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Andrew Steane
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Existing comments on the question givesgive links to answers. These are that (1) a wavelength can be arbitrarily small because for any given wavelength you can always get a smaller one by jumping to another inertial reference frame; and (2) nevertheless it is hard to maintain any claim that existing physical theories correctly treat interactions at Planck scale or below in the rest frame of the interacting systems.

The main thing wrong with the argument in the question is that the photon need not have its energy concentrated in a small region. A 'photon' is not necessarily a little thing spatialspatially concentrated at a point or some small region. It can be spread out over huge volumes. Think of it like a plane wave having energy $E = h c/\lambda$, width $a$ and length $L$. So even if its energy is high, the energy per unit volume $E/(L a^2)$ need not be high, so no black hole will form. More generally, to form a black hole you need some stuff which is not moving at light speed.

Existing comments on the question gives links to answers. These are that (1) a wavelength can be arbitrarily small because for any given wavelength you can always get a smaller one by jumping to another inertial reference frame; and (2) nevertheless it is hard to maintain any claim that existing physical theories correctly treat interactions at Planck scale or below in the rest frame of the interacting systems.

The main thing wrong with the argument in the question is that the photon need not have its energy concentrated in a small region. A 'photon' is not necessarily a little thing spatial concentrated at a point or some small region. It can be spread out over huge volumes. Think of it like a plane wave having energy $E = h c/\lambda$, width $a$ and length $L$. So even if its energy is high, the energy per unit volume $E/(L a^2)$ need not be high, so no black hole will form. More generally, to form a black hole you need some stuff which is not moving at light speed.

Existing comments on the question give links to answers. These are that (1) a wavelength can be arbitrarily small because for any given wavelength you can always get a smaller one by jumping to another inertial reference frame; and (2) nevertheless it is hard to maintain any claim that existing physical theories correctly treat interactions at Planck scale or below in the rest frame of the interacting systems.

The main thing wrong with the argument in the question is that the photon need not have its energy concentrated in a small region. A 'photon' is not necessarily a little thing spatially concentrated at a point or some small region. It can be spread out over huge volumes. Think of it like a plane wave having energy $E = h c/\lambda$, width $a$ and length $L$. So even if its energy is high, the energy per unit volume $E/(L a^2)$ need not be high, so no black hole will form. More generally, to form a black hole you need some stuff which is not moving at light speed.

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Andrew Steane
  • 61.8k
  • 3
  • 86
  • 252

Existing comments on the question gives links to answers. These are that (1) a wavelength can be arbitrarily small because for any given wavelength you can always get a smaller one by jumping to another inertial reference frame; and (2) nevertheless it is hard to maintain any claim that existing physical theories correctly treat interactions at Planck scale or below in the rest frame of the interacting systems.

The main thing wrong with the argument in the question is that the photon need not have its energy concentrated in a small region. A 'photon' is not necessarily a little thing spatial concentrated at a point or some small region. It can be spread out over huge volumes. Think of it like a plane wave having energy $E = h c/\lambda$, width $a$ and length $L$. So even if its energy is high, the energy per unit volume $E/(L a^2)$ need not be high, so no black hole will form. More generally, to form a black hole you need some stuff which is not moving at light speed.