Not trying to project the Planck length to have a deeper meaning, but according to current quantum theory, basically E=hc/lamda is the Planck length the smallest difference possible in wavelength between two photons with different wavelengths? So for example, if one photon has a wavelength of x, a different photons could have a wavelength of x+Lp but not x + .5 Lp?
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No, the planck length is a blurring, not a grid
The planck length is approximately the smallest length for which distances can be measured. Higher accuracy measurements require more energy to perform (actually it's the center-of-mass energy that matters). When we reach the Planck length, our measurement attempts pack so much energy into such a tiny space we create a black hole.
What does this mean for the wavelength of a photon? Lack of measurability doesn't magically create a lower limit (or a quantization) on the photon's wavelength; there is no upper limit on it's energy. However, at shorter wavelengths a photon is more and more particle-like: It gets very hard to see wave-like behavior such as interference and diffraction. Directly measuring the wavelength to a precision to differentiate multiples of the Planck length would be extremly hard if not impossible.
Kevin Kostlan
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