I read somewhere that you cannot tell the difference in position between a photon (Or any other particle) at some point in time and the same photon (Or other particle) less than a planck time later, because it would not have traveled further than a planck length, which apparently is the smallest measurable distance. I don't know how accurate that is, but it seems to lead to a contradiction. Consider a photon at three points in time, called A, B and C. Each point in time is separated by half a planck time and half a planck length, According to the theory, you cannot tell the difference between states A and B, nor can you tell the difference between B and C. If there is no measurable difference between states A and B and no measurable difference between B and C then there should be no difference between A and C, but A and C are separated by a planck time and a planck length, so a difference in position and time should be possible to measure. So which is it, can a difference be measured or not?(adsbygoogle = window.adsbygoogle || []).push({});

Does this contradiction Imply that distances smaller than a planck length do not exist, and that space is a discrete grid?

The same paradox occurs when considering photon energies. By measuring a photon's energy you are measuring its wavelength. Consider three photons, the first photon "A", has some arbitrary energy, the second photon "B", has a wavelength of half a planck length larger than the first photon, the third photon "C", has half a planck length larger still. The same effect applies to the energy of these three photons. If the planck length is the smallest measurable length then Photon "A" has indistinguishable energy from photon "B", which has indistinguishable energy from photon "C", but "A" and "C" are separated by a planck length, which will allegedly allow us to measure a difference in energy. Which is a paradox. Alternatively, If the planck length is the smallest measurable distance, then you might expect that all photon wavelengths occur in discrete multiples of the planck length. I don't really know, any ideas?

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# I Planck length/Time Paradox

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