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

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

#11

Post by madengr » Sun, Jan 06, 2019, 6:07 PM UTC

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…

Maxwell unified electromagnetism into a propagating wave. That was the big leap. Before that, things were disparate.

Hertz proved it experimentally, and Heaviside turned it into an engineering discipline.

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

#12

Post by tntn » Sun, Jan 06, 2019, 6:38 PM UTC

madengr wrote: post #11

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…

Maxwell unified electromagnetism into a propagating wave. That was the big leap. Before that, things were disparate. Hertz proved it experimentally, and Heaviside turned it into an engineering discipline.

This is true of the mathematics, but it's worth noting that Faraday had already proposed EM waves ~30 years earlier based on his intuitive understanding.

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

#13

Post by Retric » Sun, Jan 06, 2019, 6:40 PM UTC

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…

Wasted implies the solution is somehow obvious but that’s hindsite bias. Looking at lotto winners it feels easy. But, the reality is a lot of effort went to things both promising and wacky to get those steps forward. And other less major progress is being glossed over.

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

#14

Post by wmnwmn » Sun, Jan 06, 2019, 6:43 PM UTC

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 Newtonian theory.

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

#15

Post by tntn » Sun, Jan 06, 2019, 6:47 PM UTC

earthicus wrote: post #9

paulpauper wrote: post #8

Maxwell did not use vector calculus, which actually makes it pisser to understand because it bypasses having to convert the vectors to coordinates. I find short hand notion more confusing than writing it all out even if the latter takes more room. I did not understand general relativity at all until I saw an example where everything was written out and then it made much more sense

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 from Hamilton and Tait.

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

#16

Post by nonbel » Sun, Jan 06, 2019, 6:53 PM UTC

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/wiki/Conway%27s_Game_of_Life

EDIT:

I can't begin to imagine why this would trigger a downvote. Are there people out there who prefer complex theories that make things more difficult to understand than necessary? Perhaps because it makes them feel smart or something, I don't know.

But that is basically saying you dislike science, because the point of science is to synthesize information into a small set of simple "laws" that allow us to deduce accurate and precise predictions.

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

#17

Post by tntn » Sun, Jan 06, 2019, 6:55 PM UTC

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…

Dyson's statement was about Maxwell's theory, not all of E&M and its interactions with every other physical theory. There are no point charges in Maxwell's theory, for example.

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

#18

Post by bsder » Sun, Jan 06, 2019, 7:02 PM UTC

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 strange integration surfaces to make Maxwell's equations work out for things like capacitors or motors. (The Heaviside-Hertz pedagogy that everybody is STILL taught is particularly problematic to use for motors.)

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

#19

Post by tim333 » Sun, Jan 06, 2019, 7:05 PM UTC

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

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

#20

Post by NotAnEconomist » Sun, Jan 06, 2019, 7:10 PM UTC

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 research that eventually led to special relativity, which rules out a stationary aether.

It seems that LIGO merely confirmed properties of an existent aether, not that we no longer believe in one:

> Aether theories (also known as ether theories) in physics propose the existence of a medium, the aether (also spelled ether, from the Greek word (αἰθήρ), meaning "upper air" or "pure, fresh air"[1]), a space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic or gravitational forces.

Naively, spacetime and quantum fields are both forms of aether theories.