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Re:Part two of Grant Sanderson's video with Terry Tao on the... by ijustlovemath on Wednesday February 26, 2025 @08:18AM (#43183361)
The physics of the 1800s had a lot of low hanging fruit. Most undergrads in physics can show you a derivation of Maxwell's equations from first principles, and I think a fair few of them could have come up with it themselves if they were in Maxwell's shoes. The hard truth is that the physics/math of today is just much further afield, and much harder.
Re:Part two of Grant Sanderson's video with Terry Tao on the... by varjag on Wednesday February 26, 2025 @08:56AM (#43183619)
Very little of the stuff physicists came up with in the 19th century was obvious or low hanging at the time. And no your undergrads would likely have never came up with Maxwell's equations on their own.
Re:Part two of Grant Sanderson's video with Terry Tao on the... by 7thaccount on Thursday February 27, 2025 @04:54PM (#43198943)
Yeah, I agree with you on this one. It's kind of easy once you understand it, but it took Maxwell to figure it out. I might not have figured that out in ten centuries by myself lol.
Re:Part two of Grant Sanderson's video with Terry Tao on the... by ijustlovemath on Thursday February 27, 2025 @10:07PM (#43201281)
I definitely think it takes a Maxwell to describe the physics behind displacement current (which I think was not around in Maxwell's initial drafts), but the derivations of the four classic Maxwell equations are fairly straightforward multivariable calculus problems that start with fairly simple assumptions. Multivariable calculus was relatively young in his era, but I think a motivated student from the current era could discover it given a summer of thought experimentation.

See for yourself: https://m.youtube.com/watch?v=AWI70HXrbG0

If you want some true genius, behold the shear terror of the near field of a dipole antenna. All shall view her and despair.

Re:Part two of Grant Sanderson's video with Terry Tao on the... by ijustlovemath on Friday February 28, 2025 @10:43AM (#43206875)
For those interested, see slide 4 of section 7: Hertzian dipoles

https://courses.grainger.illinois.edu/ece350/ece350lecture_n...

Re:Part two of Grant Sanderson's video with Terry Tao on the... by pepinator on Wednesday February 26, 2025 @04:43PM (#43188572)
That's a highly biased opinion. The Newtonian conception of physics is trivial for us, and we can say that most people could come up with the ideas by their own, but that's because our world conception is based on those ideas; it's already implicit in how we understand the world. That's why Newton was so important, there was a shift in the whole conceptualization of the physical world. With Maxwell's equations is similar. The interpretation as waves, the fact that the equations are Lorentz symmetric but no Newton symmetric, etc. All that is free for us, and it is not obvious at all.