BBC Scotland (the glories of iPlayer) has just run a documentary on James Clerk Maxwell; I'm saddened that BBC doesn't think it worth running the programme for the whole of the UK. http://www.bbc.co.uk/programmes/b06rd56j
They say you halve your audience with each formula in a talk, any talk about Maxwell is going to have four formulae in it, the secret is to put them at the end... or a subliminal frame; science by blipverts!
I take it Egyptology has this problem with hieroglyphs.
I learned long ago that when managers see an equation in a report, they assume that the work is incomplete, otherwise you would have solved the equation and reported the answer.
Serious physics question here. So Maxwell showed that electromagnetic waves travel at the speed of light. But I don't believe he actually proved that light is electromagnetic waves. The question: Has anyone shown a model of light using Maxwells equations, that behaves in all the ways light does? That needs to include packets of energy like photons - can any form of soliton exist with Maxwell, and does it behave like a photon? Is there an actual model of light based on his work?
Disclaimer: I'm a physicist, but have been out of physics research for 20+ years.
The answer is No. The photon model doesn't come out of Maxwell's equations. You can tell, at a glance, by the absence of Planck's constant.
Digging just a bit deeper, there are some problems that can be solved using Maxwell's equations, but I don't know which of those problems already had adequate solutions before Maxwell. For instance the laws of reflection and refraction (e.g., Snell's Law) can be solved by applying Maxwell's equations at a surface boundary between two materials, but I believe they were empirically known already.
As for photons, it's actually the reverse of what you are asking for. Maxwell's equations come out of the photon model. The reason is that classical electromagnetic theory was already successful by the time that quantum mechanics emerged, so the corresponding QM theories were designed so that classical theory would be preserved as a limiting case. One of the tests of any candidate QM theory would have been: Does it preserve our existing observational evidence about the macroscopic world?
> Is there an actual model of light based on his work?
Yes: classical electromagnetism. It's an outrageously successful model of how light behaves. It doesn't predict photons, but that doesn't mean it's not an "actual" model of light.
You can include photons by taking Maxwell's equations and doing something called second quantization (https://en.wikipedia.org/wiki/Quantization_of_the_electromag...). That gets you quantum effects that can explain behaviors like shot noise, but it misses things like photon-photon scattering. (Nonetheless, I would still call this an "actual" model of light.)
Then there is full-on quantum electrodynamics (https://en.wikipedia.org/wiki/Quantum_electrodynamics), but that doesn't capture certain behaviors, like what happens to photons at the electroweak scale. But I would still call QED an "actual" model of light.
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[ 2.6 ms ] story [ 18.0 ms ] threadhttp://www.bbc.co.uk/programmes/b06rlkwb/episodes/downloads
Hopefully they are available outside the UK!
They say you halve your audience with each formula in a talk, any talk about Maxwell is going to have four formulae in it, the secret is to put them at the end... or a subliminal frame; science by blipverts!
I take it Egyptology has this problem with hieroglyphs.
The answer is No. The photon model doesn't come out of Maxwell's equations. You can tell, at a glance, by the absence of Planck's constant.
Digging just a bit deeper, there are some problems that can be solved using Maxwell's equations, but I don't know which of those problems already had adequate solutions before Maxwell. For instance the laws of reflection and refraction (e.g., Snell's Law) can be solved by applying Maxwell's equations at a surface boundary between two materials, but I believe they were empirically known already.
As for photons, it's actually the reverse of what you are asking for. Maxwell's equations come out of the photon model. The reason is that classical electromagnetic theory was already successful by the time that quantum mechanics emerged, so the corresponding QM theories were designed so that classical theory would be preserved as a limiting case. One of the tests of any candidate QM theory would have been: Does it preserve our existing observational evidence about the macroscopic world?
Yes: classical electromagnetism. It's an outrageously successful model of how light behaves. It doesn't predict photons, but that doesn't mean it's not an "actual" model of light.
You can include photons by taking Maxwell's equations and doing something called second quantization (https://en.wikipedia.org/wiki/Quantization_of_the_electromag...). That gets you quantum effects that can explain behaviors like shot noise, but it misses things like photon-photon scattering. (Nonetheless, I would still call this an "actual" model of light.)
Then there is full-on quantum electrodynamics (https://en.wikipedia.org/wiki/Quantum_electrodynamics), but that doesn't capture certain behaviors, like what happens to photons at the electroweak scale. But I would still call QED an "actual" model of light.