Maxwell's equations.

[ollypenrice]

From my arts background I read history of science rather than 'practitioner' science and have just been astonished to read about Maxwell's equations. I knew that they put Faraday on a mathematical footing and that they were to play a role in launching relativity and quantum theory. What I didn't know, and what has left me utterly bemused, is that his second paper described the field in terms of an entirely metaphorical system of spinning, rotating cells separated by little things like imaginary ballbearings. If I understand this correctly he designed this imaginary machine to meet four existing observations in electricity and magnetism and the model satisfied these. But when he set the imaginary cells to an infinite density the machine promptly predicted the speed of light as an electromagnetic wave. I find this utterly bizarre - the fact that an entirely metaphorical machine can make predictions beyond its own remit. In one sense the machine has no basis in physical reality (so far as we know there are no cells and no ballbearings) but on the other hand it does because it can predict the speed of light.

How can this be? Is it because the metaphorical machine put all the known information into mathematical form and then the maths itself took over to make the prediction? I suppose what bothers me is that I'd have expected the metaphor to break down outside its own remit but it didn't. Does anybody see the source of my surprise or am I coming at this wrongly somehow?

Olly

[Tiki]

Does anybody see the source of my surprise or am I coming at this wrongly somehow?

Olly

It is surprising to say the least. You are not coming at this wrongly either.

Such surprising descriptions and machinery abound across physics. eg. The wave function in quantum mechanics.

I know very little of the history of Maxwell's equations but I do remember hearing once that there was a certain reluctance to accept his ieas on account of his 'goofy' model. A few experiments later and the prejudice to his 'goofy' model disappeared. It has to be remembered of course that in Maxwell's time physicists weren't used to thinking in terms of abstract fields. His equations of course speak for themselves, it doesn't matter to me where they come from as long as they are logically consistent in themselves.

[ollypenrice]

It is surprising to say the least. You are not coming at this wrongly either.

Such surprising descriptions and machinery abound across physics. eg. The wave function in quantum mechanics.

I know very little of the history of Maxwell's equations but I do remember hearing once that there was a certain reluctance to accept his ieas on account of his 'goofy' model. A few experiments later and the prejudice to his 'goofy' model disappeared. It has to be remembered of course that in Maxwell's time physicists weren't used to thinking in terms of abstract fields. His equations of course speak for themselves, it doesn't matter to me where they come from as long as they are logically consistent in themselves.

Thanks. I wasn't sure whether my surprise was justified. It's certainly clear that the idea of a field took some swallowing. Little did the doubters know how much worse than that it was going to get!! ('All this jumping...')

Olly

[acey]

Maxwell was inspired by the work of William Thomson (who later became Lord Kelvin). Thomson proposed an analogy between Faraday's "lines of force" and fluid mechanics. Maxwell developed this into a model where the lines of force were represented by tubes of fluid, though he initially saw this as nothing more than an analogy, the fluid being imaginary.

However he then began to speculate that filamentary vortices in a physically real fluid (ether) might be a way of explaining electromagnetism. He presented this vortex theory using the mechanical model of rotating cells separated by "idle wheel" particles. Rotation of the cells corresponded to the magnetic field, and the idle wheels represented electricity. He admitted the model was awkward and the vortex theory itself was only a hypothesis.

Maxwell built the known physics into these models, so they worked as a way of representing the maths, though they didn't work as physical explanation. Maxwell clung to the idea that electromagnetism should ultimately be explainable by ether, but in the end the ether was discarded and only the equations remained.

[nameunknown]

For me also the weird/special/trippy thing about Maxwell's equation is that he got the math right and the model wrong. By sticking the whole thing in vector calculus (where "spin" vectors pointed along the axis of rotation) all the right answers fall out even if the vectors don't represent something "spinning". Amazing that - does it mean the only thing that's really real is maths - and everything else (i.e. "physics" and more complicated forms of physics (chemistry (biology (sociology (economics (retail therapy (why shoes and handbags proliferate))))) is just a convenient but approximate model to try and make the maths understandable to apes with four fingers and an opposable thumb?

[gkec]

Wasn't the real surprise that was overlooked as inconvenient at the time was that it predicted that the speed of light was constant in any frame of reference.

[Macavity]

Ironic the average undergrad, even when they can write down the maths:

Divs, Curls, Del² 's etc., rarely (thankfully) performs practical calculations?

Pity the poor *programmer* who has to translate the Maths into code?

But this stuff is not easy, even at the height of one's youthful abilities.

Kudos to the clever! Encouragement to those a tad less so - Uhm, me!

[J_M_Franklin]

That period of time saw many towering intellects and many, sadly, are largely forgotten by history, other than those whose work or hobby involves the subjects they mastered, people such as James Clerk Maxwell, Paul Dirac, Lord Kelvin, Michael Faraday, James Prescott Joule, Rudolf Clausius, Hermon Von Helmholtz, Ernest Rutherford, Allesandro Volta, Ludwig Boltzman, Sir John Joseph Thompson to name a few.

Without these men we would not have the modern world or the science we have today... Einstein was a brilliant combiner of others work, to see the relationships they had missed and to put it across in ways people understood, but the men mentioned above were true pioneers and innovators...the modern world owes them a massive amount and we do more to celebrate talentless reality show idiots that these great men of science. It's a disgrace.

[ollypenrice]

That period of time saw many towering intellects and many, sadly, are largely forgotten by history, other than those whose work or hobby involves the subjects they mastered, people such as James Clerk Maxwell, Paul Dirac, Lord Kelvin, Michael Faraday, James Prescott Joule, Rudolf Clausius, Hermon Von Helmholtz, Ernest Rutherford, Allesandro Volta, Ludwig Boltzman, Sir John Joseph Thompson to name a few.

Without these men we would not have the modern world or the science we have today... Einstein was a brilliant combiner of others work, to see the relationships they had missed and to put it across in ways people understood, but the men mentioned above were true pioneers and innovators...the modern world owes them a massive amount and we do more to celebrate talentless reality show idiots that these great men of science. It's a disgrace.

Bravo. Yes indeed. Yes yes yes.

Olly

[DaveS]

And I hope no one's forgetting Sir Oliver Lodge who laid the framework for Heinrich Hertz who actually got the credit for inventing / discovering radio waves.

[jakeybob]

That period of time saw many towering intellects and many, sadly, are largely forgotten by history, other than those whose work or hobby involves the subjects they mastered, people such as James Clerk Maxwell, Paul Dirac, Lord Kelvin, Michael Faraday, James Prescott Joule, Rudolf Clausius, Hermon Von Helmholtz, Ernest Rutherford, Allesandro Volta, Ludwig Boltzman, Sir John Joseph Thompson to name a few.

Without these men we would not have the modern world or the science we have today... Einstein was a brilliant combiner of others work, to see the relationships they had missed and to put it across in ways people understood, but the men mentioned above were true pioneers and innovators...the modern world owes them a massive amount and we do more to celebrate talentless reality show idiots that these great men of science. It's a disgrace.

Yup. I find it extremely bizarre that Maxwell in particular isn't better known in his own (or indeed any other) country. I think most physicists would put him in the top three (certainly the top five) physicists of all time, but most people haven't heard of him.