The relativistic form of Maxwell's equations is so simple and beautiful. (Natural units are used.)pic.twitter.com/OwRymxz1rs
আপনি আপনার টুইটগুলিতে ওয়েব থেকে এবং তৃতীয়-পক্ষ অ্যাপ্লিকেশনগুলির মাধ্যমে অবস্থান তথ্য যেমন শহর বা সুনির্দিষ্ট অবস্থান যোগ করতে পারবেন। আপনার কাছে আপনার টুইটের অবস্থান ইতিহাস মোছার বিকল্প থাকবে। আরও জানুন
The relativistic form of Maxwell's equations is so simple and beautiful. (Natural units are used.)pic.twitter.com/OwRymxz1rs
It's beyond me Tamas, but I will go so far as to ask what the star operation represents.
It denotes an operator called the Hodge star. This page might be of help. It starts from the vector form of the equations and leads you to their differential form (written above). https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field …
Thanks!
@RobPhil21 @astro_WillH would this be full credit on an emag test???
Absolutely not and you'd be kicked out of school. What does mechanics have to do with emag???
I dunno, but apparently it can be used to prove Maxwell's equations
To get an intuitive idea of what Maxwell's equations say have a look at @3blue1brown's excellent video on divergence (∇⋅) and curl (∇×).https://youtu.be/rB83DpBJQsE
I've never understood why the vector calculus formulation continues to be so popular considering the language of differential forms is so much nicer and general...
They are nicer and more general, that's true. I think the vector form is easier to understand/explain to people with various background (physicists, mathematicians, engineers, etc) and hence their popularity.
I agree that visualizing vector fields and stuff is pretty helpful, and diff forms require more effort to establish; but once the machinery is there I think it simplifies things quite a bit. I'll admit I'm a bit biased since I studied them before knowing much about EM though lol
I attended a talk by Freeman Dyson earlier this year. :-)
Is there a link thanks?
I have two complaints about these formulae: 1> These deal with infinitesimal vector fields and we know that atoms are governed by quantum mechanics. 2> There is no way to accurately measure the divs and curls...try using a voltmeter??? come on, impossible.
Humans invented Electric Fields and Magnetic Fields so they could more easily conceptualize Electric and Magnetic Forces. It turns out these Fields are real and they interact with each other to create light (among other things). That's the beauty of Maxwell's Eq's.
In #GeometricAlgebra, this equating is easy simpler and more beautiful:
(Nabla)F=J
Where F is the electromagnetic field (a bivector of R{3,1}) the charge and current vector J.
@like_themineral can’t believe there was a time that I kind understood this! Not very, obviously. But still!
Feynman forever.
The differential form is always much nicer to look at than the integral form.
Just scroll a little down on the pdf given in the link. You will see two 'comment' articles on this derivation. Those guys say the reconstruction given by Dyson is not a derivation of Maxwell equations.
টুইটার তার ক্ষমতার বাইরে চলে গেছে বা কোনো সাময়িক সমস্যার সম্মুখীন হয়েছে আবার চেষ্টা করুন বা আরও তথ্যের জন্য টুইটারের স্থিতি দেখুন।