When light coming from sun to earth it is traveling into the vacuum upto earth atmosphere; Because non mechanical waves don`t need a medium to travel and light can move in vacuum very fast we know. But what is the exact physics about the non-mechanical waves ?
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Google for "Feynman Magnets Why Questions Video" or read a transcript. The only accurate way to describe the exact physics of non-mechanical waves is using mathematics (probably). – RedGrittyBrick Nov 28 '16 at 12:05
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Possible duplicate of Why don't electromagnetic waves require a medium? – RedGrittyBrick Nov 28 '16 at 12:09
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What is a wave? The term is somewhat ambiguous. Griffiths, Introduction to Electrodynamics 4e (p.364) has
A wave is a disturbance of a continuous medium that propagates with a fixed shape at constant velocity.
But, if you know what a wavenumber and frequency is (no offense), then a better definition might be: "a quantity that is propagating not only in space but also along time, in the manner of $\omega t -\langle\textbf{k},\mathbf{x}\rangle$". A wave equation $$\ddot{u} =v_0^2 u,_{xx}$$ results such solution for $u$ as to be function of $\omega t -\langle\textbf{k},\mathbf{x}\rangle$; this is why it is called wave equation!
A mechanical wave is an amplitude that "waves" according to wave equation, and a electromatic wave is similar, except the object we discuss is not visible to the eye, but electric and magnetic fields.
Back to the question. You seem to be bewildered with the fact that light don't need a medium. Molecules in a rope, say, influence its neighbours, just as an $E$ field in $(x,y,z,t)$ influences that in $(x',y',z',t')$ which is near. The former is "touching each other and spreading out", but the latter is invisible, this is why you think it more abstract, though the underlying reason is the same. Actually a rope's wave equation is also derived from Hooke's law (see any commonly-used mechanics textbook, say Marion & Thornton), and Maxwell's equations are more fundamental than Hooke's law. But really, inter-atom forces are electromagnetic nature! There is nothing in light's propagation "more strange" than a rope's amplitude's propagation.
If you are really interested the derivation of the wave equation of EM wave, this is not a short story. The general idea is exactly as what I tried to convey above, but for the detail, you may take a glance in wikipedia, and if this is too difficult for you, you have to take a calculus course.... ;)
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