# Theoretical and actual limits to electromagnetic frequencies?

## Main Question or Discussion Point

i'd like to know two things

a) is there a theoretical upper and/or lower bound to electromagnetic frequencies in the universe? i'm thinking for an upper limit, 1/planck time?
for a lower limit, i have no idea-- does heisenberg uncertainty calculate into that? i suppose it would when you consider the limited size of the universe, if the frequency is so tiny that only a part of the wave exists spans the universe at one time..?

b) what are the *actual* detected or even speculated upper and lower limits for electromagnetic waves? i know there are various graphs on the internets depicting the spectrum between AM radio and gamma rays, but the upper limits range from 10^20 hertz to 10^23 hertz, and the lower limits range from 10^3 hertz to 10^6 hertz depending on the graph. and they don't give numbers with any more precision than the order of magnitude.

thanks..

## Answers and Replies

Chalnoth
Science Advisor
i'd like to know two things

a) is there a theoretical upper and/or lower bound to electromagnetic frequencies in the universe? i'm thinking for an upper limit, 1/planck time?
for a lower limit, i have no idea-- does heisenberg uncertainty calculate into that? i suppose it would when you consider the limited size of the universe, if the frequency is so tiny that only a part of the wave exists spans the universe at one time..?
The practical upper limit on electromagnetic waves is often around 1MeV (2.4 * 10^20Hz). This is because above this energy, the EM wave has enough energy for pair production (electrons have a mass of about 0.5 MeV). EM waves above this energy tend to decay very rapidly due to this process.

However, there is no known theoretical upper limit. When computing interactions in quantum electrodynamics, we do have to select some upper limit on photon energies, but our calculations are independent of the choice of upper limit, and we have as yet no evidence to indicate where it may be.

b) what are the *actual* detected or even speculated upper and lower limits for electromagnetic waves? i know there are various graphs on the internets depicting the spectrum between AM radio and gamma rays, but the upper limits range from 10^20 hertz to 10^23 hertz, and the lower limits range from 10^3 hertz to 10^6 hertz depending on the graph. and they don't give numbers with any more precision than the order of magnitude.

thanks..
Well, the highest-energy photons that we directly detect (and are sure are photons) are products of nuclear reactions, which can go up to tens or even hundreds of MeV. Higher-energy still are virtual photons produced in particle colliders that may have energies with hundreds of GeV (so far), but almost instantaneously produce other particles. The problem is, the physics work out so that at the current time, all our calculations are independent of the photon cutoff, so we just have no evidence pointing to where that might be as yet.

For the lower limit, i guess that must be very “long” radio waves (whose wavelength can reach hundreds of kilometers). That is for EM radiation generated from an antenna.
For EM radiation generated from atomic emission, that might be the transition from 2p1/2 -> 2s1/2 in the hydrogen atom (those levels are only separated by the Lamb shift)

Ich
Science Advisor
The practical upper limit on electromagnetic waves is often around 1MeV (2.4 * 10^20Hz). This is because above this energy, the EM wave has enough energy for pair production (electrons have a mass of about 0.5 MeV). EM waves above this energy tend to decay very rapidly due to this process.
Well, the highest-energy photons that we directly detect (and are sure are photons) are products of nuclear reactions, which can go up to tens or even hundreds of MeV.
Photons can't decay; if there's a high density of photons above ~0.5 MeV, you can produce electron-positron pairs in photon-photon collisions.
In interstellar space, photons with much higher energies can travel freely. http://en.wikipedia.org/wiki/Fermi_Gamma-ray_Space_Telescope" [Broken]routinely detects photons far in the GeV range. Pair production with the CMB should be an issue for Energies > 10^14 eV, if I made no math error. Ordinary background light (from stars and such) is more important there, IIRC.

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Chalnoth
Science Advisor
For the lower limit, i guess that must be very “long” radio waves (whose wavelength can reach hundreds of kilometers). That is for EM radiation generated from an antenna.
If our universe wraps back on itself, a long-wavelength cutoff would be caused by the maximum distance around the universe before wrapping back on itself (this would be at least a few times the ~50 billion light years size of the observable universe).

If our universe wraps back on itself, a long-wavelength cutoff would be caused by the maximum distance around the universe before wrapping back on itself (this would be at least a few times the ~50 billion light years size of the observable universe).
OK but what would generate such an EM wave ?! Can you imagine the size of the antenna ?

Chalnoth
Science Advisor
OK but what would generate such an EM wave ?! Can you imagine the size of the antenna ?
Well, it's actually impossible to physically generate a wave that large now, just due to causality reasons. But such a wave that was produced in the very early universe might well have grown to that size through redshifting. It's obscenely unlikely to have survived through the hot early period of our universe, but it's not fundamentally impossible.