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PeterR280
PoohBah
Reged: 05/27/13

Re: Light is Eternal
[Re: deSitter]
#6151448  10/22/13 10:47 AM

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Faraday is an iconic figure. He was an experimentalist and made his discoveries. He conceptualized it but was not able to present them in mathematical form because of his lack of formal training. Maxwell did. Do you think Faraday would have developed the mathematical models if he had formal training in math?

deSitter
Still in Old School
Reged: 12/09/04

Re: Light is Eternal
[Re: deSitter]
#6151456  10/22/13 10:52 AM

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What Maxwell is describing here of course, is nothing less than the birth of the field concept in Faraday's thought. We are so used to thinking now in terms of fields and partial differential equations, that it is impossible for us to understand what an heroic achievement Faraday made with nothing more than his own intuition and rigorous experimental methods using primitive equipment. Maxwell is not exaggerating  he certainly would have regarded his own work as impossible without the groundwork of Faraday.
Maxwell's discovery of the complete laws of electromagnetism were published in a series of papers from 1855 to 1865. The first great paper was called "On Faraday's Lines of Force" and appeared in 1855. Then in 1861, "On the Physical Lines of Force", and finally in 1865, "On a Dynamical Theory of the Electromagnetic Field". He spent 10 years codifying Faraday's thought in equations, then completing the picture with radiation via his displacement current. Without Faraday, none of this would have happened.
Today we have various powerful tools, such as vector analysis, for the study of these problems. Even so, the subject challenges every generation of the best physics students. The great physicist Paul Ehrenfest had Maxwell's Treatise as his constant companion, and despaired of ever fully understanding it. We simply cannot imagine the scale of an intuition that could deal accurately with electromagnetic phenomena without even the benefit of linear algebra.
drl

deSitter
Still in Old School
Reged: 12/09/04

Re: Light is Eternal
[Re: deSitter]
#6151478  10/22/13 11:09 AM

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I might point out another historical development, parallel to that of Maxwell and Faraday. The Irish mathematician William Rowan Hamilton singlehandedly invented most of the mathematical structure behind modern physics. With the tools at his disposal, of his own creation, he could have discovered not only relativity, but also quantum mechanics in its fully developed form. Indeed one of the most exciting moments of my young life was when I found out, quite independently, how to use his quaternion algebra to derive the main results of special relativity. But Hamilton did not have a Faraday to build on, and most of his later life was spent in a fruitless attempt to establish quaternion analysis as the basis of all science. He was right in a sense  but having no experimental data to crunch, all he could do was speculate and calculate on chimeras.
The modern schism between experiment and theory is projected retroactively into the past. I assure you this is not only unjust, it is a great error in understanding the history of science.
drl

PeterR280
PoohBah
Reged: 05/27/13

Re: Light is Eternal
[Re: deSitter]
#6151492  10/22/13 11:17 AM

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Lagrange has perhaps done more than any other to give extent and harmony to such deductive researches by showing that the most varied consequences … may be derived from one radical formula, the beauty of the method so suiting the dignity of the results as to make his great work a kind of scientific poem. W. R. Hamilton


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