What is the highest possible frequency for an EM wave?

Question

What is the highest possible frequency, shortest wavelength, for an electromagnetic wave in free space, and what limits it? Is the answer different for EM waves in other materials or circumstances? How could waves of this frequency be generated and transmitted, again if that is possible?

Answer 1

String theory assumes that lorentz covariance is a perfect symmetry of our world. If that is true, it means a single photon is allowed to have an arbitrary energy, even greater than Planck length.

You need at least two photons that are not parallel to have a rest frame where something like a Planckian black hole might be generated that will absorb them. But single-photon states cannot be bounded in energy like this in a pure vacuum.

If the vacuum is not pure, presumably the ultra-planckian photon will react with background photons creating black holes in the rest frame and being absorbed by it.

Answer 2

The highest measured frequencies of EM waves are Gamma-rays and are typically produced from the decay of atomic nuclei. The most powerful sources of gamma-rays (and usually the sources with the shortest wavelength) are caused by astronomical events. Recently there was a very strong gamma-ray burst from Cygnus-A, the super-massive black hole at the center of the Milky Way Galaxy. It is estimated that the gamma ray burst was the result of the black hole gobbling up something with three times the mass of the Earth.

There is no theoretical upper limit for the frequency of gamma-rays. To make one bigger than what we've seen so far will require starting with a super-massive black hole and something much larger than the Earth. Not quite reproducible in the laboratory.

Answer 3

It's theorized that the Planck length is the smallest meaningful unit of distance. A wave with that wavelength would have a frequency of $\approx 6.2\cdot 10^{34}\,\text{Hz}$. A gamma ray typically has a frequency of $>10^{19}\,\text{Hz}$. Since the energy of a photon is directly proportional to its frequency, this theoretical upper bound would require vastly more energetic processes than those we presently conceive of. The individual photons involved would each be carrying $41\,\text{joules}$, or $2.56\cdot 10^{20}\,\text{eV}$, of energy.

That's a lot of volts!