Doppler Shift and photons with a wavelength of one Plank length

[l3un1t]

If this is the wrong place to be posting this, feel free to lock this thread. I wasn't sure if this belonged in "classical physics" or "quantum physics"; this seemed like the appropriate place, but I'm not 100% certain, as it does involve subatomic particles.

Anyways, to get to the matter at hand.

Suppose I had a machine that could detect the wavelength of a photon. If this machine moved directly toward a photon with a wavelength of one Plank length ( so that the photon and the machine would collide perpendicularly), what wavelength would the machine register? Would it register a wavelength of less than one Plank length?

If so, does this have any implications for the validity of String Theory? If not, why?

 

[jfy4]

I don't think anyone would assert that the plank length is the smallest unit of length, so smaller is certainly okay. There are theories of quantum gravity that predict a discrete spectrum of lengths, with there being a fundamental one. This thought experiment was thought to discredit the idea of having a smallest unit of length, but it is not the case. This is because we must treat the situation quantum mechanically, not classically. Then what is contracted in the expectation value of the length, not the spectrum of values of the operators.