# What is the highest possible frequency for an EM wave?

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?

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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.

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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!

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I think you dropped a factor of c somewhere in your calculation. –  Dave Tweed Oct 30 '12 at 16:38
well, but there you got a nice paradox: since string theory assumes that lorentz covariance is a perfect symmetry of the world, a single photon could have any energy, even greater than Planck energy. You need at least two photons to have a rest frame where a plancking black hole will form –  lurscher Oct 30 '12 at 17:43
The Planck length isn't actually the smallest meaningful unit of distance - that's a widely held misconception. But it is theorized that there is some size below which any object collapses to a black hole, and that size is probably on the order of the Planck length. –  David Z Oct 30 '12 at 17:46
@lurscher: It's not a paradox, because the answer doesn't assume string theory is correct. –  Ben Crowell Sep 5 '13 at 1:50

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.

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I suspect that there might be an upper limit where the wavelength of the photon approaches the Planck length (1.6162e-35 m). If my math is correct, this single photon would have an energy on the order of 12.3 GJ. –  Dave Tweed Oct 30 '12 at 16:25
You probably either meant Cygnus A, the very distant radio galaxy, or Sagittarius A*, the black hole at the center of our galaxy. –  Chris White Feb 11 '13 at 23:05
@ChrisWhite It's probably about this. Also I believe that even if there is no perfect definition of gamma-ray bursts then this event was definitely not one of them. –  Kuba Sep 5 '13 at 0:16

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