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Suppose I had the superposition of two electromagnetic waves whose angular frequency was in the X-ray region. Together they form a composite made of a carrier wave and a modulation wave where the modulation has relatively low angular frequency (compared to the angular frequency of X-rays).

Since both the two components are X-rays I can't physically see them with my eyes on their own. But now suppose I choose these rays such that the angular frequency of the modulation is $5.5 \times 10^14 \text{Hz}$, which corresponds to visible green light.

Will I be able to see the composite wave now through some sort of aliasing effect where the oscilations of the carrier are so fast the detectors in my eye completely miss them (just like how they miss X-rays) but they are able to detect the comparatively lower modulation wave?

Also, assuming this is the case will looking at such light still be dangerous? On their own the X-rays would be dangerous because they would ionise particles in my eyes so we might expect that putting them together would still lead to something potentially dangerous.

Equally though people say things like "the carrier wave carries no information (and hence the fact that it can be faster than light doesn't break causality)" in which case we'd expect the carrier waves to have no physical impact (ionisation or otherwise). This is because if they did then we could create a situation where we send a signal from a source to a destination faster than light to let the destination know a certain event has occured if we use carrier waves which are faster than light and can ionise particles at the destination as soon as they reach there. (I know in my particular case above the group and phase velocities are the same, $c$, so this contradictio it doesn't apply here but other cases with different dispersion relations do exist e.g. X-rays inside metal waveguides where you can have carrier waves with a phase velocity faster than light).

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  • $\begingroup$ You would have to demodulate the signal. $\endgroup$
    – my2cts
    Commented May 21 at 9:39
  • $\begingroup$ no ... we really can't modulate X-rays ... you would just get a mix of X-rays. we modulate laser light by pulsing it ... but that's not the type of modulation you were asking about $\endgroup$ Commented May 22 at 1:11

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They would still be X-rays, so you wouldn't see them, and I wouldn't recommend trying to see them either if you value your retinas. All that matters with EM radiation is the frequency of the photons themselves, since this determines their energy - if you suspend any knowledge of electrodynamics and optics that you might have, you can think of it as how many wavefronts are hitting your eyes in a given time interval. The modulation then changes only the amplitude of the wavefronts, but not their amount. Note that this is a gross oversimplification, but it should get the general idea across.

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