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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]

#21

Post by kragen »

eru wrote: post #18
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 condition…

yes, i thought that was too obvious to be worth saying, but i'm glad you've said it so the knuckle-dragging contingent don't think i'm endorsing their untutored 'theories'

for that matter i use the aristotelian paradigm of physics when i expect my bed to stop moving when i stop pushing it across the floor; i don't bother with calculating the deceleration due to the friction coefficient with the floor

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

#22

Post by [deleted] »

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…

[deleted]

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

#23

Post by [deleted] »

Onavo wrote: post #5

> The moral of this story is that modesty is not always a virtue. Maxwell and Mendel were both excessively modest. Mendel's modesty setback the progress of biology by fifty years. Maxwell's modesty setback the progress of physics by twenty years. It is better for the progress of science if people who make great discoveries are not too modest to blow their own trumpets. If Maxwell had had an ego like Galileo or Newton…

[deleted]

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

#24

Post by bsder »

LeapingLennie wrote: post #15
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?

I do not. None of the books I know of are very good because they are mostly targeted at Mathematics majors rather than physicists or engineers.

Gerard ’t Hooft used to have a humongous list of textbooks for aspiring theoretical physicists. I'd sure look there for starters.

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

#25

Post by sidlls »

LeapingLennie wrote: post #15
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?

EM’s vector fields formulation is fairly straightforward: it’s all curls and divergence. Any 3rd (-ish) semester undergrad multivariate calculus course is likely to cover it in sufficient depth. “Mathematical Methods for Physicists” covers it in sufficient depth, for example, provided you already have a thorough understanding of the prerequisite material. Most undergrad physics degree curriculums should have E&M courses whose texts (e.g. Introduction to Electricity and Magnetism, Griffiths) cover enough of the details. If you want to pursue it further than an undergraduate level study, you’ll also want a good text on differential equations that has or is supplemented by material covering, e.g., spherical harmonics and Bessel functions (among other things). I wish I could remember what I used, but it was…more years ago than I care to say when I was an grad student.

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

#27

Post by bigboy12 »

eru wrote: post #16
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 spre…

Everyone seems to think they would have figured out Einstein’s theory but they didn’t until Einstein did.

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

#28

Post by DiogenesKynikos »

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…

Maxwell's Equations have already been superseded by Quantum Electrodynamics, in the same way that Newtonian gravity has been superseded by General Relativity.

Both Newtonian gravity and Maxwell's Equations are still very good approximations in their regimes of validity.

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

#29

Post by mitthrowaway2 »

bsder wrote: post #20
mitthrowaway2 wrote: post #14

Earlier quoted context omitted.

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/Michel…

Maxwell saying that his theory "attributes electric action to tensions and pressures in an all-pervading medium... the medium being identical with that in which light is supposed to be propagated" suggests that Maxwell himself did not view his theory to be contradicting the existence of an aether (or was being coy about it). Which is especially interesting because Maxwell based his theory on Faraday's, and Faraday didn't believe in the aether.[1]

[1] Michael Faraday's Thoughts on Ray Vibrations, 1846, cited by Maxwell in his paper. Faraday says: "The view which I am so bold to put forth considers, therefore, radiation as a kind of species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavors to dismiss the aether, but not the vibration." (https://pwg.gsfc.nasa.gov/Education/wfarad1846.html)

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

#30

Post by kragen »

DiogenesKynikos wrote: post #28
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…

Maxwell's Equations have already been superseded by Quantum Electrodynamics, in the same way that Newtonian gravity has been superseded by General Relativity. Both Newtonian gravity and Maxwell's Equations are still very good approximations in their regimes of validity.

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