# Minimum frequency of an electromagnetic wave [duplicate]

Is it possible to create an electromagnetic wave of near zero frequency?

An electromagnetic wave carries energy. If we can make the frequency of an EM wave vanishingly small and make it practicality DC, will it also carry energy? I don't think it is possible. Hence there should be some fundamental limit on the minimum frequency of an EM wave.

Is there any such thing?

• DC is seen as 0 frequency and infinite wavelength. Truly you can just asymptotically approach 0 Hz. – M Barbosa Jun 19 '16 at 13:37
• Given the inverse relationship between frequency and wavelength, the minimum frequency is the maximum wavelength. Therefore, this may be a duplicate of physics.stackexchange.com/q/246896 – HDE 226868 Jun 19 '16 at 13:52
• @HDE 226868 Thank you for showing me the very similar question. one of the motive behind this question was to understand if one can transmit energy via near DC electromagnetic waves, and how much we can stretch this limit. – hsinghal Jun 19 '16 at 15:49
• There is no such thing. If you have the time and space, I can make as slow an electromagnetic wave for you as you like. – CuriousOne Jun 19 '16 at 21:09
• The longest wave I can think of that would be practical to make, would be to mount an ion source in orbit and use it to give Luna a net (-) charge and Earth a (+) charge; they'll radiate at a frequency of one inverse lunar month (about 0.4 microhertz). – Whit3rd Jun 20 '16 at 0:11

There is no lower limit on the frequency of electromagnetic fields. One can consider a DC field as the lowest frequency being of zero Hz. Perhaps somebody would argue that to be truly of zero Hz the DC field have to exist for all eternity. However, if one expands the DC field that exists for only a finite duration with a Fourier transform, one obtains a spectrum that is continuous and nonzero at the origin. This shows that nonzero frequencies exist all the way down to zero.

What about the quantum mechanical view of this? As pointed out by tparker, one can get low frequency "soft" photons that contribute to the dynamics. Moreover, DC fields such as the Coulomb field around charged particles are also included in quantum mechanics (or quantum field theory).

One view that is expressed is that the lowest frequency should be determined by some cavity effect due to the size of the universe. However, such a view has a few practical problems. For the universe to act as a cavity, the field must be able to bounce back and forth in it so that it can constructively interfere with itself. This assumes particular boundary conditions. It also assumes that the field will exist for long enough to build up this constructive interference and obviously it must still be coherent with itself for something like that to work correctly. Just thinking about this a little bit, one quickly realized that such requirements are unlikely to be satisfied. Hence, the size of the universe probably does not set a limit to the lowest allowed frequency.

In a sense, the size of the universe limits the wavelength of a photon: any photon that has larger wavelength than the size of the universe, cannot exist entirely within this universe. It is not clear that this can ever be tested, however.

In high energy (short wavelength) the lack of a limit to thermal radiated light was an important reason for the ascendancy of early quantum mechanics the violet catastrophe. Classical physics couldn't explain radiant heat flow, because it had no upper photon energy limit. Quantum mechanical atoms DO have such limits (for Hydrogen, it's 13.6 eV = 1 Rydberg).

Yes, extremely low-energy "soft photons" exist and can have important effects even when their energy is too low to be directly detected.

Lowest possible amplitudes and maximum lenght demands very low electric moving charge and voltage, but the wave will disappear, as a ghost.

Brian Dodson has posted a brief explanation to this at Quora. Basically it is suggested that "the largest energy that is sustainable as an electromagnetic wave is approximately 1 MeV, or a wavelength of 0.01 Angstrom."