It was recently in astronomy news that gamma rays emanating from the Crab Nebula supernova remnent have energies measured as high as 200 GeV. I was wondering what limits there can be to a photon’s energy?
I presume that when the wavelength shrank to the Planck length the corresponding energy would be the Planck mass and the photon would be a micro-black hole; but are there other limits before you reach that extreme? Like maybe above a certain point the electric and magnetic fields become powerful enough to spontaneously split into monopole pairs or somesuch.
There are no known limits. If there is a limit at the Planck scale, it would imply Lorentz invariance. Which, admittedly, some quantum gravity models do predict, but it’s still not exactly something I’d bet on.
A photon can be arbitrarily large for any wavelength. If I quantize a microwave cavity, the photons are excitations of the electromagnetic modes of the cavity. If I put one photon in the cavity, the energy in the cavity is proportional to the frequency of that photon, but the energy density is inversely proportional to the volume of the cavity. Thus, saying that the wavelength is the Planck length, does not imply that there is a high energy density or high electric and magnetic field, since the volume of the cavity can be arbitrarily large.