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  1. This asked: What is the minimum wavelength of electromagnetic radiation?

  2. And also this: What is the maximum possible frequency and wavelength?

The second question is contradictory; maximum frequency -> minimum wavelength.

I am asking the very opposite;

What is the minimum frequency and maximum wavelenght of electromagnetic radiation?

The lowest measured/defined seems to be 3 Hz; ELF-waves Which means a wavelenght 1/3 of the speed of light; ~100 000 000 m.

But this can't be the physical limit for the wavelenght.
Does such a physical limit for the wavelength exist? (Similar limit like the speed of light is for velocity).

Qmechanic
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Jokela
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    In principle there is no lower limit of frequency. It might be argued that there is a higher limit, if you were to convert all the energy in the universe equal to $h \nu$? By the way, you have $\lambda = c/ \nu$ a bit misleading when you say "1/3 of the speed of light; ~100 000 000 m" since the speed of light has units $m/s$, but most people would realise that you mean $\frac{1}{3 Hz} 3 \times 10^8 m/s$. – jim Apr 02 '16 at 09:16
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    @jim The wave lenght makes the energy of a photon smaller. So the maximum wavelenght would simultaniuosly present the minimum energy of a single photon. Though you can have something just "non zero", the energy aspect is not relevant, the point it that at this length, I expect the photon-wave would be just a straight line, and this would open us views to issues shown in the answer of JohnRennie. Maybe the size of the universe is limited through this lenght? – Jokela Apr 02 '16 at 10:56
  • I assume the limit is DC, which has infinite wavelength. – jim Apr 02 '16 at 15:34
  • @jim DirectCurrent has nothing to do with photons/radiation; Current is a flow of moving electrons. – Jokela Apr 02 '16 at 16:11
  • Something's wrong here: The lowest measured/defined seems to be 3 Hz; ELF-waves Which means a wavelenght 1/3 of the speed of light; ~100 000 000 m. makes no sense: a wavelength is not measured in m/s as is the speed of light, and the speed of light isn't measured in meters. – ZeroTheHero Apr 19 '19 at 13:12
  • @ZeroTheHero You are right in the first view. But pls. check the SI-definition of time and length, and you might notice that you can reduce the speed of light this way. I've tried to write it open here; https://www.researchgate.net/publication/331314978_Planck_constant_Light_length_Heisenberg%27s_uncertainty_principle_Josephson_constant_Klitzing_constant_Quantization_revisited – Jokela Apr 19 '19 at 14:25
  • As an illustrating example: What is the longest water wave? Under offshore oil drilling platforms, you find extremely high waves. But the longest? Tsunamis, or the ebb and flow change. – Volker Siegel Mar 09 '21 at 13:32
  • The reason that ebb and flow are the largest wavelength water waves is because waves are limited by the medium, and we do not have bodies of water that are longer than the circumference of the Earth. We could theoretically build canals longer than that. They can be curved, for example a tight spiral... – Volker Siegel Mar 09 '21 at 13:43
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    I think there is likely maximum wavelength of a photon, due to there being (if I understand correctly) a lowest possible unit of energy due to quantum effects. It would be interesting to calculate what the wavelength of the lowest level of energy is. – Jonathan Nov 06 '21 at 00:39
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    @Jonathan I agree with you, but have accepted the answer of John Rennie because it admits that this length is not known. Basically I think this is very simple; Planck constant is the lowest energy which quantifies photon. – Jokela Nov 11 '21 at 18:19

3 Answers3

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There is no theoretical physical limit on the wavelength, though there are some practical limits on the generation of very long wavelengths and their detection.

To generate a long wavelength requires an aerial of roughly one wavelength in size. The accelerated expansion of the universe due to dark energy means the size of the observable universe is tending to a constant, and that will presumably make it hard to generate any wavelengths longer than this size.

As for detection, we tend to measure the change in the electric field associated with an EM wave not its absolute value. As frequencies get lower we will need either increased intensity waves or ever more sensitive equipment. Both of these have practical limits, though I hesitate to speculate what they are.

John Rennie
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  • Thank's for this answer. This was exactly what I was expecting to hear, and the aspect which I wanted to verify; "There is no theoretical physical limit on the wavelength". No wonder I couldn't find any with google either. I think this is an area where some work should be done, as you point out "universe is tending to a constant, and that will presumably limit the wave length" so creating this theoretical limit through some model might give us quite some answers about the universe. – Jokela Apr 02 '16 at 10:44
  • There are also limits at large(small) $\lambda$ imposed by the instrument response, i.e., you generally need larger/longer(smaller/shorter) antennas for larger(smaller) $\lambda$. – honeste_vivere Apr 02 '16 at 15:28
  • Instruments may be more efficient if matched to the wavelength, but this is not a necessity. – jim Apr 02 '16 at 16:17
  • maybe a black hole could produce really low frequency radiation due red shifting? – Enrique Apr 19 '19 at 12:48
  • How could something in the universe create a wave with a longer wavelength than the universe's causality horizon? Is that even theoreticaly possible? Or a wave period longer than the age of the universe itself? – Cham Sep 19 '19 at 02:13
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Adding to what others have said, here's a little proof that there is no maximum wavelength:

Let us assume that there is a maximum photon wavelength.

Observer B is moving away from Source A. Source A emits a photon of maximum wavelength towards Observer B. Due to the Doppler effect, the photon is red-shifted from Observer B's perspective, meaning it is observed to have longer wavelength.

This observed wavelength is now greater than the maximum wavelength. Contradiction.

Therefore there is no maximum photon wavelength, q.e.d.

Conversely, a photon would be blue-shifted if the observer is moving towards the source, by the same logic proving there is no minimum wavelength either.

But realistically there are limits on the frequencies which can be produced or observed. Extremely high energy photons can spontaneously produce a particle/antiparticle pair. If those later annihilate, they produces two photons which therefore have less energy each.

And good luck trying to build a detector which can detect photons with a wavelength greater than the size of the observable universe.

TheMoonRover
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  • The definition of maximum wavelength should be updated/redefined as maximum emitted wavelength, which would be defined as the locally measured length of the maximum wavelength (whatever that is) at the moment of emission. Since EM radiation is quantized, this should always be the same. That is, if indeed there is a maximum wavelength.

    Light seems to only have certain sizes that it can manifest as. So, that minimum size may not correspond to the energy derived from "maximum wavelength".

     – Paul Easter Dec 26 '23 at 16:12
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The maximum wavelength of an electromagnetic wave on Earth is

40,075 km.

We need at least a distance of one wavelength for a standing wave (I assume), and the longest distance we have is the equator, the longest circumference around the Earth (40,075 km), which is not exactly spherical.

The corresponding frequency of this wavelength is

7.48 Hz.

I see no reason such a wave can not exist, because we even have a water wave of this wavelength, seen as ebb and flow.

Volker Siegel
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  • That's interesting. Did you know that if you defined an astronomical unit as:

    AU-x = Earth Circumference x 500.

    This astronomical unit would create an orbital radius for Earth of 7.48 AU-x.

    In addition, this distance corresponds to 500 light seconds. This number (7.48) also corresponds to the number of times light can circle the Earth in 1 second.

     – Paul Easter Dec 26 '23 at 16:23