# B Does "wave–particle duality" exist in low frequency waves?

1. Jan 5, 2017

### Dante Meira

Hello, I'm new to the forum, and Physics is not my area of study, but I have a doubt that I couldn't find a satisfactory answer on Google, so I created this account in this forum just to ask this, because I'm really curious to know the answer to this doubt.

Does "wave–particle duality" exist in low frequency waves? For example, the electromagnetic radiation used in the "long-wave" radio AM broadcast, can "manifest" this wave–particle duality? Or the Extremely low frequency (ELF) radio waves, with frequencies from 3 to 30 Hz, do they manifest wave–particle duality as well?

In other words, my doubt is: is there a minimum frequency of electromagnetic radiation for the "particle behavior" to be possible to be experimentaly detected?

I could also extend the question and ask if there is a maximum frequency of electromagnetic radiation for it to be capable of behaving like a particle?

Thanks.

2. Jan 5, 2017

### hilbert2

You can think of a system where an elementary particle is trapped in a relatively large potential well, so that the spacing between its energy levels would be low enough for it to absorb radio frequency photons. Radio waves are also used in nuclear spin resonance spectroscopy, where the direction of the spin of a nucleus can change when it absorbs photons of low energy.

3. Jan 5, 2017

### Dante Meira

Thank you.

Is there any theoretical minimum limit of frequency for the photons of low energy to actually interact as photons, that is, as particles?

For example, if someone creates electromagnetic radiation in the form of radio waves with a frequency of only 0.1 hertz (1 deci-hertz), can the low energy photons associated to those waves actually interact as particles?

4. Jan 5, 2017

### hilbert2

There can't be a sudden change in the laws of nature when going below some length- or timescale, e.g. electromagnetic waves behaving in one way if they have a wavelength of $\lambda \geq 1$m and suddenly in another way if $\lambda < 1$m. In principle, EM waves of any frequency can be absorbed as discrete energy packets by some physical system.

If you consider the spacings between translational motion energy levels in an ideal gas that is confined in a macroscopic container, you'll see that the corresponding photon wavelengths can be of the order of magnitude of light years.

Last edited: Jan 5, 2017
5. Jan 5, 2017

### houlahound

Interesting theoretical question. I have never thought about a single photon emitting antenna at very long wavelengths in the hundreds of km range. Be a neat receiving antenna.

6. Jan 5, 2017

### Staff: Mentor

Well first the wave particle duality doesn't exist - its an outmoded idea done away with when Dirac came up with his transformation theory (which generally goes by the name QM today), at the end of 1926, but probably sooner.

But to answer the above - no there isn't - its purely a technological issue just how long an EM wavelength can be before you can detect individual photons, theory places no limits at all.

This may seem strange because in beginner texts and popularizations the wave particle duality is of invoked to explain the double slit. Its not really a good explanation - here is a much better one:
https://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Thanks
Bill