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In Jaynes' Probability Theory, he states:

There are many more analogies. In physics we are accustomed to finding that any advance in knowledge leads to consequences of great practical value, but of an unpredictable nature. Röntgen’s discovery of X-rays led to important new possibilities of medical diagnosis; Maxwell’s discovery of one more term in the equation for curl H led to practically instantaneous communication all over the Earth.

Does anyone know what is being referred to here? I think it is related to fibre optics but am not sure. More generally resources for understanding Maxwell's equations would be great.

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    $\begingroup$ That's almost certainly referring to radio transmission, or electromagnetic wave transmission in general. $\endgroup$ – DanielSank Feb 26 '16 at 6:25
  • $\begingroup$ If he is referring to Maxwell's equations alone, then he would have missed about half a century of electrical telegraphy predating them. There is a very exciting science and engineering history about that... including the famous telegraph equation, which came before somewhat before Maxwell's equations, I believe, and presented a formidable challenge to the engineering theory of the time... how to make wire-based signaling fast and reliable! That theory still plays a role in our modern DSL and 1000BaseT technologies, by the way. $\endgroup$ – CuriousOne Feb 26 '16 at 7:48
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Only Jaynes knows exactly what he meant, but my guess is that he's referring to the second term in:

$$ \nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0\frac{\partial\mathbf{E}}{\partial t} \right) $$

Long before Maxwell's time people realised that a current $\mathbf{J}$ produced a magnetic field. The second term $\partial\mathbf{E}/\partial t$ means a magnetic field can be generated by a time dependent electric field even when the current is zero. This leads directly to the existance of a propagating electromagnetic wave i.e. radio waves. It also tells us that the constant $\mu_0\varepsilon_0 = 1/c^2$ and this is the bud from which special relativity sprouted.

Learning about Maxwell's Equations requires a reasonably sophisticated grasp of calculus, but they are more straightforward than the (sometimes frightening) notation might have you think. I found A Student's Guide to Maxwell's Equations by Dan Fleisch to be a good introduction.

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This link gives a brief history of how Maxwell combined laws individually established into an electromagnetic theory.

m1 m2 m3

Maxwell's great contribution, in reformulating Faraday's law was to tie the laws into one theory unifying electric and magnetic fields and in predicting electromagnetic waves, which is what is implied in the statement you question.

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