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I hope my question will be understandable. I wonder about the sinusoidal shape of an electromagnetic wave. I have the impression that something fundamental is behind this shape. To simplify things, let's put ourselves in the case of a single electromagnetic wave. Is the curve of an electromagnetic wave always sinusoidal and continuous? Is it possible that this is a periodic staircase curve, for example at the Planck scale? Especially in a discrete space-time like that of the LQG (Loop Quantum Gravity)? Isn't the sinusoidal shape and continuity just a matter of scale and/or measuring device?

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  • $\begingroup$ My answer here also applies to the first part of this question. $\endgroup$ – The Photon Aug 10 '20 at 21:45
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It is sinusoidal when produced by an alternating current, as in the case of radiowaves. In this case it is sinusoidal by construction, because LC circuits behave as an harmonic oscillator.

But I don't see any reason for the light coming from the sun (for example) to be sinusoidal. It is a resultant of chaotic interactions of ionized particles from hydrogen and helium atoms at the sun surface.

But it comes to the Earth as a plane wave, where $\mathbf B$ and $\mathbf E$ are expressed as:

$\mathbf E = \mathbf E(u)$, and $\mathbf B = \mathbf B(u)$ where $u = \mathbf {k.x} - \omega t$ and $\omega = |\mathbf k|c$.

However, as any function can be expressed as a Fourier integral, it can be expressed by sinusoidal functions.

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  • $\begingroup$ I think the OP isn't asking whether non-sinusoidal waves exist. The question is, is it possible that what appears to be a smooth sinusoidal wave is actually, at the very fine level, composed of quantum jumps, looking perhaps like a high frequency square wave imposed on a low frequency sine wave. $\endgroup$ – Ray Butterworth Aug 12 '20 at 0:41
  • $\begingroup$ Ray Butterworth, I thank you for your precision. You understood my question perfectly. $\endgroup$ – Jean-Michel Tengang Aug 13 '20 at 12:54

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