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| Questions for those who know electromagnetism better than I do |
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| T3sl4co1l:
Yes, Heaviside invented the form of vector calculus as we know it today, simplifying E&M down to the four field equations we use most commonly. He also brought complex numbers to electronics! Maxwell himself only collected the known laws/relationships, IIRC. We could also credit Einstein for inventing the tensor shorthand, in which the whole law is merely a single equation. The expressiveness is no accident, as relativity is built upon E&M, an extrapolation of the curious form of Lorentz invariance. Tim |
| iMo:
My first lecture on "EM Field Theory" started with an intro given by the professor - "..do you really think the electrons transfer the energy from the power station to your household?? Have you ever seen an electron?? Electron is small and lightweight, almost nothing.. Moreover, the electrons travel a few centimeters in a second in a copper wire.. You would never have lit a lamp on your desk if it had worked that way.." And he followed with Maxwell's equations, messing with calculus integrating EM fields over the entire spacetime of Universe, as that is the way the EM energy lights up my lamp.. A positive part of this EM Field Theory nightmare - the professor was a passionate Sinclair ZX Spectrum user and he was encouraging us to write some code solving his EM stuff numerically (as the Basic computers were pretty common among students in that time already).. :D |
| T3sl4co1l:
Reminds me of the classic: http://www2.hawaii.edu/~darlene4/dmed120/assignment12.htm |
| Slartibartfast:
--- Quote from: T3sl4co1l on August 25, 2021, 08:24:37 am ---Yes, Heaviside invented the form of vector calculus as we know it today, simplifying E&M down to the four field equations we use most commonly. He also brought complex numbers to electronics! Maxwell himself only collected the known laws/relationships, IIRC. We could also credit Einstein for inventing the tensor shorthand, in which the whole law is merely a single equation. The expressiveness is no accident, as relativity is built upon E&M, an extrapolation of the curious form of Lorentz invariance. --- End quote --- With that, you have the causal relationships all upside down. You'd be right if you only wanted to describe the historic sequence and linkage of discoveries, but as a causal chain of nature's features, it does not make sense. You cannot consider electromagnetism more fundamental than space and time. Lorentz invariance is a fundamental property of spacetime, it is a subset of the full set of symmetries of spacetime described by the Poincaré group. It is this fact, where Lorentz invariance of electromagnetism comes from, not the other way round. Being a symmetry of spacetime, every physical law must be rewritable in a manifestly Lorentz invariant form; this has been an important guidance principle for physics research since it's discovery in the early 1900s. Maxwell's equations is just the first instance where Lorentz invariance had been discovered, and it took until around 1900 because the Maxwell equations in the forms known before are not manifestly Lorentz invariant. It could be argued that Heaviside helped obscuring it, by introducing a form of vector algebra and calculus that only works in three dimensions and cannot be simply extended to spacetime's four dimensions. Tensors are not shorthand, they are mathematical (geometric, in fact) objects, just like vectors. They are not an invention of Einstein either. Riemann and Christoffel used them many decades earlier to built the then new field of differential geometry, which later turned out to be an essential ingredient for General Relativity. When Einstein had his main insights about the principles that would allow him to generalise Special Relativity, he was searching for ways to express them in mathematical ways. He had his mathematician friends teach him about matrices (not at all commonly known at the time) and differential geometry, and tensors. |
| Slartibartfast:
--- Quote from: imo on August 25, 2021, 09:28:56 am ---My first lecture on "EM Field Theory" started with an intro given by the professor - "..do you really think the electrons transfer the energy from the power station to your household?? Have you ever seen an electron?? Electron is small and lightweight, almost nothing.. Moreover, the electrons travel a few centimeters in a second in a copper wire.. You would never have lit a lamp on your desk if it had worked that way.." --- End quote --- An exceedingly silly rant, if it really happened. Of course the marching electrons (a.k.a. current) need the electric field (a.k.a.) voltage, to, as the multiplicative product, deliver the power. Makes you wonder, if the uphill bicyling professor cannot find out where his efforts go, surely not into the movement (a.k.a. velocity)? Completely analogous, the velocity needs the backwards pulling force, to, as the product, become the power sink that makes him pant. I'd consider this a way to confuse students, a pedagogical desaster. |
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