# Limits to the electromagnetic spectrum?

Are there any limits to the size (of wavelength) of electromagnetic waves? I imagine that the smallest possible size would be one Planck length, but is there an upper limit?

I suspect that it would be difficult to have a wave with a wavelength greater that the width of the universe…

Or shorter than the Planck length.

At first I nodded. Now I’m trying to figure out why this should be so. It seems to me you could have 1/2 wavelength equal to the diameter of the universe, an 1/10 and 1/100 and so on.

But I can be convinced otherwise.

I think you could have an electric or magnetic field intensity distribution along a line tha was a sine wave having period as long as, or much longer than, the width of the (observable) universe. Would there be anything to prevent a source being able to generate that distribution? If it wasn’t radiating from a source, would you call it electromagnetic radiation or electromagnetic waves?

A source that cycled at one cycle per the age of the universe would create a wavelength the same as the size of the universe (if i reasoned that out right - it’s confusing because there could be several definitions of the speed of the edge of the universe right now, etc). A source cycling more slowly than that would have emitted less than a single cycle. Can we say that radiation has a wavelength if it has not completed a single cycle?

Corrolary question: Is there an upper bound to length that is normally seen? I.e., longest wavelength ever measured?

According to the textbook Conceptual Physics, ninth edition by Paul G. Hewitt says: “Electromagnetic waves have been detected with a frequency as low as 0.01 hertz (Hz).” (pg. 498)

Which I suppose means that there ARE waves of lower frequency, but we don’t deal with them at all in real life.

Eh. Delete “says.” I rephrased and then didn’t fix it up neatly.

Maybe there is an upper limit to wavelength. EM radiation results from accelerating electrical charges. If there is a minimum acceleration, there is a maximum wavelength. Is there a minimum acceleration?

There may or may not be an upper limit to wavelangth, but detecting large-wavelength EM radiation would be interesting.

:: pulls up memories of electronics school ::

You’d start to need antennas that were thousands or millions of likometres long, for one thing. And then the speed of voltage/current propagation in the antenna would become significant, among other things. I have no idea how that would affect the antenna design and functioning.

I agree that detecting a signal with a wavelength of 50 light-years would be a problem. However, I’m not convinced that it is a matter of antenna length. Antennas that are a lot smaller than a wavelength, or quarter wavelength are used in AM broadcast band receiving all of the time. Antennas that are tuned to the correct frequency are useful in giving directivity but directivity isn’t needed for this. I think the minimum directive gain for an antenna is 1. The capture area of such an antenna then is L[sup]2[/sup]/2*pi. L = wavelength of the signal. EM field strength is in watts/meter[sup]2[/sup] so for an exteremly long wavelength the area of the antenna is huge so that even a weak signal of of fractions of a femtowatt should produce an antenna output above the noise for a cooled detector.

Of course I’ve never tried to detect such a signal and there could be some little glitches that I haven’t thought of on short notice.

In fact one problem is recognizing the signal. For a looooong wavelengh signal the detector would be signal the amplitude of which would vary over a period of 15 or 20 years. Sorting that out from all the other junk would be quite a challenge. Using integrative filters to separate the signal out might mean waiting a couple of hundred years.