in nature and mathematics? Why not more 3-fold symmetries?

As the other reply said, in QCD you have "3 things that combine to nothing." If I had to guess why they are not so common I would say that the more variables you add in a theory the more complicated you make it. So by Occam's razor we try to go for the simpler models/structures.

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

#13

Post by im3w1l »

GolDDranks wrote: post #10
DrDeWitt wrote: post #8

Earlier quoted context omitted.

Which are the two things that combine to nothing?

Particles and antiparticles. But I think he's trying to make a slightly more general point: why are "parities" (2-fold symmetries) so common in nature and mathematics? Why not more 3-fold symmetries?

Maybe sound is an illustrative example. The air pressure is a positive scalar quantity. We are interested in the deviations from the mean. Deviations can be both positive and negative. A positive and a negative deviation cancel (in absolute terms: a larger than normal pressure and lesser than normal pressure will average to something more typical)

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

#14

Post by mitthrowaway2 »

bsder wrote: post #3

Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…

I think the essay is not about Maxwell's theory being hard for college students to understand, but rather, for other 19th century physicists to understand. And that's mainly because Maxwell himself didn't do a very good job of communicating his theory at the time, so it took other talented physicists to rework, explain, and popularize his ideas.

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

#15

Post by LeapingLennie »

bsder wrote: post #3

Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…

Are there any textbooks you would recommend for learning vector analysis / vector fields before studying EM?

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

#16

Post by eru »

DrDeWitt wrote: post #7

Excellent essay. The thing I do not agree with is how they mention that one has to abandon natural language to understand quantum mechanics. The only reason why we made the jump from Newton to Einstein through Maxwell's theory is Einstein's intuition of the physics behind electrodynamics

> The only reason why we made the jump from Newton to Einstein through Maxwell's theory is Einstein's intuition of the physics behind electrodynamics

I'm not sure that's true. What kind of model of causality are you using here?

Other people were also on the cusp of doing (most of) what Einstein did. Ultimately, without Einstein most likely progress would have been delayed by a few years, and the laurels would be spread amongst more people. (Eg Lorentz' work was on the way to formulating special relativity.)

So it's hard to say that there was any single 'only reason' for any discovery here.

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

#17

Post by deepnet »

DrDeWitt wrote: post #7

Excellent essay. The thing I do not agree with is how they mention that one has to abandon natural language to understand quantum mechanics. The only reason why we made the jump from Newton to Einstein through Maxwell's theory is Einstein's intuition of the physics behind electrodynamics

Natural language can conjure the visual imagination of intuition, but it is less specific than images themselves.

Einstein reportedly ran thought experiments in his imagination.

His intuition was visual and dynamic.

That is images that change - animations.

A natural language description of relativity is one step removed from the moving images of Einstein's intuition.

Fields are not grounded in everyday experience but most modern movie-goers are happy with rapid and grand changes of scale and thanks to wizard and superhero movies there exists a sophisticated visual grammar of rapidly propagating fields, strange paradoxes and simultanous weakly interacting realities.

Many of the concepts of quantum field theory can be grasped by a wide audience when presented as animations.

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

#18

Post by eru »

kragen wrote: post #4

i wonder if further progress in physics will require abandoning the maxwellian paradigm in the same way that maxwell had to abandon the newtonian paradigm? presumably for something even further removed from everyday experience. dyson must have thought about that possibility, but evidently at least at the time of this paper he rejected it. i'd like to read his reasoning unrelatedly, i feel like i kind of understand ma…

Keep in mind that we for all the talk of 'abandoning' the Newtonion paradigm, it's predictions are still valid for a large space of conditions. Eg NASA uses Newtonian mechanics to fly all their spacecraft.

Special relativity includes classical mechanics when speeds are low. In the same way, any replacement for Maxwell's paradigm must reproduce the predictions of Maxwell's equations under the large swathe of conditions where they agree with reality.

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

#19

Post by nimish »

mitthrowaway2 wrote: post #14
bsder wrote: post #3

Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…

I think the essay is not about Maxwell's theory being hard for college students to understand, but rather, for other 19th century physicists to understand. And that's mainly because Maxwell himself didn't do a very good job of communicating his theory at the time, so it took other talented physicists to rework, explain, and popularize his ideas.

Admittedly the tools to make the mathematics more compact and clearer weren't invented yet (except as quaternions).

We did get stuck with Gibbs' vector calculus formulation as the canonical view unfortunately.

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

#20

Post by bsder »

mitthrowaway2 wrote: post #14
bsder wrote: post #3

Maxwell's theory is not hard to understand--once you have the proper tools. The problem is that because of trying to cram a degree into 4 years, you wind up having a class on electromagnetics without any understanding of vector fields . Electrical engineering is particularly bad about this. You never get exposed to the Hamiltonian formulations of classical mechanics, and you never get exposed to vector analysis. Cons…

I think the essay is not about Maxwell's theory being hard for college students to understand, but rather, for other 19th century physicists to understand. And that's mainly because Maxwell himself didn't do a very good job of communicating his theory at the time, so it took other talented physicists to rework, explain, and popularize his ideas.

People forget that Maxwell's Theory contradicts the prevailing belief of the time that waves ALWAYS require a medium for propagation--the so called "aether".

That's a really large conceptual jump and physicists did not make that jump lightly or easily.

Maxwell's paper was 1865. The Michelson–Morley experiment was 1887. Michelson himself couldn't make the shift. Quoting Wikipedia (https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_exper...): "The negative result led Michelson to the conclusion that there is no measurable aether drift.[1] However, he never accepted this on a personal level, and the negative result haunted him for the rest of his life (Source; The Mechanical Universe, episode 41[8])."

In an attempt to preserve "aether", Lorentz contraction then enters the picture as an ad hoc explanation for the Michelson-Morley result. It turns out Lorentz contraction is correct, but not because of the existence of "aether" but because of the constancy of the speed of light--c (Einstein Special Relativity--1905).

Once you finally give up on "aether" after 40 years of trying otherwise, you can finally just roll with the mathematical implications of Maxwell's equations.

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