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The maximum frequency is defined by the Planck frequency $\omega_P$. Also there is the Shannon theorem which tells us that to lossless capture a signal, you have to sample it with minimum of the double frequency. That states that you cannot measure frequencies higher than $\frac{\omega_P}{2}$.

Is this correct? I saw sites telling the highest frequencies measured are about $10^{30}$Hz which is under $\frac{\omega_P}{2}=9.27435\cdot10^{42}$Hz. So obviously there are some borders in test equipment and other physical boundaries, but could it be that in theory this is not possible to measure such high frequencies?

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You seem to be imagining spacetime as a discrete lattice at the Planck scale, but that's wrong. There can't be a minimum length, because Lorentz contraction would make it shorter. – Ben Crowell May 2 '13 at 0:39
related: (See Ted Bunn's answer.) – Ben Crowell May 2 '13 at 1:45
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The Nyquist-Shannon sampling theorem is about continuously sampling a waveform. This really matters when a waveform is a mix of many different frequencies. The theorem says you must sample at a rate double the highest frequency. With light you only need to take one "sample" (the energy of the photon or its momentum) to fully know its frequency: $E = \frac{h c}{\lambda}$ and $p = \frac{h}{\lambda}$

In this sense, a light wave is much simpler than the sampling waves where the Nyquist limit matters.

I'm not sure you can learn about phase and polarization in this way and you certainly can't know the position (due to the uncertainty principle) if you very accurately measure the momentum. Besides this though, I don't think the Nyquist limit really applies to light.

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