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I was thinking about blue-shifting of light and I couldn't help my self but think about the limits of blue shifting mechanism and since we know energy of a photon is directly proportional to the wavelength of light by the well-known formula: $E = \frac{hc}{\lambda}$

We know this therefore we can say that the maximum energy an single photon can carry must be equal to the energy of the universe so we can say $E = E_{universe}$ now if we assume the energy of universe is $ E_{universe} = \infty$ then we could also say that $\lambda$ must be $0$ which cannot make any sense as it implies all the waves all exists in the same place. Which in my opinion seems unimaginable.

That said, we must assume the $E_{universe}$ is an finite value therefore suggesting $\lambda = \frac{hc}{E_{uniserve}} $. Now we can say as the energy increases the the $\lambda$ must decrease in value, but I concluded there must come a point at which the wavelength gets smaller than the smallest length possible $h$ (planks length) surely that must mean that after a photon reaches that level of blues-shifting it should be impossible for it to blue-shift anymore, as any more blue shifting may push it beyond the limit of $h$ and therefore break laws of physics but I am a mere speculative student therefore can someone answer my questions.

So my question is what is the limit of the most energetic wavelength in electromagnetic-spectrum? If so what if a photon attains such energy levels what will happen if we attempt to blue-shift the light even more, what will or should happen?

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    $\begingroup$ By taking the Doppler effect in consideration, for an objects light to be blue shifted to zero wavelength, the object must be moving towards you at the speed of light. and since this is considered impossible for objects with mass, the minimum possible wavelength is surely not zero. (Also since a wavelength of 0 implies an infinite amount of energy for a photon.) According to me, the smallest possible wavelength for a photon would tend towards zero, but never quite reach it. $\endgroup$ Commented Nov 30, 2014 at 12:45
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/16391/2451 , physics.stackexchange.com/q/86531/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Nov 30, 2014 at 13:03
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    $\begingroup$ possible duplicate of What is the minimum wavelength of electromangetic radiation? $\endgroup$
    – user65081
    Commented Nov 30, 2014 at 13:08

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