61–70 of 95 posts
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What's the point of "understanding” QM intuitively if it brings confusion rather than understanding?
You literally can't understand something if you are confused by it. Your question makes no sense.
According to the epigraph, God said something about D and H, but those were carefully avoided in the text. What's up with that.
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True generally in Physics as well. What's the point of "understanding" Quantum Mechanics intuitively when you can do computations blindly without it!
What's the point of "understanding” QM intuitively if it brings confusion rather than understanding?
There's also no such thing as 'observation'. Fields interact by a precise and well-tested mathematical function. That function does have the effect of mutating the state, but why should there be such a thing as pure observation? There's nothing magic about conscious observation.
According to the epigraph, God said something about D and H, but those were carefully avoided in the text. What's up with that.
To get Maxwell's equations in a vacuum, just replace D with εₒE and replace H with B/μₒ.
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You can even write them in terms of the four-vector A rather than F (related by F = dA) to reduce them to d dA = J.
Discovering that the Maxwell equations can be written in this succinct form is kind of mind-blowing, but I'm wondering whether it provides any additional insight? It seems like one needs to do a significant "unpacking" to actually use the equation or gain insight from it. I would love to hear an explanation of electrodynamics starting with "star ddA = J".
It's also interesting once you understand what Maxwell's equations mean to look at their geometric algebra formulation[1]. In particular it makes their use in special and general relativity somewhat more elegant, since the GA form explicitly includes a spacetime component. Of course that page isn't an elementary introduction, it assumes familiarity with GA and the divergence & curl operators, as well as some concepts…
This is awesome. What a concept, identifying the variables in the equations and providing diagrams to show the geometric meaning of the equations. Really wish wikipedia (or some sort of companion website) would similarly present an explanation of the practical meaning of variables and operators in the heavy math pages so that people with an understanding of algebra could understand the formulaic descriptions in addit…
Also an FYI - I made a similar guide to linear algebra which you can also find here:
https://github.com/photonlines/Intuitive-Overview-of-Linear-...
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Well, it's not Wikipedia's fault if people producing intuitive content are not contributing to it. It's not like editors go out of their way to remove nice explanations.
I think it is wikipedia's fault, but that it's not far from how it should be. Wikipedia is a secondary source, designed have be a reference taken from primary sources, rather than be a primary source teaching information. It's a weird blurry distinction, but seems to work well. It'd be great to have a pedagogy section that either explicitly linked out to pedagogical primary sources, or a section explicitly designed t…
As a side note there was a historical debate, and the shape of these equations is the end result of the chosen system. In geometric algebra which did not prevail, these are one equation.
These kinds of visual, well thought out explanations of topics which are often taught with terse, obscure and uninviting methods are a gift. On a tangent: I remember asking my Calculus 101 professor what the "intuitive meaning" of divergence and curl was, outside of the formal math and equations. He was shocked that one could ask to sully these perfect mathematical concepts with dirty intuitive reductions. A guide li…
Wikipedia is probably the most obvious modern exemplar of this. The editors of most mathematics articles clearly are much fonder of playing with the equations editor than they are of actually explaining things.