# measure higher frequencies then half of Planck-frequency?

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?

• 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: physics.stackexchange.com/a/4115/4552 (See Ted Bunn's answer.) – Ben Crowell May 2 '13 at 1:45

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 $p = \frac{h}{\lambda}$